Table of contents

  1. December 2010
  2. November 2010
  3. October 2010
  4. September 2010
  5. August 2010
  6. July 2010
  7. June 2010
  8. May 2010
  9. April 2010
  10. March 2010
  11. February 2010
  12. January 2010

December 2010

December 31, 2010

Serge Batalov proved 1 near-repdigit-related prime by PFGW and CHG.

Proven near-repdigit-related primes (except ru/nr/pd/qr)
 digitsflabelwlabelexpressionwhenwho
1604718 34w11(31·104717-301)/9December 31, 2010Serge Batalov

Maksym Voznyy proved 1 near-repdigit prime by Primo 3.0.9 and PFGW 3.4.4.

Proven near-repdigit primes
 digitsflabelwlabelexpressionwhenwho
2794809111011w01(104809-91)/9December 31, 2010Maksym Voznyy

December 30, 2010

Maksym Voznyy proved 6 near-repdigit primes by Primo 3.0.9.

Proven near-repdigit primes
 digitsflabelwlabelexpressionwhenwho
31833089777797w(88·103307-7)/9December 30, 2010Maksym Voznyy
3213247888818w1(8·103247-71)/9December 30, 2010Maksym Voznyy
32929988111181w(73·102997-1)/9December 30, 2010Maksym Voznyy
3332968333373w7(102968+11)/3December 30, 2010Maksym Voznyy
3382906888838w3(8·102906-53)/9December 30, 2010Maksym Voznyy
3422811333373w7(102811+11)/3December 30, 2010Maksym Voznyy

Maksym Voznyy proved 1 prime by Primo 3.0.9 and PFGW.

Proven near-repdigit-related primes (except ru/nr/pd/qr)
 digitsflabelwlabelexpressionwhenwho
14157378008180w818·105736+81December 30, 2010Maksym Voznyy

December 29, 2010

Thanks to Ray Chandler, obsolete links from our tables of the form AABAA to OEIS were corrected.

December 27, 2010

Bob Price found 5 near-repdigit-related PRPs by PFGW.

Unprovable near-repdigit-related PRPs (except ru/nr/pd/qr)
 digitsflabelwlabelexpressionwhenwho
4470271005110w511047026+51December 27, 2010Bob Price
5424581001910w191042457+19December 27, 2010Bob Price
6420821008110w811042081+81December 27, 2010Bob Price
7414571004910w491041456+49December 27, 2010Bob Price
8409301001910w191040929+19December 27, 2010Bob Price

December 26, 2010

Ray Chandler found 30 primes and 181 PRPs by srsieve and PFGW.

Proven near-repdigit primes
 digitsflabelwlabelexpressionwhenwho
11429126 999999959w99999996·1029118-1December 26, 2010Ray Chandler
12026200 99999919w9999992·1026193-1December 26, 2010Ray Chandler
Proven quasi-repdigit primes
 digitsflabelwlabelexpressionwhenwho
112979134999349w35·1029789-1December 26, 2010Ray Chandler
122955168999689w69·1029549-1December 26, 2010Ray Chandler
132933432999329w33·1029332-1December 26, 2010Ray Chandler
142846016999169w17·1028458-1December 26, 2010Ray Chandler
152810946999469w47·1028107-1December 26, 2010Ray Chandler
162809483999839w84·1028092-1December 26, 2010Ray Chandler
182763834999349w35·1027636-1December 26, 2010Ray Chandler
192757762999629w63·1027575-1December 26, 2010Ray Chandler
202749146999469w47·1027489-1December 26, 2010Ray Chandler
212725020999209w21·1027248-1December 26, 2010Ray Chandler
222703665999659w66·1027034-1December 26, 2010Ray Chandler
232678325999259w26·1026781-1December 26, 2010Ray Chandler
242657638999389w39·1026574-1December 26, 2010Ray Chandler
2526415 779w78·1026413-1December 26, 2010Ray Chandler
262634250999509w51·1026340-1December 26, 2010Ray Chandler
272623814999149w15·1026236-1December 26, 2010Ray Chandler
282603423999239w24·1026032-1December 26, 2010Ray Chandler
302567285999859w86·1025670-1December 26, 2010Ray Chandler
312554626999269w27·1025544-1December 26, 2010Ray Chandler
322524662999629w63·1025244-1December 26, 2010Ray Chandler
332512165999659w66·1025119-1December 26, 2010Ray Chandler
342505676999769w77·1025054-1December 26, 2010Ray Chandler
352494765999659w66·1024945-1December 26, 2010Ray Chandler
362435747999479w48·1024355-1December 26, 2010Ray Chandler
372431070999709w71·1024308-1December 26, 2010Ray Chandler
382411216999169w17·1024110-1December 26, 2010Ray Chandler
392327713999139w14·1023275-1December 26, 2010Ray Chandler
402322546999469w47·1023223-1December 26, 2010Ray Chandler
Unprovable quasi-repdigit PRPs
 digitsflabelwlabelexpressionwhenwho
106299136995969w597·1029912-41December 26, 2010Ray Chandler
107296284997949w795·1029627-21December 26, 2010Ray Chandler
108295387996979w698·1029537-31December 26, 2010Ray Chandler
1192909197991979w198·1029089-9December 26, 2010Ray Chandler
127285281990919w092·1028527-91December 26, 2010Ray Chandler
129283517996979w698·1028350-31December 26, 2010Ray Chandler
130283465990959w096·1028345-91December 26, 2010Ray Chandler
133280732995929w593·1028072-41December 26, 2010Ray Chandler
138277498995989w599·1027748-41December 26, 2010Ray Chandler
1432740794993949w395·1027405-7December 26, 2010Ray Chandler
157265667991979w198·1026565-81December 26, 2010Ray Chandler
164261831997919w792·1026182-21December 26, 2010Ray Chandler
177256415996959w696·1025640-31December 26, 2010Ray Chandler
178255757993979w398·1025574-61December 26, 2010Ray Chandler
180252431990919w092·1025242-91December 26, 2010Ray Chandler
185250234994949w495·1025022-51December 26, 2010Ray Chandler
193247455990959w096·1024744-91December 26, 2010Ray Chandler
195245997996979w698·1024598-31December 26, 2010Ray Chandler
196245891990919w092·1024588-91December 26, 2010Ray Chandler
199242003998939w894·1024199-11December 26, 2010Ray Chandler
2002416093991939w194·1024158-9December 26, 2010Ray Chandler
20124146999479w471024146-53December 26, 2010Ray Chandler
204238372998929w893·1023836-11December 26, 2010Ray Chandler
207236804991949w195·1023679-81December 26, 2010Ray Chandler
216230718998989w899·1023070-11December 26, 2010Ray Chandler
Unprovable near-repdigit-related PRPs (except ru/nr/pd/qr)
 digitsflabelwlabelexpressionwhenwho
10300001996319w632·1029999-37December 26, 2010Ray Chandler
1129994 559w756·1029992-3December 26, 2010Ray Chandler
12299593991739w174·1029958-83December 26, 2010Ray Chandler
13299412994729w473·1029940-53December 26, 2010Ray Chandler
1429928 20w772·1029927+77December 26, 2010Ray Chandler
16296046003760w376·1029603+37December 26, 2010Ray Chandler
17295965008150w815·1029595+81December 26, 2010Ray Chandler
1829589 80w118·1029588+11December 26, 2010Ray Chandler
19295474003940w394·1029546+39December 26, 2010Ray Chandler
2029507 19w332·1029506-67December 26, 2010Ray Chandler
22293888994789w479·1029387-53December 26, 2010Ray Chandler
23293396001760w176·1029338+17December 26, 2010Ray Chandler
2429303 70w337·1029302+33December 26, 2010Ray Chandler
2529293 779w378·1029291-7December 26, 2010Ray Chandler
2629254 49w335·1029253-67December 26, 2010Ray Chandler
27292224990749w075·1029221-93December 26, 2010Ray Chandler
28292068003980w398·1029205+39December 26, 2010Ray Chandler
30291816993169w317·1029180-69December 26, 2010Ray Chandler
31291641995119w512·1029163-49December 26, 2010Ray Chandler
33291337003970w397·1029132+39December 26, 2010Ray Chandler
34290964006140w614·1029095+61December 26, 2010Ray Chandler
35290899004190w419·1029088+41December 26, 2010Ray Chandler
36290692007120w712·1029068+71December 26, 2010Ray Chandler
37290634003140w314·1029062+31December 26, 2010Ray Chandler
38290632009320w932·1029062+93December 26, 2010Ray Chandler
40290272994729w473·1029026-53December 26, 2010Ray Chandler
41290086997369w737·1029007-27December 26, 2010Ray Chandler
42289743004330w433·1028973+43December 26, 2010Ray Chandler
43289233995339w534·1028922-47December 26, 2010Ray Chandler
44288908995389w539·1028889-47December 26, 2010Ray Chandler
4528882 220w722·1028880+7December 26, 2010Ray Chandler
4628861 39w114·1028860-89December 26, 2010Ray Chandler
4728819 119w312·1028817-7December 26, 2010Ray Chandler
48287322008120w812·1028731+81December 26, 2010Ray Chandler
51284715005350w535·1028470+53December 26, 2010Ray Chandler
52284557994379w438·1028454-57December 26, 2010Ray Chandler
53283493003130w313·1028348+31December 26, 2010Ray Chandler
54283193003130w313·1028318+31December 26, 2010Ray Chandler
55282759004390w439·1028274+43December 26, 2010Ray Chandler
56282717006170w617·1028270+61December 26, 2010Ray Chandler
58282207996179w618·1028219-39December 26, 2010Ray Chandler
59281623006730w673·1028161+67December 26, 2010Ray Chandler
60280746009760w976·1028073+97December 26, 2010Ray Chandler
61280646997169w717·1028063-29December 26, 2010Ray Chandler
6227868 339w734·1027866-3December 26, 2010Ray Chandler
63277148005380w538·1027713+53December 26, 2010Ray Chandler
64276703992339w234·1027669-77December 26, 2010Ray Chandler
65276493005930w593·1027648+59December 26, 2010Ray Chandler
66276243002930w293·1027623+29December 26, 2010Ray Chandler
67276073002930w293·1027606+29December 26, 2010Ray Chandler
68275329002990w299·1027531+29December 26, 2010Ray Chandler
69275033007330w733·1027502+73December 26, 2010Ray Chandler
70274417996179w618·1027440-39December 26, 2010Ray Chandler
71274195004750w475·1027418+47December 26, 2010Ray Chandler
72274032008320w832·1027402+83December 26, 2010Ray Chandler
73273462991729w173·1027345-83December 26, 2010Ray Chandler
74273192003920w392·1027318+39December 26, 2010Ray Chandler
75272083003730w373·1027207+37December 26, 2010Ray Chandler
76270519006190w619·1027050+61December 26, 2010Ray Chandler
77270038998789w879·1027002-13December 26, 2010Ray Chandler
8026745 79w338·1026744-67December 26, 2010Ray Chandler
81266688990389w039·1026667-97December 26, 2010Ray Chandler
82266638005180w518·1026662+51December 26, 2010Ray Chandler
83266117005770w577·1026610+57December 26, 2010Ray Chandler
84265658006380w638·1026564+63December 26, 2010Ray Chandler
85264906997369w737·1026489-27December 26, 2010Ray Chandler
87264004006740w674·1026399+67December 26, 2010Ray Chandler
88263785997159w716·1026377-29December 26, 2010Ray Chandler
89263612006320w632·1026360+63December 26, 2010Ray Chandler
90262943004330w433·1026293+43December 26, 2010Ray Chandler
91262538008780w878·1026252+87December 26, 2010Ray Chandler
9226201 440w344·1026199+3December 26, 2010Ray Chandler
93261989008390w839·1026197+83December 26, 2010Ray Chandler
9426126 40w994·1026125+99December 26, 2010Ray Chandler
95261238996389w639·1026122-37December 26, 2010Ray Chandler
96260857991379w138·1026084-87December 26, 2010Ray Chandler
97259863994139w414·1025985-59December 26, 2010Ray Chandler
9825963 110w911·1025961+9December 26, 2010Ray Chandler
99258829004390w439·1025881+43December 26, 2010Ray Chandler
100258253003730w373·1025824+37December 26, 2010Ray Chandler
10125762 339w134·1025760-9December 26, 2010Ray Chandler
10225738 339w734·1025736-3December 26, 2010Ray Chandler
10325733 40w994·1025732+99December 26, 2010Ray Chandler
104257274009740w974·1025726+97December 26, 2010Ray Chandler
10525716 29w333·1025715-67December 26, 2010Ray Chandler
106256869001990w199·1025685+19December 26, 2010Ray Chandler
108255264009740w974·1025525+97December 26, 2010Ray Chandler
109254753009730w973·1025474+97December 26, 2010Ray Chandler
11025452 19w332·1025451-67December 26, 2010Ray Chandler
111254387002770w277·1025437+27December 26, 2010Ray Chandler
11225428 50w775·1025427+77December 26, 2010Ray Chandler
113254191990319w032·1025418-97December 26, 2010Ray Chandler
11425408 50w995·1025407+99December 26, 2010Ray Chandler
115253933001330w133·1025392+13December 26, 2010Ray Chandler
116253045006350w635·1025303+63December 26, 2010Ray Chandler
11725257 20w112·1025256+11December 26, 2010Ray Chandler
118252335006950w695·1025232+69December 26, 2010Ray Chandler
119252124006340w634·1025211+63December 26, 2010Ray Chandler
120252065992759w276·1025205-73December 26, 2010Ray Chandler
121251948995389w539·1025193-47December 26, 2010Ray Chandler
122251878998189w819·1025186-19December 26, 2010Ray Chandler
123251803006130w613·1025179+61December 26, 2010Ray Chandler
12425179 220w922·1025177+9December 26, 2010Ray Chandler
125251735995159w516·1025172-49December 26, 2010Ray Chandler
12625104 889w189·1025102-9December 26, 2010Ray Chandler
127250435005350w535·1025042+53December 26, 2010Ray Chandler
12825019 339w734·1025017-3December 26, 2010Ray Chandler
12924957 79w338·1024956-67December 26, 2010Ray Chandler
130249492008120w812·1024948+81December 26, 2010Ray Chandler
132249353990139w014·1024934-99December 26, 2010Ray Chandler
133249098002780w278·1024908+27December 26, 2010Ray Chandler
134248434998749w875·1024842-13December 26, 2010Ray Chandler
135248422008720w872·1024841+87December 26, 2010Ray Chandler
13624818 20w332·1024817+33December 26, 2010Ray Chandler
138247759004990w499·1024774+49December 26, 2010Ray Chandler
139247573008930w893·1024756+89December 26, 2010Ray Chandler
14024746 990w799·1024744+7December 26, 2010Ray Chandler
141247137990779w078·1024712-93December 26, 2010Ray Chandler
144245655008150w815·1024564+81December 26, 2010Ray Chandler
145244987992179w218·1024497-79December 26, 2010Ray Chandler
146244133004930w493·1024412+49December 26, 2010Ray Chandler
147243734996149w615·1024372-39December 26, 2010Ray Chandler
148243535009350w935·1024352+93December 26, 2010Ray Chandler
149243386007960w796·1024337+79December 26, 2010Ray Chandler
150243277998779w878·1024326-13December 26, 2010Ray Chandler
151242907006170w617·1024289+61December 26, 2010Ray Chandler
152242866996769w677·1024285-33December 26, 2010Ray Chandler
153242148995189w519·1024213-49December 26, 2010Ray Chandler
154241759005390w539·1024174+53December 26, 2010Ray Chandler
155240975995359w536·1024096-47December 26, 2010Ray Chandler
157240734006340w634·1024072+63December 26, 2010Ray Chandler
158240646002960w296·1024063+29December 26, 2010Ray Chandler
159240424008740w874·1024041+87December 26, 2010Ray Chandler
16023947 550w755·1023945+7December 26, 2010Ray Chandler
161239304006940w694·1023929+69December 26, 2010Ray Chandler
162239015004150w415·1023900+41December 26, 2010Ray Chandler
163238987994379w438·1023897-57December 26, 2010Ray Chandler
164238949006790w679·1023893+67December 26, 2010Ray Chandler
166238293003730w373·1023828+37December 26, 2010Ray Chandler
167238136001360w136·1023812+13December 26, 2010Ray Chandler
168238133006130w613·1023812+61December 26, 2010Ray Chandler
169237833001330w133·1023782+13December 26, 2010Ray Chandler
170237404006140w614·1023739+61December 26, 2010Ray Chandler
17123733 20w332·1023732+33December 26, 2010Ray Chandler
173236805004150w415·1023679+41December 26, 2010Ray Chandler
174236427008170w817·1023641+81December 26, 2010Ray Chandler
175235674992749w275·1023566-73December 26, 2010Ray Chandler
17723374 559w156·1023372-9December 26, 2010Ray Chandler
178233667009770w977·1023365+97December 26, 2010Ray Chandler
18023328 50w775·1023327+77December 26, 2010Ray Chandler
182232394003940w394·1023238+39December 26, 2010Ray Chandler
183232184005740w574·1023217+57December 26, 2010Ray Chandler
184231686002360w236·1023167+23December 26, 2010Ray Chandler
185231654009140w914·1023164+91December 26, 2010Ray Chandler
186231256001760w176·1023124+17December 26, 2010Ray Chandler
187230305996359w636·1023029-37December 26, 2010Ray Chandler

Bob Price proved 1 prime by Primo.

Proven near-repdigit-related primes (except ru/nr/pd/qr)
 digitsflabelwlabelexpressionwhenwho
46111801009710w97101179+97December 26, 2010Bob Price

December 25, 2010

Bob Price found 13 primes and 36 PRPs by PFGW and Primo.

Proven near-repdigit-related primes (except ru/nr/pd/qr)
 digitsflabelwlabelexpressionwhenwho
27819431006710w67101942+67December 25, 2010Bob Price
28219241003910w39101923+39December 25, 2010Bob Price
31217651006110w61101764+61December 25, 2010Bob Price
31917321005110w51101731+51December 25, 2010Bob Price
36615291003910w39101528+39December 25, 2010Bob Price
36815241006910w69101523+69December 25, 2010Bob Price
43412441008710w87101243+87December 25, 2010Bob Price
45911851009310w93101184+93December 25, 2010Bob Price
46911521009710w97101151+97December 25, 2010Bob Price
48511001007310w73101099+73December 25, 2010Bob Price
49610711005110w51101070+51December 25, 2010Bob Price
52510101005110w51101009+51December 25, 2010Bob Price
52810041006910w69101003+69December 25, 2010Bob Price
Unprovable near-repdigit PRPs
 digitsflabelwlabelexpressionwhenwho
2937169999599w591037169-41December 25, 2010Bob Price
3136271999299w291036271-71December 25, 2010Bob Price
3435371999899w891035371-11December 25, 2010Bob Price
3535316999599w591035316-41December 25, 2010Bob Price
4727312999599w591027312-41December 25, 2010Bob Price
6223932999599w591023932-41December 25, 2010Bob Price
Unprovable quasi-repdigit PRPs
 digitsflabelwlabelexpressionwhenwho
6439922999439w431039922-57December 25, 2010Bob Price
7737344999419w411037344-59December 25, 2010Bob Price
9034399999439w431034399-57December 25, 2010Bob Price
9134313 9w771034313-23December 25, 2010Bob Price
9332909999079w071032909-93December 25, 2010Bob Price
10131123999079w071031123-93December 25, 2010Bob Price
10230791999739w731030791-27December 25, 2010Bob Price
10729455 9w111029455-89December 25, 2010Bob Price
11529091999719w711029091-29December 25, 2010Bob Price
12328437999079w071028437-93December 25, 2010Bob Price
13327681 9w771027681-23December 25, 2010Bob Price
16225727999479w471025727-53December 25, 2010Bob Price
17724693999079w071024693-93December 25, 2010Bob Price
18023936999619w611023936-39December 25, 2010Bob Price
18123854999019w011023854-99December 25, 2010Bob Price
Unprovable near-repdigit-related PRPs (except ru/nr/pd/qr)
 digitsflabelwlabelexpressionwhenwho
4395841009110w911039583+91December 25, 2010Bob Price
5391881004910w491039187+49December 25, 2010Bob Price
7353941004310w431035393+43December 25, 2010Bob Price
8346241006310w631034623+63December 25, 2010Bob Price
9326461005710w571032645+57December 25, 2010Bob Price
10298851005710w571029884+57December 25, 2010Bob Price
11294721004910w491029471+49December 25, 2010Bob Price
15287001005110w511028699+51December 25, 2010Bob Price
17282211006310w631028220+63December 25, 2010Bob Price
19267801008710w871026779+87December 25, 2010Bob Price
20264261009710w971026425+97December 25, 2010Bob Price
21256721002110w211025671+21December 25, 2010Bob Price
26240951008110w811024094+81December 25, 2010Bob Price
29235001009110w911023499+91December 25, 2010Bob Price
879611801009710w97101179+97December 25, 2010Bob Price

Factorizations of 100...009 have been extended up to n=250. Composite numbers that appeared newly got through ECM 118 times at level 35. Most unknown factors are supposed to be greater than 1030.

Ray Chandler's research found some inconsistencies between Henri & Renaud Lifchitz's PRP Top records and primesize.txt. The following records were corrected or added.

Unprovable near-repdigit PRPs
 digitsflabelwlabelexpressionwhenwho
9018236111311w31(1018236+179)/9August 2007Paul Bourdelais
10316922111011w01(1016922-91)/9August 2007Paul Bourdelais
10716401111911w91(1016401+719)/9August 2007Paul Bourdelais
12515189111911w91(1015189+719)/9August 2007Paul Bourdelais
13014724111211w21(1014724+89)/9May 2004Donovan Johnson
13514549111711w71(1014549+539)/9August 2007Paul Bourdelais
15313290111211w21(1013290+89)/9May 2004Donovan Johnson
15613224111511w51(1013224+359)/9August 2007Paul Bourdelais
15713222111811w81(1013222+629)/9August 2007Paul Bourdelais
16113151111611w61(1013151+449)/9August 2007Paul Bourdelais
16712685111711w71(1012685+539)/9August 2007Paul Bourdelais
16912626111611w61(1012626+449)/9August 2007Paul Bourdelais
19011254111511w51(1011254+359)/9August 2007Paul Bourdelais
20610555111711w71(1010555+539)/9August 2007Paul Bourdelais
Unprovable quasi-repdigit PRPs
 digitsflabelwlabelexpressionwhenwho
22420818111931w93(1020818+737)/9August 2007Paul Bourdelais
24719920111431w43(1019920+287)/9October 2007Paul Bourdelais
28319530111571w57(1019530+413)/9October 2007Paul Bourdelais
29119380111031w03(1019380-73)/9October 2007Paul Bourdelais
44617314111291w29(1017314+161)/9August 2007Paul Bourdelais
50816749111631w63(1016749+467)/9August 2007Paul Bourdelais
53516471 1w99(1016471+791)/9August 2007Paul Bourdelais
62715584111471w47(1015584+323)/9August 2007Paul Bourdelais
68015060111271w27(1015060+143)/9August 2007Paul Bourdelais
73814440111291w29(1014440+161)/9August 2007Paul Bourdelais
76414181111271w27(1014181+143)/9August 2007Paul Bourdelais
78614004111791w79(1014004+611)/9August 2007Paul Bourdelais
78913963111931w93(1013963+737)/9August 2007Paul Bourdelais
93212549111791w79(1012549+611)/9August 2007Paul Bourdelais
98112107111471w47(1012107+323)/9August 2007Paul Bourdelais
105811582111971w97(1011582+773)/9August 2007Paul Bourdelais
111910981111271w27(1010981+143)/9August 2007Paul Bourdelais
113510894111031w03(1010894-73)/9August 2007Paul Bourdelais
118610591111891w89(1010591+701)/9August 2007Paul Bourdelais
119210550111471w47(1010550+323)/9August 2007Paul Bourdelais
122610271111491w49(1010271+341)/9August 2007Paul Bourdelais
Unprovable near-repdigit-related PRPs (except ru/nr/pd/qr)
 digitsflabelwlabelexpressionwhenwho
1224676 226w9(68·1024674+7)/3October 2010Ray Chandler
13245895332753w27(16·1024588-19)/3October 2010Ray Chandler
2076109791006310w631010978+63April 2010Patrick De Geest

December 23, 2010

Giovanni Di Maria's website: http://www.elektrosoft.it/matematica/repunit/repunit.htm

December 22, 2010

Maksym Voznyy proved 1 near-repdigit prime and 1 near-repdigit-related prime by Primo 3.0.9, PFGW 3.4.4, CHG.GP and chgcertd.gp.

Proven near-repdigit primes
 digitsflabelwlabelexpressionwhenwho
33328742111121w(19·102873-1)/9December 22, 2010Maksym Voznyy
Proven near-repdigit-related primes (except ru/nr/pd/qr)
 digitsflabelwlabelexpressionwhenwho
14754375332753w27(16·105436-19)/3December 22, 2010Maksym Voznyy

December 21, 2010

Maksym Voznyy proved 1 near-repdigit prime, 2 quasi-repdigit primes and 1 near-repdigit-related prime by Primo 3.0.9, PFGW 3.4.4, CHG.GP and chgcertd.gp.

Proven near-repdigit primes
 digitsflabelwlabelexpressionwhenwho
33428112111121w(19·102810-1)/9December 21, 2010Maksym Voznyy
Proven quasi-repdigit primes
 digitsflabelwlabelexpressionwhenwho
1604881111091w09(104881-19)/9December 21, 2010Maksym Voznyy
17042294888348w3(44·104228-53)/9December 21, 2010Maksym Voznyy
Proven near-repdigit-related primes (except ru/nr/pd/qr)
 digitsflabelwlabelexpressionwhenwho
15350897110371w03(64·105088-73)/9December 21, 2010Maksym Voznyy

December 20, 2010

Maksym Voznyy proved 2 near-repdigit primes, 1 quasi-repdigit prime and 2 near-repdigit-related primes by Primo 3.0.9, PFGW 3.4.4, CHG.GP and chgcertd.gp.

Proven near-repdigit primes
 digitsflabelwlabelexpressionwhenwho
3432744555595w9(5·102744+31)/9December 20, 2010Maksym Voznyy
3452720777737w3(7·102720-43)/9December 20, 2010Maksym Voznyy
Proven quasi-repdigit primes
 digitsflabelwlabelexpressionwhenwho
1853757111091w09(103757-19)/9December 20, 2010Maksym Voznyy
Proven near-repdigit-related primes (except ru/nr/pd/qr)
 digitsflabelwlabelexpressionwhenwho
17737585772157w21(52·103757-511)/9December 20, 2010Maksym Voznyy
18435935772157w21(52·103592-511)/9December 20, 2010Maksym Voznyy

Factorizations of 66...661 have been extended up to n=250. Composite numbers that appeared newly got through ECM 118 times at level 35. Most unknown factors are supposed to be greater than 1030.

December 19, 2010

David Broadhurst found the largest known near-repdigit prime. Congratulations!

Proven near-repdigit primes
 digitsflabelwlabelexpressionwhenwho
13645228999989w9·10364521-1December 19, 2010David Broadhurst

Maksym Voznyy proved 1 near-repdigit prime by Primo 3.0.9.

Proven near-repdigit primes
 digitsflabelwlabelexpressionwhenwho
3422691888878w7(8·102691-17)/9December 19, 2010Maksym Voznyy

December 18, 2010

Maksym Voznyy proved 1 near-repdigit prime by Primo 3.0.9.

Proven near-repdigit primes
 digitsflabelwlabelexpressionwhenwho
3482586333373w7(102586+11)/3December 18, 2010Maksym Voznyy

December 17, 2010

Maksym Voznyy proved 2 near-repdigit primes by Primo 3.0.9.

Proven near-repdigit primes
 digitsflabelwlabelexpressionwhenwho
36423807333373w(22·102379-1)/3December 17, 2010Maksym Voznyy
36623565777757w(52·102355-7)/9December 17, 2010Maksym Voznyy

Maksym Voznyy proved 1 near-repdigit-palindrome prime by Primo 3.0.9.

Proven near-repdigit-palindrome primes
 digitsflabelwlabelexpressionwhenwho
233089114111w41w(103089+27·101544-1)/9December 17, 2010Maksym Voznyy

Ray Chander found 3 near-repdigit primes, 9 quasi-repdigit primes, 2 near-repdigit PRPs, 19 quasi-repdigit PRPs and 85 near-repdigit-related PRPs (except ru/nr/pd/qr) by srsieve and PFGW.

Proven near-repdigit primes
 digitsflabelwlabelexpressionwhenwho
11522592 999999959w99999996·1022584-1December 17, 2010Ray Chandler
11921761 999999929w99999993·1021753-1December 17, 2010Ray Chandler
12720112 999999949w99999995·1020104-1December 17, 2010Ray Chandler
Proven quasi-repdigit primes
 digitsflabelwlabelexpressionwhenwho
142280532999329w33·1022803-1December 17, 2010Ray Chandler
152274525999259w26·1022743-1December 17, 2010Ray Chandler
162222137999379w38·1022219-1December 17, 2010Ray Chandler
172202450999509w51·1022022-1December 17, 2010Ray Chandler
182160883999839w84·1021606-1December 17, 2010Ray Chandler
192151513999139w14·1021513-1December 17, 2010Ray Chandler
202103437999379w38·1021032-1December 17, 2010Ray Chandler
222057085999859w86·1020568-1December 17, 2010Ray Chandler
252024641999419w42·1020244-1December 17, 2010Ray Chandler

December 16, 2010

Maksym Voznyy proved 1 near-repdigit prime, 1 quasi-repdigit prime and 5 near-repdigit-related primes (except ru/nr/pd/qr) by Promo 3.0.9.

Proven near-repdigit primes
 digitsflabelwlabelexpressionwhenwho
3591949111011w01(101949-91)/9December 16, 2010Maksym Voznyy
Proven quasi-repdigit primes
 digitsflabelwlabelexpressionwhenwho
32720694991949w195·102068-81December 16, 2010Maksym Voznyy
Proven near-repdigit-related primes (except ru/nr/pd/qr)
 digitsflabelwlabelexpressionwhenwho
21033924995149w515·103391-49December 16, 2010Maksym Voznyy
28620611003110w31102060+31December 16, 2010Maksym Voznyy
29120388332983w29(25·102037-13)/3December 16, 2010Maksym Voznyy
29420012665726w57(8·102000-29)/3December 16, 2010Maksym Voznyy
29619793885138w51(35·101978-341)/9December 16, 2010Maksym Voznyy

December 15, 2010

Maksym Voznyy proved 3 quasi-repdigit primes and 4 near-repdigit-related primes (except ru/nr/pd/qr) by Primo 3.0.9.

Proven quasi-repdigit primes
 digitsflabelwlabelexpressionwhenwho
3561935999619w61101935-39December 15, 2010Maksym Voznyy
3571932999839w83101932-17December 15, 2010Maksym Voznyy
3611916444174w17(4·101916-247)/9December 15, 2010Maksym Voznyy
Proven near-repdigit-related primes (except ru/nr/pd/qr)
 digitsflabelwlabelexpressionwhenwho
29719483773937w39(34·101947-349)/9December 15, 2010Maksym Voznyy
30019311332713w27(4·101930-19)/3December 15, 2010Maksym Voznyy
30119242668926w89(8·101923+67)/3December 15, 2010Maksym Voznyy
30219236330763w07(19·101922-79)/3December 15, 2010Maksym Voznyy

Gary Barnes's 61 near-repdigit primes were imported from his page.

Proven near-repdigit primes
 digitsflabelwlabelexpressionwhenwho
289874095999959w96·1098738-1November 2010Gary Barnes
2995299 9919w992·1095296-1November 2010Gary Barnes
3580772 9999919w999992·1080766-1November 2010Gary Barnes
3680730 9989w999·1080727-1November 2010Gary Barnes
3878719 999919w99992·1078714-1November 2010Gary Barnes
3974980 9929w993·1074977-1November 2010Gary Barnes
4272631 99919w9992·1072627-1November 2010Gary Barnes
4567870 9979w998·1067867-1November 2010Gary Barnes
4667770 9999979w999998·1067764-1November 2010Gary Barnes
4766851 9929w993·1066848-1November 2010Gary Barnes
4866686 9989w999·1066683-1November 2010Gary Barnes
5063337 9999989w999999·1063331-1November 2010Gary Barnes
5162469 99949w9995·1062465-1November 2010Gary Barnes
5361254 99959w9996·1061250-1November 2010Gary Barnes
5459475 9979w998·1059472-1November 2010Gary Barnes
5655540 9999919w999992·1055534-1November 2010Gary Barnes
5854593 9999919w999992·1054587-1November 2010Gary Barnes
5954548 99919w9992·1054544-1November 2010Gary Barnes
6054464 9999949w999995·1054458-1November 2010Gary Barnes
6154065 999949w99995·1054060-1November 2010Gary Barnes
6253717 9989w999·1053714-1November 2010Gary Barnes
6353583 9999949w999995·1053577-1November 2010Gary Barnes
6650217 9999929w999993·1050211-1November 2010Gary Barnes
6750103 9999959w999996·1050097-1November 2010Gary Barnes
7148894 9949w995·1048891-1November 2010Gary Barnes
7446849 9999929w999993·1046843-1November 2010Gary Barnes
7645820 9999959w999996·1045814-1November 2010Gary Barnes
7844868 9919w992·1044865-1November 2010Gary Barnes
7944278 99959w9996·1044274-1November 2010Gary Barnes
8042636 9989w999·1042633-1November 2010Gary Barnes
8241686 999919w99992·1041681-1November 2010Gary Barnes
8341497 999959w99996·1041492-1November 2010Gary Barnes
8540227 99959w9996·1040223-1November 2010Gary Barnes
8638403 9959w996·1038400-1November 2010Gary Barnes
8935899 999979w99998·1035894-1November 2010Gary Barnes
9035881 9999989w999999·1035875-1November 2010Gary Barnes
9135215 9949w995·1035212-1November 2010Gary Barnes
9334923 9999929w999993·1034917-1November 2010Gary Barnes
9533090 999959w99996·1033085-1November 2010Gary Barnes
9832192 9949w995·1032189-1November 2010Gary Barnes
10130848 9999949w999995·1030842-1November 2010Gary Barnes
10329005 9919w992·1029002-1October 2010Gary Barnes
10428861 9999959w999996·1028855-1October 2010Gary Barnes
10528360 9929w993·1028357-1October 2010Gary Barnes
10627482 999929w99993·1027477-1October 2010Gary Barnes
10726781 9919w992·1026778-1October 2010Gary Barnes
11025982 9989w999·1025979-1October 2010Gary Barnes
11125821 9929w993·1025818-1October 2010Gary Barnes
11225644 999949w99995·1025639-1October 2010Gary Barnes
11325058 9999919w999992·1025052-1October 2010Gary Barnes
11424692 999989w99999·1024687-1October 2010Gary Barnes
11522482 999989w99999·1022477-1October 2010Gary Barnes
11622180 999989w99999·1022175-1October 2010Gary Barnes
11722014 9959w996·1022011-1October 2010Gary Barnes
11821574 999949w99995·1021569-1October 2010Gary Barnes
12120614 9929w993·1020611-1October 2010Gary Barnes
12220608 999989w99999·1020603-1October 2010Gary Barnes
12320546 99949w9995·1020542-1October 2010Gary Barnes
12420360 9919w992·1020357-1October 2010Gary Barnes
558767 999989w99999·10762-1October 2010Gary Barnes
888202 999919w99992·10197-1October 2010Gary Barnes

Serge Batalov proved the second largest known plateau-and-depression prime and a quasi-repdigit prime by CHG.

Proven plateau and depression primes
 digitsflabelwlabelexpressionwhenwho
252093777337w3(34·105208-43)/9December 15, 2010Serge Batalov
Proven quasi-repdigit primes
 digitsflabelwlabelexpressionwhenwho
14051336888368w3(62·105132-53)/9December 15, 2010Serge Batalov

December 14, 2010

Erik Branger searched near-repdigit prime number of the form 22...221;(2·10n-11)/9, up to n=100000. No additional (probable) prime number was found.

Stefano D'Urso found the seventh largest known near-repdigit prime number.

Proven near-repdigit primes
 digitsflabelwlabelexpressionwhenwho
722562095999959w96·10225618-1December 14, 2010Stefano D'Urso

Maksym Voznyy proved 3 quasi-repdigit primes and 10 near-repdigit-related primes by Primo.

Proven quasi-repdigit primes
 digitsflabelwlabelexpressionwhenwho
3831819555195w19(5·101819-329)/9December 14, 2010Maksym Voznyy
385181737339373w9(112·101815+17)/3December 14, 2010Maksym Voznyy
38718119332393w23(28·101810-31)/3December 14, 2010Maksym Voznyy
Proven near-repdigit-related primes (except ru/nr/pd/qr)
 digitsflabelwlabelexpressionwhenwho
30119121665716w57(5·101911-29)/3December 14, 2010Maksym Voznyy
30518883885138w51(35·101887-341)/9December 14, 2010Maksym Voznyy
30618846221762w17(56·101883-47)/9December 14, 2010Maksym Voznyy
3081877 23w11(7·101876-67)/3December 14, 2010Maksym Voznyy
31118466449764w97(58·101845+473)/9December 14, 2010Maksym Voznyy
3131841 83w11(25·101840-67)/3December 14, 2010Maksym Voznyy
31418352775127w51(25·101834-241)/9December 14, 2010Maksym Voznyy
31518227554975w49(68·101821-59)/9December 14, 2010Maksym Voznyy
31618125882958w29(53·101811-539)/9December 14, 2010Maksym Voznyy
31818053551335w13(32·101804-383)/9December 14, 2010Maksym Voznyy

December 13, 2010

Ray Chandler found the fourth largest known plateau-and-depression PRP by srsieve and PFGW.

Unprovable plateau and depression PRPs
 digitsflabelwlabelexpressionwhenwho
4801633777337w3(34·1080162-43)/9December 13, 2010Ray Chandler

Factorizations of 22...223 have been extended up to n=250. Composite numbers that appeared newly got through ECM 118 times at level 35. Most unknown factors are supposed to be greater than 1030.

December 12, 2010

Ray Chandler found 3 near-repdigit prime numbers, 6 quasi-repdigit prime numbers, 2 near-repdigit PRPs, 53 quasi-repdigit PRPs and 165 near-repdigit-related PRPs by srsieve, PFGW. The upper limit of searched near-repdigit-related prime numbers reached to n=20000.

Proven near-repdigit primes
 digitsflabelwlabelexpressionwhenwho
6519614 99999959w9999996·1019607-1December 12, 2010Ray Chandler
6619560 999999979w99999998·1019552-1December 12, 2010Ray Chandler
6719256 999999959w99999996·1019248-1December 12, 2010Ray Chandler
Proven quasi-repdigit primes
 digitsflabelwlabelexpressionwhenwho
171977323999239w24·1019771-1December 12, 2010Ray Chandler
1819687 889w89·1019685-1December 12, 2010Ray Chandler
191944738999389w39·1019445-1December 12, 2010Ray Chandler
201943832999329w33·1019436-1December 12, 2010Ray Chandler
211933947999479w48·1019337-1December 12, 2010Ray Chandler
2219247 779w78·1019245-1December 12, 2010Ray Chandler
Unprovable near-repdigit PRPs
 digitsflabelwlabelexpressionwhenwho
6119908777577w57(7·1019908-187)/9December 12, 2010Ray Chandler
6419524777377w37(7·1019524-367)/9December 12, 2010Ray Chandler

Maksym Voznyy proved the primality of 2 quasi-repdigit prime and 9 near-repdigit-related primes by Primo.

Proven quasi-repdigit primes
 digitsflabelwlabelexpressionwhenwho
21528054666346w3(14·102804-11)/3December 12, 2010Maksym Voznyy
39517411775717w57(16·101740-187)/9December 12, 2010Maksym Voznyy
Proven near-repdigit-related primes (except ru/nr/pd/qr)
 digitsflabelwlabelexpressionwhenwho
23028735883158w31(53·102872-521)/9December 12, 2010Maksym Voznyy
2342777 56w11(17·102776-167)/3December 12, 2010Maksym Voznyy
31017997554775w47(68·101798-77)/9December 12, 2010Maksym Voznyy
31717736997369w737·101772-27December 12, 2010Maksym Voznyy
32117501442914w29(13·101749-139)/9December 12, 2010Maksym Voznyy
3231745 26w33(8·101744-101)/3December 12, 2010Maksym Voznyy
3241737 53w99(16·101736+197)/3December 12, 2010Maksym Voznyy
32817172112921w29(19·101716+161)/9December 12, 2010Maksym Voznyy
33017087110971w09(64·101707-19)/9December 12, 2010Maksym Voznyy

December 11, 2010

Serge Batalov proved the primality of a 7412-digit near-repdigit-realted prime by CHG.

Proven near-repdigit-related primes (except ru/nr/pd/qr)
 digitsflabelwlabelexpressionwhenwho
12674121886918w69(17·107411-179)/9December 11, 2010Serge Batalov

Serge Batalov proved the primality of a 17877-digit near-repdigit-related prime by Primo, PFGW, CHG.gp and chgcertd.gp. See certifications for details.

Proven near-repdigit-related primes (except ru/nr/pd/qr)
 digitsflabelwlabelexpressionwhenwho
39178774221942w19(38·1017876-29)/9December 11, 2010Serge Batalov

December 10, 2010

Stefano D'Urso found 1 near-repdigit prime.

Proven near-repdigit primes
 digitsflabelwlabelexpressionwhenwho
921198595999959w96·10211983-1December 10, 2010Stefano D'Urso

Maksym Voznyy proved the primality of 1 quasi-repdigit prime and 3 near-repdigit-related primes by Primo.

Proven quasi-repdigit primes
 digitsflabelwlabelexpressionwhenwho
3931743 4w99(4·101743+491)/9December 10, 2010Maksym Voznyy
Proven near-repdigit-related primes (except ru/nr/pd/qr)
 digitsflabelwlabelexpressionwhenwho
31317653665336w53(11·101764-41)/3December 10, 2010Maksym Voznyy
3171733 10w99101732+99December 10, 2010Maksym Voznyy
31917108665986w59(26·101709-23)/3December 10, 2010Maksym Voznyy

December 9, 2010

Maksym Voznyy proved the primality of 4 quasi-repdigit primes and 10 near-repdigit-related primes by Primo.

Proven quasi-repdigit primes
 digitsflabelwlabelexpressionwhenwho
4091679555015w01(5·101679-491)/9December 9, 2010Maksym Voznyy
41316687110171w01(64·101667-91)/9December 9, 2010Maksym Voznyy
4221620222512w51(2·101620+259)/9December 9, 2010Maksym Voznyy
4231620111691w69(101620+521)/9December 9, 2010Maksym Voznyy
Proven near-repdigit-related primes (except ru/nr/pd/qr)
 digitsflabelwlabelexpressionwhenwho
23626301886918w69(17·102629-179)/9December 9, 2010Maksym Voznyy
23726196221762w17(56·102618-47)/9December 9, 2010Maksym Voznyy
26422774883948w39(44·102276-449)/9December 9, 2010Maksym Voznyy
31717029009190w919·101701+91December 9, 2010Maksym Voznyy
31816971006310w63101696+63December 9, 2010Maksym Voznyy
31916904336943w69(13·101689+107)/3December 9, 2010Maksym Voznyy
32016882775127w51(25·101687-241)/9December 9, 2010Maksym Voznyy
32416681660116w01(5·101667-197)/3December 9, 2010Maksym Voznyy
32816398332983w29(25·101638-13)/3December 9, 2010Maksym Voznyy
51810193556135w61(32·101018+49)/9December 9, 2010Maksym Voznyy

December 8, 2010

Bob Price found 1 prime and 3 PRPs.

Proven near-repdigit-related primes (except ru/nr/pd/qr)
 digitsflabelwlabelexpressionwhenwho
29319131007910w79101912+79December 8, 2010Bob Price
Unprovable near-repdigit-related PRPs (except ru/nr/pd/qr)
 digitsflabelwlabelexpressionwhenwho
13290591007910w791029058+79December 8, 2010Bob Price
16269901003710w371026989+37December 8, 2010Bob Price
24237331007910w791023732+79December 8, 2010Bob Price

Maksym Voznyy proved the primality of a quasi-repdigit prime and a near-repdigit-related prime by Primo.

Proven quasi-repdigit primes
 digitsflabelwlabelexpressionwhenwho
30721169776797w67(88·102115-97)/9December 8, 2010Maksym Voznyy
Proven near-repdigit-related primes (except ru/nr/pd/qr)
 digitsflabelwlabelexpressionwhenwho
26422256770967w09(61·102224-619)/9December 8, 2010Maksym Voznyy

Serge Batalov proved the primality of a quasi-repdigit prime number 11103_3258 = (103258-73)/9 by Primo and PFGW.
11103_3258+1 = (103258-73)/9+1 = 64·(5·10542+1)/3·(5·10542-1)·(25·101084-5·10542+1)/3·(25·101084+5·10542+1) = 64·16667_542·49999_542·83w16w7_542·250w50w1_542.
83w16w7_542 = 7·109·563041·869047141·147372142447·p1057.
p1057 was proved by ECPP and 11103_3258 was proved by N-1/N+1/BLS with factored part 33.82%.

Proven quasi-repdigit primes
 digitsflabelwlabelexpressionwhenwho
1873258111031w03(103258-73)/9December 8, 2010Serge Batalov

December 7, 2010

Maksym Voznyy proved 3 primes by Primo 3.0.9.

Proven near-repdigit primes
 digitsflabelwlabelexpressionwhenwho
2412894999899w89102894-11December 7, 2010Maksym Voznyy
Proven near-repdigit-related primes (except ru/nr/pd/qr)
 digitsflabelwlabelexpressionwhenwho
22529791553915w39(14·102978-149)/9December 7, 2010Maksym Voznyy
3111731 23w11(7·101730-67)/3December 7, 2010Maksym Voznyy

December 5, 2010

Stefano D'Urso found 4 near-repdigit primes.

Proven near-repdigit primes
 digitsflabelwlabelexpressionwhenwho
1018345495999959w96·10183452-1December 5, 2010Stefano D'Urso
1414032895999959w96·10140326-1December 5, 2010Stefano D'Urso
1613056795999959w96·10130565-1December 5, 2010Stefano D'Urso
1911895195999959w96·10118949-1December 5, 2010Stefano D'Urso

Maksym Voznyy proved 3 primes by Primo 3.0.9.

Proven quasi-repdigit primes
 digitsflabelwlabelexpressionwhenwho
21427899332393w23(28·102788-31)/3December 5, 2010Maksym Voznyy
Proven near-repdigit-related primes (except ru/nr/pd/qr)
 digitsflabelwlabelexpressionwhenwho
2502415 34w11(31·102414-301)/9December 5, 2010Maksym Voznyy
26721538008180w818·102152+81December 5, 2010Maksym Voznyy

Ray Chandler found 5 primes and 231 PRPs by PFGW.

Proven near-repdigit primes
 digitsflabelwlabelexpressionwhenwho
6118841 999979w99998·1018836-1December 5, 2010Ray Chandler
6318604 9999989w999999·1018598-1December 5, 2010Ray Chandler
6418212 99959w9996·1018208-1December 5, 2010Ray Chandler
Proven quasi-repdigit primes
 digitsflabelwlabelexpressionwhenwho
171882074999749w75·1018818-1December 5, 2010Ray Chandler
181802556999569w57·1018023-1December 5, 2010Ray Chandler
Unprovable near-repdigit PRPs
 digitsflabelwlabelexpressionwhenwho
6618580999499w491018580-51December 5, 2010Ray Chandler
7018236111311w31(1018236+179)/9December 5, 2010Ray Chandler
7118211999299w291018211-71December 5, 2010Ray Chandler
7418134333833w83(1018134+149)/3December 5, 2010Ray Chandler
Unprovable near-repdigit-related PRPs (except ru/nr/pd/qr)
 digitsflabelwlabelexpressionwhenwho
42189874220142w01(38·1018986-191)/9December 5, 2010Ray Chandler
43189873005330w533·1018986+53December 5, 2010Ray Chandler
44189855008750w875·1018984+87December 5, 2010Ray Chandler
4518982 35w11(32·1018981-401)/9December 5, 2010Ray Chandler
46189791445114w51(13·1018978+59)/9December 5, 2010Ray Chandler
47189781552715w27(14·1018977-257)/9December 5, 2010Ray Chandler
48189773115331w53(28·1018976+377)/9December 5, 2010Ray Chandler
4918974 886w7(266·1018972+1)/3December 5, 2010Ray Chandler
50189739220392w03(83·1018972-173)/9December 5, 2010Ray Chandler
51189488448984w89(76·1018947+401)/9December 5, 2010Ray Chandler
52189425664156w41(17·1018941-77)/3December 5, 2010Ray Chandler
53189353225132w51(29·1018934+259)/9December 5, 2010Ray Chandler
54189245885758w57(53·1018923-287)/9December 5, 2010Ray Chandler
55189236115361w53(55·1018922+377)/9December 5, 2010Ray Chandler
56188975770957w09(52·1018896-619)/9December 5, 2010Ray Chandler
57188887889778w97(71·1018887+73)/9December 5, 2010Ray Chandler
58188857882778w27(71·1018884-557)/9December 5, 2010Ray Chandler
59188768229382w93(74·1018875+637)/9December 5, 2010Ray Chandler
60188656113761w37(55·1018864+233)/9December 5, 2010Ray Chandler
61188598110781w07(73·1018858-37)/9December 5, 2010Ray Chandler
62188584882148w21(44·1018857-611)/9December 5, 2010Ray Chandler
63188572772127w21(25·1018856-511)/9December 5, 2010Ray Chandler
64188453887938w79(35·1018844-89)/9December 5, 2010Ray Chandler
65188442006920w692·1018843+69December 5, 2010Ray Chandler
66188381881718w17(17·1018837-647)/9December 5, 2010Ray Chandler
6718835 221w3(199·1018833+17)/9December 5, 2010Ray Chandler
68188299334793w47(28·1018828+41)/3December 5, 2010Ray Chandler
6918829 89w119·1018828-89December 5, 2010Ray Chandler
70188251883918w39(17·1018824-449)/9December 5, 2010Ray Chandler
71188181331913w19(4·1018817-43)/3December 5, 2010Ray Chandler
72188104774947w49(43·1018809-259)/9December 5, 2010Ray Chandler
73188099553195w31(86·1018808-221)/9December 5, 2010Ray Chandler
74188084225942w59(38·1018807+331)/9December 5, 2010Ray Chandler
75187913889338w93(35·1018790+37)/9December 5, 2010Ray Chandler
76187865331753w17(16·1018785-49)/3December 5, 2010Ray Chandler
77187852008120w812·1018784+81December 5, 2010Ray Chandler
78187811335113w51(4·1018780+53)/3December 5, 2010Ray Chandler
79187787001370w137·1018777+13December 5, 2010Ray Chandler
80187775226352w63(47·1018776+367)/9December 5, 2010Ray Chandler
81187714552145w21(41·1018770-311)/9December 5, 2010Ray Chandler
8218769 991w7(892·1018767+53)/9December 5, 2010Ray Chandler
8318768 30w773·1018767+77December 5, 2010Ray Chandler
8418762 990w799·1018760+7December 5, 2010Ray Chandler
85187606446964w69(58·1018759+221)/9December 5, 2010Ray Chandler
86187575008150w815·1018756+81December 5, 2010Ray Chandler
87187475770957w09(52·1018746-619)/9December 5, 2010Ray Chandler
88187428225782w57(74·1018741+313)/9December 5, 2010Ray Chandler
8918721 227w3(205·1018719-43)/9December 5, 2010Ray Chandler
9018715 50w775·1018714+77December 5, 2010Ray Chandler
91187127336773w67(22·1018711+101)/3December 5, 2010Ray Chandler
92187013118331w83(28·1018700+647)/9December 5, 2010Ray Chandler
93186871663916w39(5·1018686-83)/3December 5, 2010Ray Chandler
9418685 47w11(43·1018684-601)/9December 5, 2010Ray Chandler
95186813001330w133·1018680+13December 5, 2010Ray Chandler
96186805227352w73(47·1018679+457)/9December 5, 2010Ray Chandler
9718673 661w7(595·1018671+53)/9December 5, 2010Ray Chandler
98186725005750w575·1018671+57December 5, 2010Ray Chandler
99186624336143w61(13·1018661+83)/3December 5, 2010Ray Chandler
100186608775387w53(79·1018659-223)/9December 5, 2010Ray Chandler

December 4, 2010

Markus Tervooren searched prime numbers of the form 99...997 to 407197-digit but no additional PRP was found.

Maksym Voznyy proved 3 quasi-repdigit primes and 2 near-repdigit-related primes by Primo 3.0.9.

Proven quasi-repdigit primes
 digitsflabelwlabelexpressionwhenwho
2192696222012w01(2·102696-191)/9December 4, 2010Maksym Voznyy
23425894994949w495·102588-51December 4, 2010Maksym Voznyy
26723034994949w495·102302-51December 4, 2010Maksym Voznyy
Proven near-repdigit-related primes (except ru/nr/pd/qr)
 digitsflabelwlabelexpressionwhenwho
26222111664916w49(5·102210-53)/3December 4, 2010Maksym Voznyy
27220761220912w09(11·102075-119)/9December 4, 2010Maksym Voznyy

December 1, 2010

Maksym Voznyy proved 8 near-repdigit-related primes by Primo 3.0.9.

Proven near-repdigit-related primes (except ru/nr/pd/qr)
 digitsflabelwlabelexpressionwhenwho
31216146881968w19(62·101613-629)/9December 1, 2010Maksym Voznyy
31316004662146w21(14·101599-137)/3December 1, 2010Maksym Voznyy
31415993663136w31(11·101598-107)/3December 1, 2010Maksym Voznyy
31615973447334w73(31·101596+257)/9December 1, 2010Maksym Voznyy
32415898332783w27(25·101588-19)/3December 1, 2010Maksym Voznyy
32715836882168w21(62·101582-611)/9December 1, 2010Maksym Voznyy
33115715332953w29(16·101570-13)/3December 1, 2010Maksym Voznyy
33215693551335w13(32·101568-383)/9December 1, 2010Maksym Voznyy

November 2010

November 30, 2010

Primality certifications page is available.

Maksym Voznyy proved 1 quasi-repdigit prime and 26 near-repdigit-related primes by Primo 3.0.9.

Proven quasi-repdigit primes
 digitsflabelwlabelexpressionwhenwho
57013027110171w01(64·101301-91)/9November 30, 2010Maksym Voznyy
Proven near-repdigit-related primes (except ru/nr/pd/qr)
 digitsflabelwlabelexpressionwhenwho
33115466227162w71(56·101545+439)/9November 30, 2010Maksym Voznyy
33615267554775w47(68·101525-77)/9November 30, 2010Maksym Voznyy
34414895226352w63(47·101488+367)/9November 30, 2010Maksym Voznyy
34514853110731w07(28·101484-37)/9November 30, 2010Maksym Voznyy
34714792664126w41(8·101478-77)/3November 30, 2010Maksym Voznyy
34814635335153w51(16·101462+53)/3November 30, 2010Maksym Voznyy
3501461 71w99(64·101460+791)/9November 30, 2010Maksym Voznyy
36114238228782w87(74·101422+583)/9November 30, 2010Maksym Voznyy
36514162330923w09(7·101415-73)/3November 30, 2010Maksym Voznyy
37013953551335w13(32·101394-383)/9November 30, 2010Maksym Voznyy
37113873885138w51(35·101386-341)/9November 30, 2010Maksym Voznyy
37713613556135w61(32·101360+49)/9November 30, 2010Maksym Voznyy
38013497880978w09(71·101348-719)/9November 30, 2010Maksym Voznyy
38513361554115w41(14·101335-131)/9November 30, 2010Maksym Voznyy
39313043550135w01(32·101303-491)/9November 30, 2010Maksym Voznyy
39513002665926w59(8·101299-23)/3November 30, 2010Maksym Voznyy
4081242 53w99(16·101241+197)/3November 30, 2010Maksym Voznyy
41312242442124w21(22·101223-211)/9November 30, 2010Maksym Voznyy
41712212664126w41(8·101220-77)/3November 30, 2010Maksym Voznyy
41812209776997w69(88·101219-79)/9November 30, 2010Maksym Voznyy
41912189445394w53(85·101217+77)/9November 30, 2010Maksym Voznyy
42212143550135w01(32·101213-491)/9November 30, 2010Maksym Voznyy
42312103773937w39(34·101209-349)/9November 30, 2010Maksym Voznyy
4241209 26w33(8·101208-101)/3November 30, 2010Maksym Voznyy
42711924336943w69(13·101191+107)/3November 30, 2010Maksym Voznyy
42911902779127w91(25·101189+119)/9November 30, 2010Maksym Voznyy

November 28, 2010

David Broadhurst proved the primality of 2 near-repdigit-related primes by chgcertd.gp. p2367 and p1692, the largest known prime factors of N-1/N+1, were certified by Primo.

Proven near-repdigit-related primes (except ru/nr/pd/qr)
 digitsflabelwlabelexpressionwhenwho
79116307992179w218·1011629-79November 28, 2010David Broadhurst
92100302330923w09(7·1010029-73)/3November 28, 2010David Broadhurst

November 27, 2010

Serge Batalov proved the primality of N=(22·104095-19)/3 by PFGW. An additional prime factor of N+1 is 51844513613. The largest known prime factor of N-1 is a 428-digit number.

Proven near-repdigit-related primes (except ru/nr/pd/qr)
 digitsflabelwlabelexpressionwhenwho
18140967332773w27(22·104095-19)/3November 27, 2010Serge Batalov

Serge Batalov proved the primality of N=(8·105503-77)/3 by KonPom.gp derivative. The largest known prime factor of N-1 is a 735-digit number.

Proven near-repdigit-related primes (except ru/nr/pd/qr)
 digitsflabelwlabelexpressionwhenwho
15955042664126w41(8·105503-77)/3November 27, 2010Serge Batalov

David Broadhurst proved the primality of N=(52·1011550-61)/9 by kppm.gp. The largest known prime factor of N+1 is a 476-digit number.

Proven quasi-repdigit primes
 digitsflabelwlabelexpressionwhenwho
58115515777157w1(52·1011550-61)/9November 27, 2010David Broadhurst

November 26, 2010

Maksym Voznyy proved primality of 2 near-repdigit-related primes by Primo 3.0.9.

Proven near-repdigit-related primes (except ru/nr/pd/qr)
 digitsflabelwlabelexpressionwhenwho
40111863447334w73(31·101185+257)/9November 26, 2010Maksym Voznyy
40411729778997w89(88·101171+101)/9November 26, 2010Maksym Voznyy

November 25, 2010

Maksym Voznyy proved primality of 5 quasi-repdigit primes and 11 near-repdigit-related primes by Primo 3.0.9.

Proven quasi-repdigit primes
 digitsflabelwlabelexpressionwhenwho
3222008555495w49(5·102008-59)/9November 25, 2010Maksym Voznyy
69010797110171w01(64·101078-91)/9November 25, 2010Maksym Voznyy
69710749110191w01(82·101073-91)/9November 25, 2010Maksym Voznyy
709106218777187w(169·101060-7)/9November 25, 2010Maksym Voznyy
71010612332323w23(7·101060-31)/3November 25, 2010Maksym Voznyy
Proven near-repdigit-related primes (except ru/nr/pd/qr)
 digitsflabelwlabelexpressionwhenwho
41011552665726w57(8·101154-29)/3November 25, 2010Maksym Voznyy
41111443113731w37(28·101143+233)/9November 25, 2010Maksym Voznyy
41511263663136w31(11·101125-107)/3November 25, 2010Maksym Voznyy
41611248332983w29(25·101123-13)/3November 25, 2010Maksym Voznyy
43210931779317w93(16·101092+137)/9November 25, 2010Maksym Voznyy
43410817227972w79(65·101080+511)/9November 25, 2010Maksym Voznyy
44210685660956w09(17·101067-173)/3November 25, 2010Maksym Voznyy
44410662112921w29(19·101065+161)/9November 25, 2010Maksym Voznyy
45010561220912w09(11·101055-119)/9November 25, 2010Maksym Voznyy
45610452441924w19(22·101044-229)/9November 25, 2010Maksym Voznyy
4581043 83w11(25·101042-67)/3November 25, 2010Maksym Voznyy

November 24, 2010

Ray Chandler found 2 near-repdigit primes, 4 quasi-repdigit primes, 1 near-repdigit-related prime, 2 near-repdigit PRPs, 63 quasi-repdigit PRPs, 188 near-repdigit-related PRPs by srsieve and PFGW.

Proven near-repdigit primes
 digitsflabelwlabelexpressionwhenwho
6217872 9949w995·1017869-1November 24, 2010Ray Chandler
6417297 9949w995·1017294-1November 24, 2010Ray Chandler
Proven quasi-repdigit primes
 digitsflabelwlabelexpressionwhenwho
171775734999349w35·1017755-1November 24, 2010Ray Chandler
181745452999529w53·1017452-1November 24, 2010Ray Chandler
191716147999479w48·1017159-1November 24, 2010Ray Chandler
201709814999149w15·1017096-1November 24, 2010Ray Chandler
Proven near-repdigit-related primes (except ru/nr/pd/qr)
 digitsflabelwlabelexpressionwhenwho
3917523 550w155·1017521+1November 24, 2010Ray Chandler
Unprovable near-repdigit PRPs
 digitsflabelwlabelexpressionwhenwho
7417834999299w291017834-71November 24, 2010Ray Chandler
7517719777177w17(7·1017719-547)/9November 24, 2010Ray Chandler

Maksym Voznyy proved primality of 2 near-repdigit-related primes by Primo 3.0.9.

Proven near-repdigit-related primes (except ru/nr/pd/qr)
 digitsflabelwlabelexpressionwhenwho
45110118668186w81(26·101010+43)/3November 24, 2010Maksym Voznyy
45410029445394w53(85·101001+77)/9November 24, 2010Maksym Voznyy

Darren Bedwell found the largest known near-repdigit palindrome prime by OpenPFGW.

Proven near-repdigit-related primes (except ru/nr/pd/qr)
 digitsflabelwlabelexpressionwhenwho
1134809998999w89w10134809-1067404-1November 24, 2010Darren Bedwell

November 23, 2010

Factorizations of 811...119 have been extended up to n=250. Composite numbers that appeared newly got through ECM 118 times at level 35. Most unknown factors are supposed to be greater than 1030.

November 19, 2010

David Broadhurst found the largest known near-repdigit prime number. Congratulations!

Proven near-repdigit primes
 digitsflabelwlabelexpressionwhenwho
13198905999959w6·10319889-1November 19, 2010David Broadhurst
22931355999959w6·10293134-1November 19, 2010David Broadhurst
32706595999959w6·10270658-1November 19, 2010David Broadhurst

November 17, 2010

Factorizations of 900...001 have been extended up to n=250. Composite numbers that appeared newly got through ECM 118 times at level 35. Most unknown factors are supposed to be greater than 1030.

Ray Chandler found a plateau and depression PRP by srsieve and PFGW.

Unprovable plateau and depression PRPs
 digitsflabelwlabelexpressionwhenwho
4744357555775w7(68·1074434+13)/9November 17, 2010Ray Chandler

November 15, 2010

David Broadhurst found the largest known near-repdigit prime. Congratulations!

Proven near-repdigit primes
 digitsflabelwlabelexpressionwhenwho
12675995999959w6·10267598-1November 15, 2010David Broadhurst

Ray Chandler found 6 near-repdigit primes, 4 quasi-repdigit primes, 1 near-repdigit-related prime, 6 near-repdigit PRPs, 82 quasi-repdigit PRPs and 208 near-repdigit-related PRPs. See also primesize.txt.

Proven near-repdigit primes
 digitsflabelwlabelexpressionwhenwho
6017005 9999959w999996·1016999-1November 15, 2010Ray Chandler
6116914 999979w99998·1016909-1November 15, 2010Ray Chandler
6216478 999979w99998·1016473-1November 15, 2010Ray Chandler
6316427 999999959w99999996·1016419-1November 15, 2010Ray Chandler
6416391 99999949w9999995·1016384-1November 15, 2010Ray Chandler
6616109 999999989w99999999·1016101-1November 15, 2010Ray Chandler
Proven quasi-repdigit primes
 digitsflabelwlabelexpressionwhenwho
171697610999109w11·1016974-1November 15, 2010Ray Chandler
181683014999149w15·1016828-1November 15, 2010Ray Chandler
191671585999859w86·1016713-1November 15, 2010Ray Chandler
201608220999209w21·1016080-1November 15, 2010Ray Chandler
Proven near-repdigit-related primes (except ru/nr/pd/qr)
 digitsflabelwlabelexpressionwhenwho
4716538 330w133·1016536+1November 15, 2010Ray Chandler

November 14, 2010

Factorizations of 700...001 have been extended up to n=250. Composite numbers that appeared newly got through ECM 118 times at level 35. Most unknown factors are supposed to be greater than 1030.

Max Dettweiler reported a near-repdigit prime number at Prime posting thread, part 2. (With a catch.) - Page 2 - mersenneforum.org.

Proven near-repdigit primes
 digitsflabelwlabelexpressionwhenwho
2281906 99959w9996·1081902-1November 14, 2010Max Dettweiler

November 12, 2010

Factorizations of 233...33 have been extended up to n=250. Composite numbers that appeared newly got through ECM 118 times at level 35. Most unknown factors are supposed to be greater than 1030.

Ray Chandler found a unprovable plateau and depression PRP by srsieve and PFGW.

Unprovable plateau and depression PRPs
 digitsflabelwlabelexpressionwhenwho
4727737444774w7(67·1072772+23)/9November 12, 2010Ray Chandler

November 9, 2010

Factorizations of 877...779 have been extended up to n=200. Composite numbers that appeared newly got through ECM 118 times at level 35. Most unknown factors are supposed to be greater than 1030.

David Broadhurst found the third largest known near-repdigit prime.

Proven near-repdigit primes
 digitsflabelwlabelexpressionwhenwho
32238728999989w9·10223871-1November 9, 2010David Broadhurst

November 8, 2010

Ray Chandler found 3 near-repdigit primes and 6 quasi-repdigit primes by srsieve and PFGW.

Proven near-repdigit primes
 digitsflabelwlabelexpressionwhenwho
5815987 99999949w9999995·1015980-1November 8, 2010Ray Chandler
5915872 99959w9996·1015868-1November 8, 2010Ray Chandler
6215705 999929w99993·1015700-1November 8, 2010Ray Chandler
Proven quasi-repdigit primes
 digitsflabelwlabelexpressionwhenwho
171585116999169w17·1015849-1November 8, 2010Ray Chandler
181584225999259w26·1015840-1November 8, 2010Ray Chandler
191541134999349w35·1015409-1November 8, 2010Ray Chandler
201519626999269w27·1015194-1November 8, 2010Ray Chandler
211518380999809w81·1015181-1November 8, 2010Ray Chandler
221509020999209w21·1015088-1November 8, 2010Ray Chandler

Ray Chandler found 8 near-repdigit PRPs, 75 quasi-repdigit PRPs and 207 near-repdigit-related PRPs (except ru/nr/pd/qr) by srsieve and PFGW. See primesize.txt.

November 7, 2010

Factorizations of 877...773 have been extended up to n=200. Composite numbers that appeared newly got through ECM 118 times at level 35. Most unknown factors are supposed to be greater than 1030.

November 6, 2010

Factorizations of 877...771 have been extended up to n=200. Composite numbers that appeared newly got through ECM 118 times at level 35. Most unknown factors are supposed to be greater than 1030.

David Broadhurst found the largest known near-repdigit prime. Congratulations!

Proven near-repdigit primes
 digitsflabelwlabelexpressionwhenwho
12602548999989w9·10260253-1November 6, 2010David Broadhurst
22368927999979w8·10236891-1November 6, 2010David Broadhurst

November 4, 2010

David Broadhurst found the largest known near-repdigit prime. Congratulations!

Proven near-repdigit primes
 digitsflabelwlabelexpressionwhenwho
12129048999989w9·10212903-1November 4, 2010David Broadhurst
22110304999949w5·10211029-1November 4, 2010David Broadhurst

November 3, 2010

Factorizations of 866...669 have been extended up to n=200. Composite numbers that appeared newly got through ECM 118 times at level 35. Most unknown factors are supposed to be greater than 1030.

November 2, 2010

Factorizations of 855...559 have been extended up to n=200. Composite numbers that appeared newly got through ECM 118 times at level 35. Most unknown factors are supposed to be greater than 1030.

November 1, 2010

Ray Chandler found 8 near-repdigit primes, 8 quasi-repdigit primes and 1 near-repdigit-related prime (except ru/nr/pd/qr) by srsieve and PFGW.

Proven near-repdigit primes
 digitsflabelwlabelexpressionwhenwho
5614958 99989w9999·1014954-1November 1, 2010Ray Chandler
5714918 9999989w999999·1014912-1November 1, 2010Ray Chandler
5814788 9949w995·1014785-1November 1, 2010Ray Chandler
5914715 9999929w999993·1014709-1November 1, 2010Ray Chandler
6014703 9999989w999999·1014697-1November 1, 2010Ray Chandler
6114682 99999959w9999996·1014675-1November 1, 2010Ray Chandler
6214356 999919w99992·1014351-1November 1, 2010Ray Chandler
6314095 9979w998·1014092-1November 1, 2010Ray Chandler
Proven quasi-repdigit primes
 digitsflabelwlabelexpressionwhenwho
171491682999829w83·1014914-1November 1, 2010Ray Chandler
181481765999659w66·1014815-1November 1, 2010Ray Chandler
191476732999329w33·1014765-1November 1, 2010Ray Chandler
201475338999389w39·1014751-1November 1, 2010Ray Chandler
2114719 119w12·1014717-1November 1, 2010Ray Chandler
221436834999349w35·1014366-1November 1, 2010Ray Chandler
231433483999839w84·1014332-1November 1, 2010Ray Chandler
241433317999179w18·1014331-1November 1, 2010Ray Chandler
Proven near-repdigit-related primes (except ru/nr/pd/qr)
 digitsflabelwlabelexpressionwhenwho
5314871 330w133·1014869+1November 1, 2010Ray Chandler

Ray Chandler found 10 near-repdigit PRPs, 83 quasi-repdigit PRPs and 232 near-repdigit-related PRPs (except ru/nr/pd/qr) by srsieve and PFGW. See primesize.txt.

October 2010

October 31, 2010

Ray Chandler proved 8 near-repdigit-related (except ru/nr/pd/qr) primes by PFGW.

Proven near-repdigit-related primes (except ru/nr/pd/qr)
 digitsflabelwlabelexpressionwhenwho
11278553110931w09(28·107854-19)/9October 31, 2010Ray Chandler
11774246770967w09(61·107423-619)/9October 31, 2010Ray Chandler
13562241553915w39(14·106223-149)/9October 31, 2010Ray Chandler
15652851886918w69(17·105284-179)/9October 31, 2010Ray Chandler
16447223884938w49(35·104721-359)/9October 31, 2010Ray Chandler
17542129008990w899·104211+89October 31, 2010Ray Chandler
18836198665986w59(26·103618-23)/3October 31, 2010Ray Chandler
18936083002930w293·103607+29October 31, 2010Ray Chandler

October 30, 2010

Factorizations of 855...557 have been extended up to n=200. Composite numbers that appeared newly got through ECM 118 times at level 35. Most unknown factors are supposed to be greater than 1030.

Ray Chandler found 1 plateau-and-depression PRP by srsieve and PFGW.

Unprovable plateau and depression PRPs
 digitsflabelwlabelexpressionwhenwho
4685057555775w7(68·1068504+13)/9October 30, 2010Ray Chandler

October 28, 2010

Factorizations of 855...553 have been extended up to n=200. Composite numbers that appeared newly got through ECM 118 times at level 35. Most unknown factors are supposed to be greater than 1030.

Ray Chandler found 6 near-repdigit primes and 8 quasi-repdigit primes by srsieve and PFGW.

Proven near-repdigit primes
 digitsflabelwlabelexpressionwhenwho
5613782 9999979w999998·1013776-1October 28, 2010Ray Chandler
5713570 9999919w999992·1013564-1October 28, 2010Ray Chandler
5813478 99999929w9999993·1013471-1October 28, 2010Ray Chandler
591340992999929w93·1013407-1October 28, 2010Ray Chandler
6013400 9949w995·1013397-1October 28, 2010Ray Chandler
6113360 9999919w999992·1013354-1October 28, 2010Ray Chandler
Proven quasi-repdigit primes
 digitsflabelwlabelexpressionwhenwho
171378952999529w53·1013787-1October 28, 2010Ray Chandler
181372141999419w42·1013719-1October 28, 2010Ray Chandler
191359834999349w35·1013596-1October 28, 2010Ray Chandler
201356352999529w53·1013561-1October 28, 2010Ray Chandler
221336450999509w51·1013362-1October 28, 2010Ray Chandler
231322713999139w14·1013225-1October 28, 2010Ray Chandler
241312874999749w75·1013126-1October 28, 2010Ray Chandler
251304783999839w84·1013045-1October 28, 2010Ray Chandler

Ray Chandler found 13 near-repdigit PRPs, 77 quasi-repdigit PRPs and 242 near-repdigit-related PRPs (except ru/nr/pd/qr) by srsieve and PFGW. See primesize.txt for PRPs.

Ray Chandler proved 3 near-repdigit primes and 10 near-repdigit-related (except ru/nr/pd/qr) primes by PFGW.

Proven quasi-repdigit primes
 digitsflabelwlabelexpressionwhenwho
1214681111091w09(104681-19)/9October 28, 2010Ray Chandler
1314082666016w01(2·104082-197)/3October 28, 2010Ray Chandler
1403781777697w69(7·103781-79)/9October 28, 2010Ray Chandler
Proven near-repdigit-related primes (except ru/nr/pd/qr)
 digitsflabelwlabelexpressionwhenwho
11970221887118w71(17·107021-161)/9October 28, 2010Ray Chandler
13759419554795w47(86·105940-77)/9October 28, 2010Ray Chandler
15352339554795w47(86·105232-77)/9October 28, 2010Ray Chandler
16842421998119w812·104241-19October 28, 2010Ray Chandler
16942142664126w41(8·104213-77)/3October 28, 2010Ray Chandler
17538899776997w69(88·103888-79)/9October 28, 2010Ray Chandler
18036735110751w07(46·103672-37)/9October 28, 2010Ray Chandler
18535304883948w39(44·103529-449)/9October 28, 2010Ray Chandler
18834514221942w19(38·103450-29)/9October 28, 2010Ray Chandler
18934381220912w09(11·103437-119)/9October 28, 2010Ray Chandler

October 27, 2010

Ray Chandler proved 3 quasi-repdigit primes and 27 near-repdigit-related prime numbers (except ru/nr/pd/qr) by PFGW.

Proven quasi-repdigit primes
 digitsflabelwlabelexpressionwhenwho
1702929222192w19(2·102929-29)/9October 27, 2010Ray Chandler
24521984994949w495·102197-51October 27, 2010Ray Chandler
2572156666016w01(2·102156-197)/3October 27, 2010Ray Chandler
Proven near-repdigit-related primes (except ru/nr/pd/qr)
 digitsflabelwlabelexpressionwhenwho
18732676221762w17(56·103266-47)/9October 27, 2010Ray Chandler
18832305660956w09(17·103229-173)/3October 27, 2010Ray Chandler
19431224995149w515·103121-49October 27, 2010Ray Chandler
19531102663926w39(8·103109-83)/3October 27, 2010Ray Chandler
19630323884938w49(35·103031-359)/9October 27, 2010Ray Chandler
2042732 23w11(7·102731-67)/3October 27, 2010Ray Chandler
20825849554795w47(86·102583-77)/9October 27, 2010Ray Chandler
21125671443114w31(13·102566-121)/9October 27, 2010Ray Chandler
21924425660956w09(17·102441-173)/3October 27, 2010Ray Chandler
22523599776997w69(88·102358-79)/9October 27, 2010Ray Chandler
22623516882168w21(62·102350-611)/9October 27, 2010Ray Chandler
23621558665986w59(26·102154-23)/3October 27, 2010Ray Chandler
23821504995149w515·102149-49October 27, 2010Ray Chandler
24021356882168w21(62·102134-611)/9October 27, 2010Ray Chandler
2412135 45w11(41·102134-401)/9October 27, 2010Ray Chandler
24221261553915w39(14·102125-149)/9October 27, 2010Ray Chandler
25619521664916w49(5·101951-53)/3October 27, 2010Ray Chandler
25719458665986w59(26·101944-23)/3October 27, 2010Ray Chandler
25819382664126w41(8·101937-77)/3October 27, 2010Ray Chandler
25919132885928w59(26·101912-269)/9October 27, 2010Ray Chandler
26518506882168w21(62·101849-611)/9October 27, 2010Ray Chandler
26818025771957w19(52·101801-529)/9October 27, 2010Ray Chandler
27017874773147w31(43·101786-421)/9October 27, 2010Ray Chandler
2721782 34w11(31·101781-301)/9October 27, 2010Ray Chandler
27617626443764w37(58·101761-67)/9October 27, 2010Ray Chandler
28016824772947w29(43·101681-439)/9October 27, 2010Ray Chandler
28116705771957w19(52·101669-529)/9October 27, 2010Ray Chandler

October 26, 2010

Factorizations of 855...551 have been extended up to n=200. Composite numbers that appeared newly got through ECM 118 times at level 35. Most unknown factors are supposed to be greater than 1030.

Ray Chandler proved 3 quasi-repdigit primes and 28 near-repdigit-related prime numbers (except ru/nr/pd/qr) by PFGW.

Proven quasi-repdigit primes
 digitsflabelwlabelexpressionwhenwho
42614999332393w23(28·101498-31)/3October 26, 2010Ray Chandler
42714979776797w67(88·101496-97)/9October 26, 2010Ray Chandler
49713669776797w67(88·101365-97)/9October 26, 2010Ray Chandler
Proven near-repdigit-related primes (except ru/nr/pd/qr)
 digitsflabelwlabelexpressionwhenwho
28216639110391w03(82·101662-73)/9October 26, 2010Ray Chandler
28416491443114w31(13·101648-121)/9October 26, 2010Ray Chandler
28515978665786w57(26·101596-29)/3October 26, 2010Ray Chandler
29315866770967w09(61·101585-619)/9October 26, 2010Ray Chandler
29415862886128w61(26·101585-251)/9October 26, 2010Ray Chandler
30015621665116w51(5·101561-47)/3October 26, 2010Ray Chandler
30315505882958w29(53·101549-539)/9October 26, 2010Ray Chandler
31215077332773w27(22·101506-19)/3October 26, 2010Ray Chandler
32114522330923w09(7·101451-73)/3October 26, 2010Ray Chandler
3311400 12w11(11·101399-101)/9October 26, 2010Ray Chandler
33813618665786w57(26·101360-29)/3October 26, 2010Ray Chandler
33913517110371w03(64·101350-73)/9October 26, 2010Ray Chandler
34713316882168w21(62·101330-611)/9October 26, 2010Ray Chandler
34813215110751w07(46·101320-37)/9October 26, 2010Ray Chandler
35712776443964w39(58·101276-49)/9October 26, 2010Ray Chandler
36012669554795w47(86·101265-77)/9October 26, 2010Ray Chandler
36312621886918w69(17·101261-179)/9October 26, 2010Ray Chandler
36612317332773w27(22·101230-19)/3October 26, 2010Ray Chandler
37112216221762w17(56·101220-47)/9October 26, 2010Ray Chandler
37611904661946w19(14·101189-143)/3October 26, 2010Ray Chandler
39111203110931w09(28·101119-19)/9October 26, 2010Ray Chandler
40210936221762w17(56·101092-47)/9October 26, 2010Ray Chandler
40810702553125w31(23·101069-221)/9October 26, 2010Ray Chandler
41410583440934w09(31·101057-319)/9October 26, 2010Ray Chandler
41810523663136w31(11·101051-107)/3October 26, 2010Ray Chandler
42410323110731w07(28·101031-37)/9October 26, 2010Ray Chandler
42510283662936w29(11·101027-113)/3October 26, 2010Ray Chandler
43010066882168w21(62·101005-611)/9October 26, 2010Ray Chandler

October 25, 2010

Factorizations of 844...449 have been extended up to n=200. Composite numbers that appeared newly got through ECM 118 times at level 35. Most unknown factors are supposed to be greater than 1030.

Ray Chandler found 5 near-repdigit primes, 6 quasi-repdigit primes, 3 near-repdigit-related primes (except ru/nr/pd/qr), 9 near-repdigit PRPs, 86 quasi-repdigit PRPs and 249 near-repdigit-related PRPs (except ru/nr/pd/qr). See primesize.txt for PRPs.

Proven near-repdigit primes
 digitsflabelwlabelexpressionwhenwho
5612929 99989w9999·1012925-1October 25, 2010Ray Chandler
5712892 999999989w99999999·1012884-1October 25, 2010Ray Chandler
5912383 9929w993·1012380-1October 25, 2010Ray Chandler
6112067 999999949w99999995·1012059-1October 25, 2010Ray Chandler
6212067 99929w9993·1012063-1October 25, 2010Ray Chandler
Proven quasi-repdigit primes
 digitsflabelwlabelexpressionwhenwho
181279647999479w48·1012794-1October 25, 2010Ray Chandler
191257217999179w18·1012570-1October 25, 2010Ray Chandler
201250820999209w21·1012506-1October 25, 2010Ray Chandler
211249074999749w75·1012488-1October 25, 2010Ray Chandler
221236383999839w84·1012361-1October 25, 2010Ray Chandler
231201856999569w57·1012016-1October 25, 2010Ray Chandler
Proven near-repdigit-related primes (except ru/nr/pd/qr)
 digitsflabelwlabelexpressionwhenwho
6712592 220w122·1012590+1October 25, 2010Ray Chandler
6812518 330w133·1012516+1October 25, 2010Ray Chandler
7012111 660w166·1012109+1October 25, 2010Ray Chandler

October 23, 2010

Factorizations of 988...887 have been extended up to n=200. Composite numbers that appeared newly got through ECM 118 times at level 35. Most unknown factors are supposed to be greater than 1030.

Ray Chandler found 9 near-repdigit primes, 8 quasi-repdigit primes, 6 near-repdigit PRPs, 93 quasi-repdigit PRPs and 268 near-repdigit-related PRPs (except ru/nr/pd/qr). See primesize.txt for details.

Proven near-repdigit primes
 digitsflabelwlabelexpressionwhenwho
5811870 99989w9999·1011866-1October 23, 2010Ray Chandler
5911345 9999919w999992·1011339-1October 23, 2010Ray Chandler
6111304 999999979w99999998·1011296-1October 23, 2010Ray Chandler
6211274 999999949w99999995·1011266-1October 23, 2010Ray Chandler
6311271 999929w99993·1011266-1October 23, 2010Ray Chandler
6411234 9999929w999993·1011228-1October 23, 2010Ray Chandler
6511211 99929w9993·1011207-1October 23, 2010Ray Chandler
6611181 99999989w9999999·1011174-1October 23, 2010Ray Chandler
681111297999979w98·1011110-1October 23, 2010Ray Chandler
Proven quasi-repdigit primes
 digitsflabelwlabelexpressionwhenwho
181199850999509w51·1011996-1October 23, 2010Ray Chandler
191199214999149w15·1011990-1October 23, 2010Ray Chandler
2011961 449w45·1011959-1October 23, 2010Ray Chandler
211188361999619w62·1011881-1October 23, 2010Ray Chandler
221134661999619w62·1011344-1October 23, 2010Ray Chandler
231130286999869w87·1011300-1October 23, 2010Ray Chandler
241114535999359w36·1011143-1October 23, 2010Ray Chandler
251105826999269w27·1011056-1October 23, 2010Ray Chandler

October 22, 2010

5 quasi-repdigit prime numbers have been certified by N-1/N+1 test.

Proven quasi-repdigit primes
 digitsflabelwlabelexpressionwhenwho
1552941333293w29(102941-13)/3October 22, 2010Makoto Kamada
2742004333013w01(102004-97)/3October 22, 2010Makoto Kamada
2931902777017w01(7·101902-691)/9October 22, 2010Makoto Kamada
3051874555015w01(5·101874-491)/9October 22, 2010Makoto Kamada
3231796333013w01(101796-97)/3October 22, 2010Makoto Kamada

October 21, 2010

Factorizations of 988...883 have been extended up to n=200. Composite numbers that appeared newly got through ECM 118 times at level 35. Most unknown factors are supposed to be greater than 1030.

The ratio of factored part of repunit-related PRPs is available on primesize.txt. Execute `grep "%" primesize.txt`.

The algebraic factorization type of PRPs is also available on primesize.txt. Execute `grep ":" primesize.txt`.

October 20, 2010

Erik Branger proved primality of near-repdigit number (2·103649-17)/3 by N-1 test.

Proven near-repdigit primes
 digitsflabelwlabelexpressionwhenwho
1623649666616w1(2·103649-17)/3October 20, 2010Erik Branger

October 19, 2010

Factorizations of 988...881 have been extended up to n=200. Composite numbers that appeared newly got through ECM 118 times at level 35. Most unknown factors are supposed to be greater than 1030.

Ray Chandler's research found some inconsistencies between Henri & Renaud Lifchitz's PRP Top records, Plateau and Depression Primes and primesize.txt. The following records were corrected.

Unprovable near-repdigit PRPs
 digitsflabelwlabelexpressionwhenwho
8214602888818w1(8·1014602-71)/9May 2002Daniel Heuer
9912130333313w1(1012130-7)/3May 2002Daniel Heuer
10111960333313w1(1011960-7)/3May 2002Daniel Heuer
10511245333313w1(1011245-7)/3May 2002Daniel Heuer
9412456666676w7(2·1012456+1)/3May 2002Daniel Heuer
Unprovable plateau and depression PRPs
 digitsflabelwlabelexpressionwhenwho
19377859222992w9(83·1037784+61)/9June 26, 2005Patrick De Geest

October 17, 2010

Factorizations of 977...773 have been extended up to n=200. Composite numbers that appeared newly got through ECM 118 times at level 35. Most unknown factors are supposed to be greater than 1030.

Serge Batalov proved primality of near-repdigit number (5·102774-23)/9 by N-1 test. (5·102774-23)/9-1 = 32·(25·10923-1)/3·(625·101846+25·10923+1)/3. (25·10923-1)/3 = 4409·84653·43201253·2957799751·79596993237627302347·119042686224571112175325031·P853.

Proven near-repdigit primes
 digitsflabelwlabelexpressionwhenwho
1912774555535w3(5·102774-23)/9October 17, 2010Serge Batalov

October 16, 2010

Markus Tervooren found the largest known unprovable near-repdigit PRP by using sr2sieve, mprime and PFGW. Congratulations!

Unprovable near-repdigit PRPs
 digitsflabelwlabelexpressionwhenwho
1232599999979w710232599-3October 16, 2010Markus Tervooren
# pfgw -f0 -tc -u0 -q"10^232599-3"
PFGW Version 3.3.6.20100907.x86_Stable [GWNUM 25.14]

No factoring at all, not even trivial division
Primality testing 10^232599-3 [N-1/N+1, Brillhart-Lehmer-Selfridge]
Running N-1 test using base 2                                                  
Running N+1 test using discriminant 5, base 4+sqrt(5)
Calling N-1 BLS with factored part 0.01% and helper 0.00% (0.02% proof)
10^232599-3 is Fermat and Lucas PRP! (4500.3722s+0.0064s)

October 15, 2010

Ray Chandler found 9 near-repdigit primes by using srsieve and PFGW.

Proven near-repdigit primes
 digitsflabelwlabelexpressionwhenwho
5210817 999999929w99999993·1010809-1October 15, 2010Ray Chandler
5310720 9999919w999992·1010714-1October 15, 2010Ray Chandler
5410649 9999929w999993·1010643-1October 15, 2010Ray Chandler
5510531 99989w9999·1010527-1October 15, 2010Ray Chandler
5610453 9919w992·1010450-1October 15, 2010Ray Chandler
5710412 999999929w99999993·1010404-1October 15, 2010Ray Chandler
5810206 999999949w99999995·1010198-1October 15, 2010Ray Chandler
5910168 99949w9995·1010164-1October 15, 2010Ray Chandler
6010106 999919w99992·1010101-1October 15, 2010Ray Chandler

Ray Chandler found 6 quasi-repdigit primes by using srsieve and PFGW.

Proven quasi-repdigit primes
 digitsflabelwlabelexpressionwhenwho
181099086999869w87·1010988-1October 15, 2010Ray Chandler
191085934999349w35·1010857-1October 15, 2010Ray Chandler
201076240999409w41·1010760-1October 15, 2010Ray Chandler
221034671999719w72·1010344-1October 15, 2010Ray Chandler
231019570999709w71·1010193-1October 15, 2010Ray Chandler
241002610999109w11·1010024-1October 15, 2010Ray Chandler

Ray Chandler found 9 near-repdigit PRPs by using srsieve and PFGW.

Unprovable near-repdigit PRPs
 digitsflabelwlabelexpressionwhenwho
10810941777277w27(7·1010941-457)/9October 15, 2010Ray Chandler
See primesize.txt
12210214333433w43(1010214+29)/3October 15, 2010Ray Chandler

Ray Chandler found 101 quasi-repdigit PRPs by using srsieve and PFGW.

Unprovable quasi-repdigit PRPs
 digitsflabelwlabelexpressionwhenwho
425109948779787w97(79·1010993+173)/9October 15, 2010Ray Chandler
See primesize.txt
5561002960667606w7(182·1010027+1)/3October 15, 2010Ray Chandler

Ray Chandler found 309 near-repdigit-related PRPs (except ru/nr/pd/qr) by using srsieve and PFGW.

Unprovable near-repdigit-related PRPs (except ru/nr/pd/qr)
 digitsflabelwlabelexpressionwhenwho
8411001 32w11(29·1011000-101)/9October 15, 2010Ray Chandler
See primesize.txt
398100103119331w93(28·1010009+737)/9October 15, 2010Ray Chandler

Ray Chandler noticed that Patrick De Geest reported 2 quasi-repdigit PRPs at Henri & Renaud Lifchitz's PRP Top on December 2004.

Unprovable quasi-repdigit PRPs
 digitsflabelwlabelexpressionwhenwho
405116538998989w899·1011652-11December 2004Patrick De Geest
519104508998989w899·1010449-11December 2004Patrick De Geest

Serge Batalov proved primality of 12891-digit near-repdigit number (1012891+11)/3 by using Primo 3.0.9.1 and PFGW.

Proven near-repdigit primes
 digitsflabelwlabelexpressionwhenwho
4912891333373w7(1012891+11)/3October 15, 2010Serge Batalov

Serge Batalov proved primality of 2915-digit quasi-repdigit number 9·102914+7 by using Primo 3.0.9.

Proven quasi-repdigit primes
 digitsflabelwlabelexpressionwhenwho
15529159000790w79·102914+7October 15, 2010Serge Batalov

October 14, 2010

Factorizations of 977...771 have been extended up to n=200. Composite numbers that appeared newly got through ECM 118 times at level 35. Most unknown factors are supposed to be greater than 1030.

Serge Batalov found 3 quasi-repdigit PRPs.

Unprovable quasi-repdigit PRPs
 digitsflabelwlabelexpressionwhenwho
56432138777387w3(79·1043212-43)/9October 14, 2010Serge Batalov
62401588666986w9(26·1040157+7)/3October 14, 2010Serge Batalov
63399928666986w9(26·1039991+7)/3October 14, 2010Serge Batalov

Ray Chandler found 7 near-repdigit primes by using srsieve and PFGW.

Proven near-repdigit primes
 digitsflabelwlabelexpressionwhenwho
619646 999999959w99999996·109638-1October 14, 2010Ray Chandler
63962395999959w96·109621-1October 14, 2010Ray Chandler
649603 9959w996·109600-1October 14, 2010Ray Chandler
65948095999959w96·109478-1October 14, 2010Ray Chandler
679163 99919w9992·109159-1October 14, 2010Ray Chandler
689136 9949w995·109133-1October 14, 2010Ray Chandler
699045 9929w993·109042-1October 14, 2010Ray Chandler

Ray Chandler found 8 quasi-repdigit primes by using srsieve and PFGW.

Proven quasi-repdigit primes
 digitsflabelwlabelexpressionwhenwho
25977182999829w83·109769-1October 14, 2010Ray Chandler
27953823999239w24·109536-1October 14, 2010Ray Chandler
28951065999659w66·109508-1October 14, 2010Ray Chandler
29935031999319w32·109348-1October 14, 2010Ray Chandler
30925116999169w17·109249-1October 14, 2010Ray Chandler
31918768999689w69·109185-1October 14, 2010Ray Chandler
32914482999829w83·109142-1October 14, 2010Ray Chandler
33902161999619w62·109019-1October 14, 2010Ray Chandler

Ray Chandler found 1 near-repdigit-related prime (except ru/nr/pd/qr) by using srsieve and PFGW.

Proven near-repdigit-related primes (except ru/nr/pd/qr)
 digitsflabelwlabelexpressionwhenwho
929135 330w133·109133+1October 14, 2010Ray Chandler

Ray Chandler found 5 near-repdigit PRPs by using srsieve and PFGW.

Unprovable near-repdigit PRPs
 digitsflabelwlabelexpressionwhenwho
123995517111171w(154·109953-1)/9October 14, 2010Ray Chandler
See primesize.txt
136916531333313w(94·109163-1)/3October 14, 2010Ray Chandler

Ray Chandler found 121 quasi-repdigit PRPs by using srsieve and PFGW.

Unprovable quasi-repdigit PRPs
 digitsflabelwlabelexpressionwhenwho
559999774111741w(667·109995-1)/9October 14, 2010Ray Chandler
See primesize.txt
713901680883808w3(728·109014-53)/9October 14, 2010Ray Chandler

Ray Chandler found 361 near-repdigit-related PRPs (except ru/nr/pd/qr) by using srsieve and PFGW.

Unprovable near-repdigit-related PRPs (except ru/nr/pd/qr)
 digitsflabelwlabelexpressionwhenwho
39999986993169w317·109997-69October 14, 2010Ray Chandler
See primesize.txt
76490048221982w19(74·109003-29)/9October 14, 2010Ray Chandler

October 13, 2010

Serge Batalov found 2 near-repdigit PRPs.

Unprovable near-repdigit PRPs
 digitsflabelwlabelexpressionwhenwho
17410342777727w(25·1041033-7)/9October 13, 2010Serge Batalov
23379233111131w(28·1037922-1)/9October 13, 2010Serge Batalov

October 12, 2010

Serge Batalov found 2 quasi-repdigit PRPs.

Unprovable quasi-repdigit PRPs
 digitsflabelwlabelexpressionwhenwho
40575073999739w74·1057506-3October 12, 2010Serge Batalov
80348899888798w7(89·1034888-17)/9October 12, 2010Serge Batalov

October 9, 2010

Factorizations of 966...667 have been extended up to n=200. Composite numbers that appeared newly got through ECM 118 times at level 35. Most unknown factors are supposed to be greater than 1030.

Ray Chandler found 10 near-repdigit primes and 6 quasi-repdigit primes by using srsieve and PFGW.

Proven near-repdigit primes
 digitsflabelwlabelexpressionwhenwho
548968 9979w998·108965-1October 9, 2010Ray Chandler
55886695999959w96·108864-1October 9, 2010Ray Chandler
568845 9999929w999993·108839-1October 9, 2010Ray Chandler
578823 9999989w999999·108817-1October 9, 2010Ray Chandler
598670 99959w9996·108666-1October 9, 2010Ray Chandler
60863792999929w93·108635-1October 9, 2010Ray Chandler
618619 9929w993·108616-1October 9, 2010Ray Chandler
62852698999989w99·108524-1October 9, 2010Ray Chandler
648366 99999979w9999998·108359-1October 9, 2010Ray Chandler
658264 999919w99992·108259-1October 9, 2010Ray Chandler
Proven quasi-repdigit primes
 digitsflabelwlabelexpressionwhenwho
21898846999469w47·108986-1October 9, 2010Ray Chandler
23878647999479w48·108784-1October 9, 2010Ray Chandler
24834247999479w48·108340-1October 9, 2010Ray Chandler
25833143999439w44·108329-1October 9, 2010Ray Chandler
26830113999139w14·108299-1October 9, 2010Ray Chandler
27806483999839w84·108062-1October 9, 2010Ray Chandler

Ray Chandler found 14 near-repdigit PRPs, 118 quasi-repdigit PRPs and 355 near-repdigit-related PRPs (except ru/nr/pd/qr) by using srsieve and PFGW.

Unprovable near-repdigit PRPs
 digitsflabelwlabelexpressionwhenwho
1228984777677w67(7·108984-97)/9October 9, 2010Ray Chandler
123893317111171w(154·108931-1)/9October 9, 2010Ray Chandler
See primesize.txt
1438105333233w23(108105-31)/3October 9, 2010Ray Chandler
1448088777977w97(7·108088+173)/9October 9, 2010Ray Chandler
Unprovable quasi-repdigit PRPs
 digitsflabelwlabelexpressionwhenwho
48689944776747w67(43·108993-97)/9October 9, 2010Ray Chandler
48789869776797w67(88·108985-97)/9October 9, 2010Ray Chandler
See primesize.txt
632800628223282w3(254·108004+7)/9October 9, 2010Ray Chandler
633800559553595w3(536·108003-23)/9October 9, 2010Ray Chandler
Unprovable near-repdigit-related PRPs (except ru/nr/pd/qr)
 digitsflabelwlabelexpressionwhenwho
9589983662336w23(11·108997-131)/3October 9, 2010Ray Chandler
9789957116371w63(64·108994+467)/9October 9, 2010Ray Chandler
See primesize.txt
45280025774157w41(52·108001-331)/9October 9, 2010Ray Chandler
4538002 26w77(8·108001+31)/3October 9, 2010Ray Chandler

October 6, 2010

Factorizations of 966...661 have been extended up to n=200. Composite numbers that appeared newly got through ECM 118 times at level 35. Most unknown factors are supposed to be greater than 1030.

Ray Chandler found 9 near-repdigit primes by using srsieve and PFGW.

Proven near-repdigit primes
 digitsflabelwlabelexpressionwhenwho
57795192999929w93·107949-1October 6, 2010Ray Chandler
58789095999959w96·107888-1October 6, 2010Ray Chandler
See primesize.txt

Ray Chandler found 10 quasi-repdigit primes by using srsieve and PFGW.

Proven quasi-repdigit primes
 digitsflabelwlabelexpressionwhenwho
22780538999389w39·107803-1October 6, 2010Ray Chandler
23775973999739w74·107757-1October 6, 2010Ray Chandler
See primesize.txt

Ray Chandler found 1 near-repdigit-related prime by using srsieve and PFGW.

Proven near-repdigit-related primes (except ru/nr/pd/qr)
 digitsflabelwlabelexpressionwhenwho
1047962 550w155·107960+1October 6, 2010Ray Chandler

Ray Chandler found 1 near-repdigit PRP by using srsieve and PFGW.

Unprovable near-repdigit PRPs
 digitsflabelwlabelexpressionwhenwho
1487128777977w97(7·107128+173)/9October 6, 2010Ray Chandler

Ray Chandler found 136 quasi-repdigit PRPs by using srsieve and PFGW.

Unprovable quasi-repdigit PRPs
 digitsflabelwlabelexpressionwhenwho
516799560777607w(547·107993-7)/9October 6, 2010Ray Chandler
5177993222612w61(2·107993+349)/9October 6, 2010Ray Chandler
See primesize.txt

Ray Chandler found 454 near-repdigit-related PRPs by using srsieve and PFGW.

Unprovable near-repdigit-related PRPs (except ru/nr/pd/qr)
 digitsflabelwlabelexpressionwhenwho
997994 21w33(19·107993+197)/9October 6, 2010Ray Chandler
10079931449314w93(13·107992+437)/9October 6, 2010Ray Chandler
See primesize.txt

October 4, 2010

Factorizations of 77...771 have been extended up to n=300 by Erik Branger. Composite numbers that appeared newly got through ECM 500 times at level 40. Most unknown factors are supposed to be greater than 1035.

Ray Chandler found 12 near-repdigit primes by using srsieve and PFGW.

Proven near-repdigit primes
 digitsflabelwlabelexpressionwhenwho
596978 99989w9999·106974-1October 4, 2010Ray Chandler
606905 999999929w99999993·106897-1October 4, 2010Ray Chandler
See primesize.txt

Ray Chandler found 19 quasi-repdigit primes by using srsieve and PFGW.

Proven quasi-repdigit primes
 digitsflabelwlabelexpressionwhenwho
23698410999109w11·106982-1October 4, 2010Ray Chandler
24697785999859w86·106975-1October 4, 2010Ray Chandler
See primesize.txt

Ray Chandler found 162 quasi-repdigit PRPs by using srsieve and PFGW.

Unprovable quasi-repdigit PRPs
 digitsflabelwlabelexpressionwhenwho
5417000111871w87(107000+683)/9October 4, 2010Ray Chandler
542699878779787w9(709·106996+11)/9October 4, 2010Ray Chandler
See primesize.txt

Ray Chandler found 1 near-repdigit-related prime by using srsieve and PFGW.

Proven near-repdigit-related primes (except ru/nr/pd/qr)
 digitsflabelwlabelexpressionwhenwho
1216456 550w155·106454+1October 4, 2010Ray Chandler

Ray Chandler found 485 near-repdigit-related PRPs by using srsieve and PFGW.

Unprovable near-repdigit-related PRPs (except ru/nr/pd/qr)
 digitsflabelwlabelexpressionwhenwho
11292049669796w97(29·1029203+91)/3October 4, 2010Ray Chandler
1328602 226w9(68·1028600+7)/3October 4, 2010Ray Chandler
1036997 880w788·106995+7October 4, 2010Ray Chandler
10469929224392w43(83·106991+187)/9October 4, 2010Ray Chandler
See primesize.txt

October 3, 2010

Factorizations of 955...557 have been extended up to n=200. Composite numbers that appeared newly got through ECM 118 times at level 35. Most unknown factors are supposed to be greater than 1030.

October 1, 2010

Ray Chandler found 20 near-repdigit primes by using srsieve and PFGW.

Proven near-repdigit primes
 digitsflabelwlabelexpressionwhenwho
4912371 9999999989w999999999·1012362-1October 1, 2010Ray Chandler
548735 9999999989w999999999·108726-1October 1, 2010Ray Chandler
See primesize.txt
387744 9999999989w999999999·10735-1October 1, 2010Ray Chandler
677231 9999999989w999999999·10222-1October 1, 2010Ray Chandler

Ray Chandler found 19 quasi-repdigit primes by using srsieve and PFGW.

Proven quasi-repdigit primes
 digitsflabelwlabelexpressionwhenwho
24598228999289w29·105980-1October 1, 2010Ray Chandler
25598032999329w33·105978-1October 1, 2010Ray Chandler
See primesize.txt
41506432999329w33·105062-1October 1, 2010Ray Chandler
42501525999259w26·105013-1October 1, 2010Ray Chandler

Ray Chandler found 213 quasi-repdigit PRPs by using srsieve and PFGW.

Unprovable quasi-repdigit PRPs
 digitsflabelwlabelexpressionwhenwho
59160018776787w67(79·106000-97)/9October 1, 2010Ray Chandler
5925996777417w41(7·105996-331)/9October 1, 2010Ray Chandler
See primesize.txt
8625009444194w19(4·105009-229)/9October 1, 2010Ray Chandler
863500840449404w9(364·105006+41)/9October 1, 2010Ray Chandler

Ray Chandler found 3 near-repdigit-related primes by using srsieve and PFGW.

Proven near-repdigit-related primes (except ru/nr/pd/qr)
 digitsflabelwlabelexpressionwhenwho
1285963 550w155·105961+1October 1, 2010Ray Chandler
1385681 330w133·105679+1October 1, 2010Ray Chandler
1415526 880w188·105524+1October 1, 2010Ray Chandler

Ray Chandler found 610 near-repdigit-related PRPs by using srsieve and PFGW.

Unprovable near-repdigit-related PRPs (except ru/nr/pd/qr)
 digitsflabelwlabelexpressionwhenwho
24223579669796w97(29·1022356+91)/3October 1, 2010Ray Chandler
10760016004760w476·106000+47October 1, 2010Ray Chandler
See primesize.txt
72050059556995w69(86·105004+121)/9October 1, 2010Ray Chandler
72150028008180w818·105001+81October 1, 2010Ray Chandler

September 2010

September 30, 2010

Factorizations of 955...553 have been extended up to n=200. Composite numbers that appeared newly got through ECM 118 times at level 35. Most unknown factors are supposed to be greater than 1030.

Ray Chandler proved 2 quasi-repdigit primes by using Primo 3.0.9.

Proven quasi-repdigit primes
 digitsflabelwlabelexpressionwhenwho
6024781333713w7(4·102477+11)/3September 30, 2010Ray Chandler
6324602888728w7(26·102459-17)/9September 30, 2010Ray Chandler

Ray Chandler found 1 near-repdigit-related PRP by using srsieve and PFGW.

Unprovable near-repdigit-related PRPs
 digitsflabelwlabelexpressionwhenwho
373190607669776w97(23·1019059+91)/3September 30, 2010Ray Chandler

September 29, 2010

Ray Chandler found 1 plateau and depression PRP by using srsieve and PFGW.

Unprovable plateau and depression PRPs
 digitsflabelwlabelexpressionwhenwho
7560437555775w7(68·1056042+13)/9September 29, 2010Ray Chandler

Ray Chandler found 29 near-repdigit-related primes by using srsieve and PFGW.

Proven near-repdigit-related primes
 digitsflabelwlabelexpressionwhenwho
562909196001960w196·1029089+1September 29, 2010Ray Chandler
See primesize.txt for 28 other primes in the range of 4007-4982 digits.

Ray Chandler found 982 near-repdigit-related PRPs by using srsieve and PFGW.

Unprovable near-repdigit-related PRPs
 digitsflabelwlabelexpressionwhenwho
168291397008770w877·1029138+87September 29, 2010Ray Chandler
391184697118371w83(64·1018468+647)/9September 29, 2010Ray Chandler
427172157669776w97(23·1017214+91)/3September 29, 2010Ray Chandler
447165883550335w03(32·1016587-473)/9September 29, 2010Ray Chandler
44816553 226w9(68·1016551+7)/3September 29, 2010Ray Chandler
468160175332753w27(16·1016016-19)/3September 29, 2010Ray Chandler
469159959669796w97(29·1015994+91)/3September 29, 2010Ray Chandler
539139377669776w97(23·1013936+91)/3September 29, 2010Ray Chandler
549136839669796w97(29·1013682+91)/3September 29, 2010Ray Chandler
58912560 226w9(68·1012558+7)/3September 29, 2010Ray Chandler
See primesize.txt for 972 other PRPs in the range of 4002-4999 digits.

September 28, 2010

Factorizations of 955...551 have been extended up to n=200. Composite numbers that appeared newly got through ECM 118 times at level 35. Most unknown factors are supposed to be greater than 1030.

Ray Chandler found 49 near-repdigit-related primes by using srsieve and PFGW.

Proven near-repdigit-related primes
 digitsflabelwlabelexpressionwhenwho
562830748001480w148·1028305+1September 28, 2010Ray Chandler
572821181001810w181·1028209+1September 28, 2010Ray Chandler
582793561001610w161·1027933+1September 28, 2010Ray Chandler
602771291001910w191·1027710+1September 28, 2010Ray Chandler
612763863001630w163·1027636+1September 28, 2010Ray Chandler
622730575001750w175·1027303+1September 28, 2010Ray Chandler
632624237001370w137·1026240+1September 28, 2010Ray Chandler
662593376001760w176·1025931+1September 28, 2010Ray Chandler
See primesize.txt for 41 other primes in the range of 3046-3928 digits.

Ray Chandler found 1131 near-repdigit-related PRP by using srsieve and PFGW. See primesize.txt for 1131 PRPs in the range of 3002-4001 digits.

September 27, 2010

Ray Chandler found 2 near-repdigit-related primes by using srsieve and PFGW.

Proven near-repdigit-related primes
 digitsflabelwlabelexpressionwhenwho
602560012001120w112·1025598+1September 27, 2010Ray Chandler
612483173001730w173·1024829+1September 27, 2010Ray Chandler

Ray Chandler found 1 near-repdigit-related PRP by using srsieve and PFGW.

Unprovable near-repdigit-related PRPs
 digitsflabelwlabelexpressionwhenwho
241248016009160w916·1024800+91September 27, 2010Ray Chandler

September 26, 2010

Factorizations of 944...447 have been extended up to n=200. Composite numbers that appeared newly got through ECM 118 times at level 35. Most unknown factors are supposed to be greater than 1030.

Ray Chandler found 52 near-repdigit-related primes by using srsieve and PFGW.

Proven near-repdigit-related primes
 digitsflabelwlabelexpressionwhenwho
632270763001630w163·1022705+1September 26, 2010Ray Chandler
642190485001850w185·1021902+1September 26, 2010Ray Chandler
652184724001240w124·1021845+1September 26, 2010Ray Chandler
See primesize.txt for 49 other primes in the range of 2012-2997 digits.

Ray Chandler found 1652 near-repdigit-related PRPs by using srsieve and PFGW.

Unprovable near-repdigit-related PRPs
 digitsflabelwlabelexpressionwhenwho
267233477008770w877·1023346+87September 26, 2010Ray Chandler
26923260 69w777·1023259-23September 26, 2010Ray Chandler
29022352 229w323·1022350-7September 26, 2010Ray Chandler
298218446009160w916·1021843+91September 26, 2010Ray Chandler
29921829 69w777·1021828-23September 26, 2010Ray Chandler
See primesize.txt for 1647 other PRPs in the range of 2002-3001 digits.

September 25, 2010

Ray Chandler proved 2 quasi-repdigit primes by using Primo 3.0.9.

Proven quasi-repdigit primes
 digitsflabelwlabelexpressionwhenwho
6324447222372w3(65·102443+7)/9September 25, 2010Ray Chandler
6424365222752w7(47·102435+43)/9September 25, 2010Ray Chandler

Erik Branger proved 2 near-repdigit-related primes by the N+1 or N-1 test with PFGW.

Proven near-repdigit-related primes
 digitsflabelwlabelexpressionwhenwho
28331615005150w515·103160+51September 25, 2010Erik Branger
39622225993959w396·102221-61September 25, 2010Erik Branger

Ray Chandler found 91 near-repdigit-related primes by using srsieve and PFGW.

Proven near-repdigit-related primes
 digitsflabelwlabelexpressionwhenwho
612162872001720w172·1021626+1September 25, 2010Ray Chandler
622158343001430w143·1021581+1September 25, 2010Ray Chandler
632150173001730w173·1021499+1September 25, 2010Ray Chandler
652145046001460w146·1021448+1September 25, 2010Ray Chandler
672123794001940w194·1021235+1September 25, 2010Ray Chandler
682118472001720w172·1021182+1September 25, 2010Ray Chandler
702060996001960w196·1020607+1September 25, 2010Ray Chandler
741993584001840w184·1019933+1September 25, 2010Ray Chandler
751960625001250w125·1019604+1September 25, 2010Ray Chandler
771874182001820w182·1018739+1September 25, 2010Ray Chandler
781873449001490w149·1018732+1September 25, 2010Ray Chandler
801821128001280w128·1018209+1September 25, 2010Ray Chandler
811796413001130w113·1017962+1September 25, 2010Ray Chandler
821787121001210w121·1017869+1September 25, 2010Ray Chandler
See primesize.txt for 77 other primes in the range of 1010-1985 digits.

Ray Chandler found 1 near-repdigit PRP by using srsieve and PFGW.

Unprovable near-repdigit PRPs
 digitsflabelwlabelexpressionwhenwho
43239396111161w(55·1023938-1)/9September 25, 2010Ray Chandler

Ray Chandler found 2207 near-repdigit-related PRPs by using srsieve and PFGW.

Unprovable near-repdigit-related PRPs
 digitsflabelwlabelexpressionwhenwho
331200316009160w916·1020030+91September 25, 2010Ray Chandler
36019171 69w777·1019170-23September 25, 2010Ray Chandler
382183316998369w837·1018330-17September 25, 2010Ray Chandler
390179727008770w877·1017971+87September 25, 2010Ray Chandler
See primesize.txt for 2204 other PRPs in the range of 1002-2001 digits.

September 24, 2010

Ray Chandler proved 2 quasi-repdigit primes by using Primo 3.0.9.

Proven quasi-repdigit primes
 digitsflabelwlabelexpressionwhenwho
6324322555925w9(23·102431+31)/9September 24, 2010Ray Chandler
6424287222372w3(65·102427+7)/9September 24, 2010Ray Chandler

September 23, 2010

Factorizations of 299...99 have been extended up to n=250. Composite numbers that appeared newly got through ECM 118 times at level 35. Most unknown factors are supposed to be greater than 1030.

Ray Chandler proved 2 quasi-repdigit primes by using Primo 3.0.9.

Proven quasi-repdigit primes
 digitsflabelwlabelexpressionwhenwho
6324257222372w3(65·102424+7)/9September 23, 2010Ray Chandler
6524195444154w1(49·102418-31)/9September 23, 2010Ray Chandler

Ray Chandler found 1 unprovable near-repdigit PRP by using srsieve and PFGW.

Unprovable near-repdigit PRPs
 digitsflabelwlabelexpressionwhenwho
71167052111121w(19·1016704-1)/9September 23, 2010Ray Chandler

Ray Chandler found 44 near-repdigit-related primes by using srsieve and PFGW.

Proven near-repdigit-related primes
 digitsflabelwlabelexpressionwhenwho
701750716001160w116·1017505+1September 23, 2010Ray Chandler
711750319001190w119·1017501+1September 23, 2010Ray Chandler
721742685001850w185·1017424+1September 23, 2010Ray Chandler
731740137001370w137·1017399+1September 23, 2010Ray Chandler
741735097001970w197·1017348+1September 23, 2010Ray Chandler
751731446001460w146·1017312+1September 23, 2010Ray Chandler
761710964001640w164·1017107+1September 23, 2010Ray Chandler
771659018001180w118·1016588+1September 23, 2010Ray Chandler
781641461001610w161·1016412+1September 23, 2010Ray Chandler
791615952001520w152·1016157+1September 23, 2010Ray Chandler
811612319001190w119·1016121+1September 23, 2010Ray Chandler
821587446001460w146·1015872+1September 23, 2010Ray Chandler
861557216001160w116·1015570+1September 23, 2010Ray Chandler
871547693001930w193·1015474+1September 23, 2010Ray Chandler
881497291001910w191·1014970+1September 23, 2010Ray Chandler
891447228001280w128·1014470+1September 23, 2010Ray Chandler
901443346001460w146·1014431+1September 23, 2010Ray Chandler
911436085001850w185·1014358+1September 23, 2010Ray Chandler
921433358001580w158·1014331+1September 23, 2010Ray Chandler
931403119001190w119·1014029+1September 23, 2010Ray Chandler
941396263001630w163·1013960+1September 23, 2010Ray Chandler
951395913001130w113·1013957+1September 23, 2010Ray Chandler
961393084001840w184·1013928+1September 23, 2010Ray Chandler
971358931001310w131·1013587+1September 23, 2010Ray Chandler
10013161 990w199·1013159+1September 23, 2010Ray Chandler
1011287891001910w191·1012876+1September 23, 2010Ray Chandler
1021281128001280w128·1012809+1September 23, 2010Ray Chandler
1031280361001610w161·1012801+1September 23, 2010Ray Chandler
1041213718001180w118·1012135+1September 23, 2010Ray Chandler
1051188391001910w191·1011881+1September 23, 2010Ray Chandler
1061186851001510w151·1011866+1September 23, 2010Ray Chandler
1081159775001750w175·1011595+1September 23, 2010Ray Chandler
1091154872001720w172·1011546+1September 23, 2010Ray Chandler
1111121524001240w124·1011213+1September 23, 2010Ray Chandler
1131096921001210w121·1010967+1September 23, 2010Ray Chandler
1141086439001390w139·1010862+1September 23, 2010Ray Chandler
1151083849001490w149·1010836+1September 23, 2010Ray Chandler
1161082384001840w184·1010821+1September 23, 2010Ray Chandler
1171058481001810w181·1010582+1September 23, 2010Ray Chandler
1191045121001210w121·1010449+1September 23, 2010Ray Chandler
1201037267001670w167·1010370+1September 23, 2010Ray Chandler
1211032793001930w193·1010325+1September 23, 2010Ray Chandler
1221014919001190w119·1010147+1September 23, 2010Ray Chandler
1231001531001310w131·1010013+1September 23, 2010Ray Chandler

Ray Chandler found 6 unprovable near-repdigit-related PRPs by using srsieve and PFGW.

Unprovable near-repdigit-related PRPs
 digitsflabelwlabelexpressionwhenwho
414171427008770w877·1017141+87September 23, 2010Ray Chandler
51214122 229w323·1014120-7September 23, 2010Ray Chandler
552130277008770w877·1013026+87September 23, 2010Ray Chandler
56212775 69w777·1012774-23September 23, 2010Ray Chandler
64710675 229w323·1010673-7September 23, 2010Ray Chandler
66810350 229w323·1010348-7September 23, 2010Ray Chandler

September 22, 2010

Ray Chandler proved (73·102410+71)/9 is prime by using Primo 3.0.9.

September 21, 2010

Factorizations of 944...443 have been extended up to n=200. Composite numbers that appeared newly got through ECM 118 times at level 35. Most unknown factors are supposed to be greater than 1030.

Ray Chandler found an unprovable plateau and depression PRP.

Unprovable plateau and depression PRPs
 digitsflabelwlabelexpressionwhenwho
7517797222772w7(65·1051778+43)/9September 21, 2010Ray Chandler

Ray Chandler proved (31·102378+41)/9, (31·102406+41)/9 and (19·102398-7)/3 are prime by using Primo 3.0.9.

Ray Chandler found a near-repdigit PRP.

Unprovable near-repdigit PRPs
 digitsflabelwlabelexpressionwhenwho
106102972111121w(19·1010296-1)/9September 21, 2010Ray Chandler

September 20, 2010

Ray Chandler proved (83·102349-11)/9 and (17·102374-53)/9 are prime by using Primo 3.0.9.

Ray Chandler found two unprovable quasi-repdigit PRPs.

Unprovable quasi-repdigit PRPs
 digitsflabelwlabelexpressionwhenwho
104286454333143w1(13·1028644-7)/3September 20, 2010Ray Chandler
145257144333143w1(13·1025713-7)/3September 20, 2010Ray Chandler

Ray Chandler found an unprovable plateau and depression PRP.

Unprovable plateau and depression PRPs
 digitsflabelwlabelexpressionwhenwho
7510093777337w3(34·1051008-43)/9September 20, 2010Ray Chandler

September 19, 2010

Ray Chandler proved (61·102316+11)/9, 4·102323+7 and (43·102340-61)/9 are prime by using Primo 3.0.9.

September 18, 2010

Ray Chandler found two unprovable quasi-repdigit PRPs.

Unprovable quasi-repdigit PRPs
 digitsflabelwlabelexpressionwhenwho
94294558111381w3(73·1029454+17)/9September 18, 2010Ray Chandler
97293376555365w3(59·1029336-23)/9September 18, 2010Ray Chandler

Ray Chandler proved (52·102199+11)/9, (41·102214-23)/9 and (58·102295-13)/9 are prime by using Primo 3.0.9.

September 17, 2010

Ray Chandler found two unprovable quasi-repdigit PRPs.

Unprovable quasi-repdigit PRPs
 digitsflabelwlabelexpressionwhenwho
107280995888158w1(53·1028098-71)/9September 17, 2010Ray Chandler
111277525777957w9(52·1027751+11)/9September 17, 2010Ray Chandler

Ray Chandler proved (74·102198+43)/9 is prime by using Primo 3.0.9.

Ray Chandler successfully proved (89·104885-17)/9, a 4886-digit number, is prime by using Primo 3.0.9. It started on August 24, 2010 and took 425 hours. Congratulations!

September 16, 2010

Ray Chandler found 2 unprovable quasi-repdigit PRPs.

Unprovable quasi-repdigit PRPs
 digitsflabelwlabelexpressionwhenwho
121268396777367w3(61·1026838-43)/9September 16, 2010Ray Chandler
185216896444764w7(58·1021688+23)/9September 16, 2010Ray Chandler

Ray Chandler proved 8·102194-7 is prime by using Primo 3.0.9.

September 15, 2010

Ray Chandler found 5 unprovable quasi-repdigit PRPs.

Unprovable quasi-repdigit PRPs
 digitsflabelwlabelexpressionwhenwho
126264308111781w7(73·1026429+53)/9September 15, 2010Ray Chandler
127264206555165w1(59·1026419-41)/9September 15, 2010Ray Chandler
131261208111381w3(73·1026119+17)/9September 15, 2010Ray Chandler
132261045111351w3(46·1026103+17)/9September 15, 2010Ray Chandler
316148886888768w7(62·1014887-17)/9September 15, 2010Ray Chandler

September 14, 2010

Ray Chandler found 7 unprovable quasi-repdigit PRPs.

Unprovable quasi-repdigit PRPs
 digitsflabelwlabelexpressionwhenwho
95293707222172w1(65·1029369-11)/9September 14, 2010Ray Chandler
98292397555375w3(68·1029238-23)/9September 14, 2010Ray Chandler
139251508777387w3(79·1025149-43)/9September 14, 2010Ray Chandler
144249498111381w3(73·1024948+17)/9September 14, 2010Ray Chandler
149243988222982w9(74·1024397+61)/9September 14, 2010Ray Chandler
152237296555165w1(59·1023728-41)/9September 14, 2010Ray Chandler
153236496111961w9(55·1023648+71)/9September 14, 2010Ray Chandler

Ray Chandler proved (23·102192-17)/3 is prime by using Primo 3.0.9.

September 13, 2010

Ray Chandler found 5 unprovable quasi-repdigit PRPs.

Unprovable quasi-repdigit PRPs
 digitsflabelwlabelexpressionwhenwho
126260117555375w3(68·1026010-23)/9September 13, 2010Ray Chandler
147237728555385w3(77·1023771-23)/9September 13, 2010Ray Chandler
160229395444754w7(49·1022938+23)/9September 13, 2010Ray Chandler
162228025222352w3(47·1022801+7)/9September 13, 2010Ray Chandler
165226836888368w3(62·1022682-53)/9September 13, 2010Ray Chandler

Ray Chandler proved (16·102179+17)/3 is prime by using Primo 3.0.9.

September 12, 2010

Ray Chandler found 5 unprovable quasi-repdigit PRPs.

Unprovable quasi-repdigit PRPs
 digitsflabelwlabelexpressionwhenwho
173214288222382w3(74·1021427+7)/9September 12, 2010Ray Chandler
174213208111381w3(73·1021319+17)/9September 12, 2010Ray Chandler
180208436555165w1(59·1020842-41)/9September 12, 2010Ray Chandler
187201035888758w7(53·1020102-17)/9September 12, 2010Ray Chandler
195197475444154w1(49·1019746-31)/9September 12, 2010Ray Chandler

September 11, 2010

Ray Chandler found 6 unprovable quasi-repdigit PRPs.

Unprovable quasi-repdigit PRPs
 digitsflabelwlabelexpressionwhenwho
94294197666976w9(23·1029418+7)/3September 11, 2010Ray Chandler
169216317444174w1(67·1021630-31)/9September 11, 2010Ray Chandler
198196266111361w3(55·1019625+17)/9September 11, 2010Ray Chandler
199195616777367w3(61·1019560-43)/9September 11, 2010Ray Chandler
210187346555165w1(59·1018733-41)/9September 11, 2010Ray Chandler
211186945888158w1(53·1018693-71)/9September 11, 2010Ray Chandler

September 10, 2010

Ray Chandler found 25 unprovable quasi-repdigit PRPs.

Unprovable quasi-repdigit PRPs
 digitsflabelwlabelexpressionwhenwho
101286127666976w9(23·1028611+7)/3September 10, 2010Ray Chandler
184200757444974w9(67·1020074+41)/9September 10, 2010Ray Chandler
193197036333163w1(19·1019702-7)/3September 10, 2010Ray Chandler
200194967555375w3(68·1019495-23)/9September 10, 2010Ray Chandler
212186117444174w1(67·1018610-31)/9September 10, 2010Ray Chandler
214182688444384w3(76·1018267-13)/9September 10, 2010Ray Chandler
218179398111381w3(73·1017938+17)/9September 10, 2010Ray Chandler
220178038444184w1(76·1017802-31)/9September 10, 2010Ray Chandler
230175006444364w3(58·1017499-13)/9September 10, 2010Ray Chandler
236172638444184w1(76·1017262-31)/9September 10, 2010Ray Chandler
239171655222352w3(47·1017164+7)/9September 10, 2010Ray Chandler
244168545222752w7(47·1016853+43)/9September 10, 2010Ray Chandler
249166776555365w3(59·1016676-23)/9September 10, 2010Ray Chandler
260161758111981w9(73·1016174+71)/9September 10, 2010Ray Chandler
261161635777357w3(52·1016162-43)/9September 10, 2010Ray Chandler
264160498111981w9(73·1016048+71)/9September 10, 2010Ray Chandler
278156335666356w3(17·1015632-11)/3September 10, 2010Ray Chandler
279156065444754w7(49·1015605+23)/9September 10, 2010Ray Chandler
281155315444754w7(49·1015530+23)/9September 10, 2010Ray Chandler
286151155222752w7(47·1015114+43)/9September 10, 2010Ray Chandler
287150986222162w1(56·1015097-11)/9September 10, 2010Ray Chandler
309139765666356w3(17·1013975-11)/3September 10, 2010Ray Chandler
347123926333163w1(19·1012391-7)/3September 10, 2010Ray Chandler
348123896333163w1(19·1012388-7)/3September 10, 2010Ray Chandler
404105425333953w9(16·1010541+17)/3September 10, 2010Ray Chandler

September 9, 2010

Ray Chandler found 35 unprovable quasi-repdigit PRPs.

Unprovable quasi-repdigit PRPs
 digitsflabelwlabelexpressionwhenwho
168215948666986w9(26·1021593+7)/3September 9, 2010Ray Chandler
227171017888378w3(71·1017100-53)/9September 9, 2010Ray Chandler
238165257555375w3(68·1016524-23)/9September 9, 2010Ray Chandler
244162137222372w3(65·1016212+7)/9September 9, 2010Ray Chandler
255159267222372w3(65·1015925+7)/9September 9, 2010Ray Chandler
270151387444974w9(67·1015137+41)/9September 9, 2010Ray Chandler
274150858777987w9(79·1015084+11)/9September 9, 2010Ray Chandler
279147087333973w9(22·1014707+17)/3September 9, 2010Ray Chandler
291141646555165w1(59·1014163-41)/9September 9, 2010Ray Chandler
295139486888768w7(62·1013947-17)/9September 9, 2010Ray Chandler
296139457888378w3(71·1013944-53)/9September 9, 2010Ray Chandler
298138947888378w3(71·1013893-53)/9September 9, 2010Ray Chandler
301137427555175w1(68·1013741-41)/9September 9, 2010Ray Chandler
302137128222982w9(74·1013711+61)/9September 9, 2010Ray Chandler
308133955444154w1(49·1013394-31)/9September 9, 2010Ray Chandler
313131115444954w9(49·1013110+41)/9September 9, 2010Ray Chandler
314130978222382w3(74·1013096+7)/9September 9, 2010Ray Chandler
334122537444174w1(67·1012252-31)/9September 9, 2010Ray Chandler
338121297555175w1(68·1012128-41)/9September 9, 2010Ray Chandler
339120105888158w1(53·1012009-71)/9September 9, 2010Ray Chandler
342118418555985w9(77·1011840+31)/9September 9, 2010Ray Chandler
343117786111961w9(55·1011777+71)/9September 9, 2010Ray Chandler
344117016111361w3(55·1011700+17)/9September 9, 2010Ray Chandler
347116586444364w3(58·1011657-13)/9September 9, 2010Ray Chandler
348116567666176w1(23·1011655-17)/3September 9, 2010Ray Chandler
351115515777157w1(52·1011550-61)/9September 9, 2010Ray Chandler
354113997111971w9(64·1011398+71)/9September 9, 2010Ray Chandler
362111175222952w9(47·1011116+61)/9September 9, 2010Ray Chandler
366110236444364w3(58·1011022-13)/9September 9, 2010Ray Chandler
371108376222162w1(56·1010836-11)/9September 9, 2010Ray Chandler
377107355777157w1(52·1010734-61)/9September 9, 2010Ray Chandler
380107056777967w9(61·1010704+11)/9September 9, 2010Ray Chandler
384106107222172w1(65·1010609-11)/9September 9, 2010Ray Chandler
388105447555175w1(68·1010543-41)/9September 9, 2010Ray Chandler
394102847555175w1(68·1010283-41)/9September 9, 2010Ray Chandler

September 8, 2010

Ray Chandler proved (76·102170-13)/9 is prime by using Primo 3.0.9.

Ray Chandler found 10 unprovable quasi-repdigit PRPs.

Unprovable quasi-repdigit PRPs
 digitsflabelwlabelexpressionwhenwho
161220969222792w7(83·1022095+43)/9September 8, 2010Ray Chandler
194192719222792w7(83·1019270+43)/9September 8, 2010Ray Chandler
213175559222192w1(83·1017554-11)/9September 8, 2010Ray Chandler
219173188666386w3(26·1017317-11)/3September 8, 2010Ray Chandler
237162958666386w3(26·1016294-11)/3September 8, 2010Ray Chandler
240160379222192w1(83·1016036-11)/9September 8, 2010Ray Chandler
250157279222392w3(83·1015726+7)/9September 8, 2010Ray Chandler
260148769222792w7(83·1014875+43)/9September 8, 2010Ray Chandler
318116939222192w1(83·1011692-11)/9September 8, 2010Ray Chandler
335111168777387w3(79·1011115-43)/9September 8, 2010Ray Chandler

September 7, 2010

Ray Chandler proved (83·102157+43)/9, 5·102157-7 and (68·102162-41)/9 are prime by using Primo 3.0.9.

Ray Chandler found four unprovable quasi-repdigit PRPs.

Unprovable quasi-repdigit PRPs
 digitsflabelwlabelexpressionwhenwho
98287689333793w7(28·1028767+11)/3September 7, 2010Ray Chandler
106277369333793w7(28·1027735+11)/3September 7, 2010Ray Chandler
112271109333793w7(28·1027109+11)/3September 7, 2010Ray Chandler
162219239444194w1(85·1021922-31)/9September 7, 2010Ray Chandler

Erik Branger found 32 unprovable quasi-repdigit PRPs.

Unprovable quasi-repdigit PRPs
 digitsflabelwlabelexpressionwhenwho
94293074555745w7(41·1029306+13)/9September 7, 2010Erik Branger
99286284666346w3(14·1028627-11)/3September 7, 2010Erik Branger
100285764555345w3(41·1028575-23)/9September 7, 2010Erik Branger
105277444333943w9(13·1027743+17)/3September 7, 2010Erik Branger
108273074888348w3(44·1027306-53)/9September 7, 2010Erik Branger
113270614666146w1(14·1027060-17)/3September 7, 2010Erik Branger
114269814555945w9(41·1026980+31)/9September 7, 2010Erik Branger
128258494333743w7(13·1025848+11)/3September 7, 2010Erik Branger
144234154666346w3(14·1023414-11)/3September 7, 2010Erik Branger
150229614111341w3(37·1022960+17)/9September 7, 2010Erik Branger
165216504222742w7(38·1021649+43)/9September 7, 2010Erik Branger
177202354111941w9(37·1020234+71)/9September 7, 2010Erik Branger
179200664111741w7(37·1020065+53)/9September 7, 2010Erik Branger
189196734111741w7(37·1019672+53)/9September 7, 2010Erik Branger
195188664333743w7(13·1018865+11)/3September 7, 2010Erik Branger
217172224111741w7(37·1017221+53)/9September 7, 2010Erik Branger
220168954555345w3(41·1016894-23)/9September 7, 2010Erik Branger
223167694666146w1(14·1016768-17)/3September 7, 2010Erik Branger
227166294888748w7(44·1016628-17)/9September 7, 2010Erik Branger
230164414555345w3(41·1016440-23)/9September 7, 2010Erik Branger
233160974222742w7(38·1016096+43)/9September 7, 2010Erik Branger
238158914333943w9(13·1015890+17)/3September 7, 2010Erik Branger
258144624666746w7(14·1014461+1)/3September 7, 2010Erik Branger
278130524111341w3(37·1013051+17)/9September 7, 2010Erik Branger
289127254222342w3(38·1012724+7)/9September 7, 2010Erik Branger
298119124222742w7(38·1011911+43)/9September 7, 2010Erik Branger
301115834111941w9(37·1011582+71)/9September 7, 2010Erik Branger
302115274555945w9(41·1011526+31)/9September 7, 2010Erik Branger
317108334333743w7(13·1010832+11)/3September 7, 2010Erik Branger
325106574222342w3(38·1010656+7)/9September 7, 2010Erik Branger
326106404666746w7(14·1010639+1)/3September 7, 2010Erik Branger
328105804111741w7(37·1010579+53)/9September 7, 2010Erik Branger

September 6, 2010

Ray Chandler proved (49·102147-31)/9 is prime by using Primo 3.0.9.

Ray Chandler found four unprovable quasi-repdigit PRPs.

Unprovable quasi-repdigit PRPs
 digitsflabelwlabelexpressionwhenwho
92299329888798w7(89·1029931-17)/9September 6, 2010Ray Chandler
183179609666796w7(29·1017959+1)/3September 6, 2010Ray Chandler
218155339666796w7(29·1015532+1)/3September 6, 2010Ray Chandler
293105599666796w7(29·1010558+1)/3September 6, 2010Ray Chandler

September 5, 2010

Ray Chandler proved (41·102139-23)/9 and 8·102146-7 are prime by using Primo 3.0.9.

Ray Chandler found an unprovable quasi-repdigit PRP.

Unprovable quasi-repdigit PRPs
 digitsflabelwlabelexpressionwhenwho
59401694999149w15·1040168-9September 5, 2010Ray Chandler

September 4, 2010

Ray Chandler proved (23·102132+7)/3 and (55·102138+71)/9 are prime by using Primo 3.0.9.

Erik Branger proved 257 prime numbers, listed in the List of near-repdigit-related prime numbers, up to 1600-digit by using Primo 3.0.9.

September 3, 2010

Ray Chandler proved (47·102103-11)/9 and (22·102105+17)/3 are prime by using Primo 3.0.9.

Ray Chandler found two unprovable quasi-repdigit PRPs.

Unprovable quasi-repdigit PRPs
 digitsflabelwlabelexpressionwhenwho
98277704999149w15·1027769-9September 3, 2010Ray Chandler
119250554999149w15·1025054-9September 3, 2010Ray Chandler

September 2, 2010

Ray Chandler proved (64·102084+71)/9 is prime by using Primo 3.0.9.

Ray Chandler found an unprovable quasi-repdigit PRP.

Unprovable quasi-repdigit PRPs
 digitsflabelwlabelexpressionwhenwho
62392674000940w94·1039266+9September 2, 2010Ray Chandler

September 1, 2010

Ray Chandler proved (74·102053+7)/9, (58·102063+23)/9 and (67·102064-31)/9 are prime by using Primo 3.0.9.

August 2010

August 31, 2010

Ray Chandler found an unprovable quasi-repdigit PRP.

Unprovable quasi-repdigit PRPs
 digitsflabelwlabelexpressionwhenwho
79344154000940w94·1034414+9August 31, 2010Ray Chandler

August 30, 2010

Ray Chandler found that 4·1032835+1 is prime.

Erik Branger proved 972 prime numbers, listed in the List of near-repdigit-related prime numbers, up to 1000-digit by using Primo 3.0.9.

August 29, 2010

Ray Chandler found two unprovable quasi-repdigit PRPs.

Unprovable quasi-repdigit PRPs
 digitsflabelwlabelexpressionwhenwho
147210624000340w34·1021061+3August 29, 2010Ray Chandler
268112944000340w34·1011293+3August 29, 2010Ray Chandler

August 27, 2010

Maksym Voznyy's web page have been moved. The new page is: http://individual.utoronto.ca/mvoznyy/

Serge Batalov found six unprovable quasi-repdigit PRPs.

Unprovable quasi-repdigit PRPs
 digitsflabelwlabelexpressionwhenwho
57416579666196w1(29·1041656-17)/3August 27, 2010Serge Batalov
68379159666196w1(29·1037914-17)/3August 27, 2010Serge Batalov
168190379777197w1(88·1019036-61)/9August 27, 2010Serge Batalov
189172399777397w3(88·1017238-43)/9August 27, 2010Serge Batalov
232136489777397w3(88·1013647-43)/9August 27, 2010Serge Batalov
254125399777197w1(88·1012538-61)/9August 27, 2010Serge Batalov

August 25, 2010

Ray Chandler found two unprovable quasi-repdigit PRPs.

Unprovable quasi-repdigit PRPs
 digitsflabelwlabelexpressionwhenwho
233131899888798w7(89·1013188-17)/9August 25, 2010Ray Chandler
240129529888798w7(89·1012951-17)/9August 25, 2010Ray Chandler

August 24, 2010

Sean A. Irvine found (79·1016824-61)/9 was PRP on September 2009. He reported it to OEIS at that time. I'm sorry that I neglected to collect it.

Unprovable quasi-repdigit PRPs
 digitsflabelwlabelexpressionwhenwho
188168258777187w1(79·1016824-61)/9September 10, 2009Sean A. Irvine

August 22, 2010

Erik Branger proved that 9·102817-91, 6·101321-61 and 5·10985-51 are prime by N+1 test. primesize.txt was updated.

August 21, 2010

Lionel Debroux proved that 102002-99 is prime by using Primo. primesize.txt was updated. NOTE: N-1 test can be used for this number.

Erik Branger proved that 2·103612-3 is prime by N+1 test.

August 18, 2010

Serge Batalov found three unprovable quasi-repdigit PRPs.

Unprovable quasi-repdigit PRPs
 digitsflabelwlabelexpressionwhenwho
125233479555195w1(86·1023346-41)/9August 18, 2010Serge Batalov
170186109555195w1(86·1018609-41)/9August 18, 2010Serge Batalov
229134809555195w1(86·1013479-41)/9August 18, 2010Serge Batalov

August 17, 2010

Serge Batalov found two unprovable quasi-repdigit PRPs.

Unprovable quasi-repdigit PRPs
 digitsflabelwlabelexpressionwhenwho
118248629888198w1(89·1024861-71)/9August 17, 2010Serge Batalov
192163519888398w3(89·1016350-53)/9August 17, 2010Serge Batalov

August 16, 2010

Serge Batalov found two unprovable quasi-repdigit PRPs.

Unprovable quasi-repdigit PRPs
 digitsflabelwlabelexpressionwhenwho
117248889555395w3(86·1024887-23)/9August 16, 2010Serge Batalov
142215599444394w3(85·1021558-13)/9August 16, 2010Serge Batalov

August 15, 2010

Serge Batalov found two unprovable quasi-repdigit PRPs.

Unprovable quasi-repdigit PRPs
 digitsflabelwlabelexpressionwhenwho
183167859444794w7(85·1016784+23)/9August 15, 2010Serge Batalov
248113919444394w3(85·1011390-13)/9August 15, 2010Serge Batalov

August 13, 2010

Serge Batalov found an unprovable quasi-repdigit PRP.

Unprovable quasi-repdigit PRPs
 digitsflabelwlabelexpressionwhenwho
168178659444194w1(85·1017864-31)/9August 13, 2010Serge Batalov

August 12, 2010

Factorizations of 944...441 have been extended up to n=200. Composite numbers that appeared newly have passed 118 times ECM runs at level 35. Unknown factors have probably 30 digits or more.

July 2010

July 28, 2010

Markus Tervooren found an unprovable near-repdigit PRP.

Unprovable near-repdigit PRPs
 digitsflabelwlabelexpressionwhenwho
587720999979w71087720-3July 28, 2010Markus Tervooren

July 25, 2010

Factorizations of 933...337 have been extended up to n=200. Composite numbers that appeared newly have passed 118 times ECM runs at level 35. Unknown factors have probably 30 digits or more.

Serge Batalov broke his own largest known unprovable quasi-repdigit PRP record again. Congratulations!

Unprovable quasi-repdigit PRPs
 digitsflabelwlabelexpressionwhenwho
11985305888958w9(53·10198529+1)/9July 25, 2010Serge Batalov

July 24, 2010

Serge Batalov found the largest known unprovable quasi-repdigit PRP in our tables again. Congratulations! It was ranked second, behind Maksym Voznyy's largest known repunit PRP, in near-repdigit-related (probable) prime numbers.

Unprovable quasi-repdigit PRPs
 digitsflabelwlabelexpressionwhenwho
11966854888948w9(44·10196684+1)/9July 24, 2010Serge Batalov

July 19, 2010

NOTE: 3·10282+1 = P8 · P14 · P32 · P37 · P44 · P45 · P107. P32 and P44: Serge Batalov, ECM, B1=2000000. P37: Ignacio Santos, ECM, B1=11000000. P45: Wataru Sakai, ECM, B1=11000000.

July 17, 2010

Serge Batalov found the largest known unprovable quasi-repdigit PRP in our tables. Congratulations! It's greater than the largest known unprovable near-repdigit PRP in our tables and greater than the largest known near-repdigit prime too. It was ranked second, behind Maksym Voznyy's largest known repunit PRP, in near-repdigit-related (probable) prime numbers.

Unprovable quasi-repdigit PRPs
 digitsflabelwlabelexpressionwhenwho
11910743888938w9(35·10191073+1)/9July 17, 2010Serge Batalov

July 11, 2010

Erik Branger proved 1199 prime numbers, listed in the List of near-repdigit-related prime numbers, up to 800-digit by using Primo 3.0.9.

June 2010

June 18, 2010

The threshold of composite numbers which are longer than 95 percent of the corresponding SNFS polynomial has been lowered from 96 percent at the suggestion of Serge Batalov.

June 14, 2010

Serge Batalov found 2 PRPs.

Unprovable quasi-repdigit PRPs
 digitsflabelwlabelexpressionwhenwho
81066503888938w9(35·10106649+1)/9June 14, 2010Serge Batalov
10984477888978w9(71·1098446+1)/9June 14, 2010Serge Batalov

June 10, 2010

Erik Branger found 25 PRPs.

Unprovable quasi-repdigit PRPs
 digitsflabelwlabelexpressionwhenwho
94269053000730w73·1026904+7June 10, 2010Erik Branger
95267453999739w74·1026744-3June 10, 2010Erik Branger
102260013666136w1(11·1026000-17)/3June 10, 2010Erik Branger
113248413555735w7(32·1024840+13)/9June 10, 2010Erik Branger
121230063888138w1(35·1023005-71)/9June 10, 2010Erik Branger
122229263777137w1(34·1022925-61)/9June 10, 2010Erik Branger
124227413666736w7(11·1022740+1)/3June 10, 2010Erik Branger
127226123222132w1(29·1022611-11)/9June 10, 2010Erik Branger
128225193222132w1(29·1022518-11)/9June 10, 2010Erik Branger
133217273777937w9(34·1021726+11)/9June 10, 2010Erik Branger
140207913555735w7(32·1020790+13)/9June 10, 2010Erik Branger
149197803222132w1(29·1019779-11)/9June 10, 2010Erik Branger
154196513222932w9(29·1019650+61)/9June 10, 2010Erik Branger
170175143666136w1(11·1017513-17)/3June 10, 2010Erik Branger
173173553555935w9(32·1017354+31)/9June 10, 2010Erik Branger
184160213888138w1(35·1016020-71)/9June 10, 2010Erik Branger
204145003555135w1(32·1014499-41)/9June 10, 2010Erik Branger
210140803888138w1(35·1014079-71)/9June 10, 2010Erik Branger
226128203888138w1(35·1012819-71)/9June 10, 2010Erik Branger
230125913666136w1(11·1012590-17)/3June 10, 2010Erik Branger
245111043555735w7(32·1011103+13)/9June 10, 2010Erik Branger
254107403666136w1(11·1010739-17)/3June 10, 2010Erik Branger
255107343777937w9(34·1010733+11)/9June 10, 2010Erik Branger
259105253222932w9(29·1010524+61)/9June 10, 2010Erik Branger
260105003777137w1(34·1010499-61)/9June 10, 2010Erik Branger

Serge Batalov found a PRP.

Unprovable quasi-repdigit PRPs
 digitsflabelwlabelexpressionwhenwho
51182175888958w9(53·10118216+1)/9June 10, 2010Serge Batalov

June 5, 2010

Serge Batalov found two PRPs.

Unprovable quasi-repdigit PRPs
 digitsflabelwlabelexpressionwhenwho
61096746888968w9(62·10109673+1)/9June 5, 2010Serge Batalov
71005433888938w9(35·10100542+1)/9June 5, 2010Serge Batalov

June 2, 2010

Factorizations of 844...447 have been extended up to n=200. Composite numbers that appeared newly have passed 118 times ECM runs at level 35. Unknown factors have probably 30 digits or more.

May 2010

May 31, 2010

Factorizations of 922...227 have been extended up to n=200. Composite numbers that appeared newly have passed 118 times ECM runs at level 35. Unknown factors have probably 30 digits or more.

May 29, 2010

Factorizations of 300...001 have been extended up to n=300. Composite numbers that appeared newly have passed 118 times ECM runs at level 35. Unknown factors have probably 30 digits or more.

May 22, 2010

Serge Batalov found the largest known near-repdigit PRP so far in our tables again. Congratulations!

  1. [38889] (35·1068718+1)/9 is PRP.
  2. [88889] (8·10148328+1)/9 is PRP.

May 21, 2010

Serge Batalov found the largest known near-repdigit PRP so far in our tables again. Congratulations!

  1. [68889] (62·1065331+1)/9 is PRP.
  2. [88889] (8·10144683+1)/9 is PRP.

May 20, 2010

Factorizations of 922...221 have been extended up to n=200. Composite numbers that appeared newly have passed 118 times ECM runs at level 35. Unknown factors have probably 30 digits or more.

May 18, 2010

Serge Batalov broke his own record again. Congratulations!

  1. [58889] (53·1059389+1)/9 is PRP.
  2. [48889] (44·1059454+1)/9 is PRP.
  3. [28889] (26·10139289+1)/9 is PRP.

May 17, 2010

Serge Batalov found the largest known quasi-repdigit PRP so far in our tables. Congratulations!

  1. [78889] (71·10137250+1)/9 is PRP.

Factorizations of 844...443 have been extended up to n=200. Composite numbers that appeared newly have passed 118 times ECM runs at level 35. Unknown factors have probably 30 digits or more.

May 16, 2010

Factorizations of 911...117 have been extended up to n=200. Composite numbers that appeared newly have passed 118 times ECM runs at level 35. Unknown factors have probably 30 digits or more.

May 15, 2010

Serge Batalov found four PRPs. (89·10133580+1)/9 is the largest known Plateau and Depression PRP. Congratulations!

  1. [38889] (35·1046799+1)/9 is PRP.
  2. [38889] (35·1049682+1)/9 is PRP.
  3. [68889] (62·1053111+1)/9 is PRP.
  4. [98889] (89·10133580+1)/9 is PRP.

May 13, 2010

Serge Batalov found a PRP.

  1. [28889] (26·1034423+1)/9 is PRP.

Factorizations of 911...113 have been extended up to n=200. Composite numbers that appeared newly have passed 118 times ECM runs at level 35. Unknown factors have probably 30 digits or more.

May 12, 2010

Serge Batalov found six PRPs.

  1. [78889] (71·1010782+1)/9 is PRP.
  2. [48889] (44·1011370+1)/9 is PRP.
  3. [38889] (35·1019854+1)/9 is PRP.
  4. [78889] (71·1025366+1)/9 is PRP.
  5. [38889] (35·1027842+1)/9 is PRP.
  6. [28889] (26·1030254+1)/9 is PRP.

May 10, 2010

Serge Batalov found four PRPs by using srsieve, sr1sieve, Prime95 and PFGW 3.3.3. One of them is the largest known quasi-repdigit PRP so far in our tables. Congratulations!

  1. [18889] (17·1037992+1)/9 is PRP.
  2. [18889] (17·1054117+1)/9 is PRP.
  3. [18889] (17·10121242+1)/9 is PRP.
  4. [18889] (17·10121621+1)/9 is PRP.

May 8, 2010

RSALS and Jeff Gilchrist factored c248 = P46 · P52 · P71 · P81 from 10250+3. It's the largest number factored by snfs in our tables so far. Congratulations!

NOTE: This number should have been factored by ECM up to 55-digit at least. To save time and energy, let's not rely on NFS against huge numbers from the beginning!

May 7, 2010

Factorizations of 844...441 have been extended up to n=200. Composite numbers that appeared newly have passed 118 times ECM runs at level 35. Unknown factors have probably 30 digits or more.

April 2010

April 29, 2010

Erik Branger reported 41 PRPs.

  1. [21113] (19·1014161+17)/9 is PRP.
  2. [21119] (19·1011383+71)/9 is PRP.
  3. [21119] (19·1015415+71)/9 is PRP.
  4. [21119] (19·1026382+71)/9 is PRP.
  5. [23339] (7·1023055+17)/3 is PRP.
  6. [24441] (22·1024989-31)/9 is PRP.
  7. [24447] (22·1023481+23)/9 is PRP.
  8. [24447] (22·1027855+23)/9 is PRP.
  9. [24449] (22·1012142+41)/9 is PRP.
  10. [24449] (22·1013048+41)/9 is PRP.
  11. [25551] (23·1018798-41)/9 is PRP.
  12. [25557] (23·1012773+13)/9 is PRP.
  13. [25557] (23·1017702+13)/9 is PRP.
  14. [25557] (23·1019128+13)/9 is PRP.
  15. [25557] (23·1022206+13)/9 is PRP.
  16. [25557] (23·1022386+13)/9 is PRP.
  17. [25557] (23·1025053+13)/9 is PRP.
  18. [25559] (23·1015886+31)/9 is PRP.
  19. [25559] (23·1019912+31)/9 is PRP.
  20. [26669] (8·1012828+7)/3 is PRP.
  21. [26669] (8·1014959+7)/3 is PRP.
  22. [26669] (8·1017995+7)/3 is PRP.
  23. [26669] (8·1019730+7)/3 is PRP.
  24. [26669] (8·1026480+7)/3 is PRP.
  25. [27771] (25·1020786-61)/9 is PRP.
  26. [27773] (25·1010069-43)/9 is PRP.
  27. [27773] (25·1017356-43)/9 is PRP.
  28. [27773] (25·1025804-43)/9 is PRP.
  29. [27773] (25·1029052-43)/9 is PRP.
  30. [27773] (25·1029082-43)/9 is PRP.
  31. [27779] (25·1014646+11)/9 is PRP.
  32. [27779] (25·1022794+11)/9 is PRP.
  33. [27779] (25·1025648+11)/9 is PRP.
  34. [28881] (26·1010895-71)/9 is PRP.
  35. [28881] (26·1017105-71)/9 is PRP.
  36. [28883] (26·1015865-53)/9 is PRP.
  37. [28887] (26·1014249-17)/9 is PRP.
  38. [29993] 3·1013122-7 is PRP.
  39. [29993] 3·1013832-7 is PRP.
  40. [29993] 3·1022676-7 is PRP.
  41. [29993] 3·1025020-7 is PRP.

April 28, 2010

Short wanted list of Phi_n(10) is available. However, no exclusive reservation system for Phi_n(10) will be provided because many people are collecting repunit factors.

April 23, 2010

RSALS + Zeta-Flux factored c241 from 17777_248: (16·10248-7)/9 by snfs/Msieve. The 250-digit polynomial is the largest in our tables so far. Congratulations!

Juno Fukos factored 150-digit composite factor of Phi_840(10) by gnfs/Msieve. Congratulations!

Number: c150
N = 191413141591299314411353617644492718709042398621746359743575335167576218516274501587918765785208170431266534615378694736680781077885837943706833300081 (150 digits)
Divisors found:
r1=1146780383632163283649175272843774050715065531735480891145232027761 (pp67)
r2=166913512232431273140362987966641859731500109846278942036790211593884632236221381121 (pp84)
Version: Msieve v. 1.44
Total time: 1321.70 hours.
Factorization parameters were as follows:
n: 191413141591299314411353617644492718709042398621746359743575335167576218516274501587918765785208170431266534615378694736680781077885837943706833300081 
skew: 581056.87 
# norm 3.49e+020 
c5: 417300 
c4: 6293707890075 
c3: 661926573905922818 
c2: -1142910230692705225820950 
c1: -305033470566634835042268478702 
c0: 13979210859054806935193981807485035 
# alpha -5.68 
Y1: 22746208757392231 
Y0: -53988855542895713658925943846 
# Murphy_E 4.74e-012 
# M 42516010405424856805684090534471339985472838519578990692918969250315963958564685692805011963349843096316919602745856301635282723806748487864856881786 
type: gnfs 
rlim: 20800000 
alim: 20800000 
lpbr: 29 
lpba: 29 
mfbr: 58 
mfba: 58 
rlambda: 2.6 
alambda: 2.6 
qintsize: 100000
Factor base limits: 20800000/20800000
Large primes per side: 3
Large prime bits: 29/29
Sieved algebraic special-q in [10400000, 33200000)
Total raw relations: 45598432
Relations: 6859564 relations
Pruned matrix : 4250955 x 4251180
Polynomial selection time: 0.00 hours.
Total sieving time: 1224.80 hours.
Total relation processing time: 0.71 hours.
Matrix solve time: 88.93 hours.
time per square root: 7.25 hours.
Prototype def-par.txt line would be: gnfs,149,5,65,2000,1e-05,0.28,250,20,50000,3600,20800000,20800000,29,29,58,58,2.6,2.6,100000
total time: 1321.70 hours.
 --------- CPU info (if available) ----------

April 21, 2010

The following sections were divided from this page.

Reserved numbers and submitted numbers page links to not the table body but the Contribution and Reservation page.

April 11, 2010

List of near-repdigit-related prime numbers was updated.

Ignacio Santos added 162 prime numbers of the form k·10n+1 and the following 16 PRPs.

  1. [69w77] 7·102037-23 is PRP.
  2. [69w77] 7·104557-23 is PRP.
  3. [69w77] 7·108995-23 is PRP.
  4. [229w3] 23·102379-7 is PRP.
  5. [229w3] 23·102615-7 is PRP.
  6. [229w3] 23·104008-7 is PRP.
  7. [229w3] 23·104295-7 is PRP.
  8. [229w3] 23·104495-7 is PRP.
  9. [229w3] 23·104526-7 is PRP.
  10. [229w3] 23·109996-7 is PRP.
  11. [69983] 7·102178-17 is PRP.
  12. [69983] 7·108916-17 is PRP.
  13. [69983] 7·109471-17 is PRP.
  14. [76697] (23·102053+91)/3 is PRP.
  15. [76697] (23·102997+91)/3 is PRP.
  16. [76697] (23·104065+91)/3 is PRP.

Lionel Debroux proved the following two prime numbers by using Primo.

  1. [40079] 4·10999+79 is prime.
  2. [77719] (7·101503-529)/9 is prime.

==== NOTE ====

In primedifficulty.txt, difficulty = 0.00% means that the sequence consists of composite numbers except finite exceptions. For example, [38111] (343·10n-1)/9 is generally a composite number because

April 10, 2010

Erik Branger proved 4424 prime numbers, listed in the List of near-repdigit-related prime numbers, up to 600-digit by using Primo 3.0.9.

April 9, 2010

List of near-repdigit-related prime numbers was updated with new prime numbers of the form k·10n+1 searched by Ignacio Santos.

April 6, 2010

Serge Batalov found a PRP.

  1. (77·1036464+13)/9 = 8(5)364637<36465> is PRP.

April 2, 2010

Serge Batalov found 2 PRPs.

  1. (77·1019835+13)/9 = 8(5)198347<19836> is PRP.
  2. (77·1020018+13)/9 = 8(5)200177<20019> is PRP.

Prime numbers of the form k·10n-1 (k:small) are easy to prove by n+1 test. 10metreh tested prime numbers of the form that had not been marked as 'proven' in primesize.txt.

April 1, 2010

The ratio of current factored part of each repunit number is available at Factorizations of 11...11 (Repunit). For example, current factored part of R4416 = (104416-1)/9 is 35.87%. Then, you can prove the primality of 4417-digit near-repdigit number 88...881 : (8·104417-71)/9 = 80·R4416+1 by using n-1 test. See also (8*10^4417-71)/9 is prime (4417 digits).

27811-digit near-repdigit number 88...881 : (8·1027811-71)/9 is PRP that was found by Erik Branger on January 31, 2010. And then, current factored part of (1027810-1)/9 is 32.99%. Additional prime factors of Phi_515(10), Phi_1030(10), Phi_1545(10), Phi_1854(10), Phi_2781(10), Phi_3090(10), Phi_4635(10), Phi_5562(10), Phi_9270(10), Phi_27810(10) and 7334-digit gigantic ECPP for Phi_13905(10)/83431/333721 will make 27811-digit near-repdigit prime number proven. Contributions are welcome.

$ ./pfgw -tc -h"88881_27811.h" -q"(8*10^27811-71)/9"
PFGW Version 3.3.3.20100325.Win_Stable [GWNUM 25.14]

Primality testing (8*10^27811-71)/9 [N-1/N+1, Brillhart-Lehmer-Selfridge]
Reading factors from helper file 88881_27811.h
Running N-1 test using base 17
Running N-1 test using base 23
Running N-1 test using base 43
Running N+1 test using discriminant 53, base 6+sqrt(53)
Calling N-1 BLS with factored part 33.00% and helper 0.03% (99.02% proof)
(8*10^27811-71)/9 is Fermat and Lucas PRP! (698.8483s+0.0032s)

March 2010

March 30, 2010

Factorizations of 822...227, Factorizations of 822...229 and Factorizations of 833...339 have been extended up to n=200. Composite numbers that appeared newly have passed 118 times ECM runs at level 35. Unknown factors have probably 30 digits or more.

March 24, 2010

RSALS and Zeta-Flux factored 2·10241+9: c165 = P54 · P112. It's the largest GNFS factorization in our tables so far. Congratulations!

March 23, 2010

Erik Branger found 20 PRPs by using PFGW.

  1. (11·1017715+7)/9 = 1(2)177143<17716> is PRP.
  2. (11·1011924+43)/9 = 1(2)119237<11925> is PRP.
  3. (4·1014630+11)/3 = 1(3)146297<14631> is PRP.
  4. (4·1020932+11)/3 = 1(3)209317<20933> is PRP.
  5. (13·1017293+41)/9 = 1(4)172929<17294> is PRP.
  6. (13·1023270+41)/9 = 1(4)232699<23271> is PRP.
  7. (13·1027197+41)/9 = 1(4)271969<27198> is PRP.
  8. (14·1010674+31)/9 = 1(5)106739<10675> is PRP.
  9. (14·1011617+31)/9 = 1(5)116169<11618> is PRP.
  10. (14·1013257+31)/9 = 1(5)132569<13258> is PRP.
  11. (14·1014371+31)/9 = 1(5)143709<14372> is PRP.
  12. (14·1020176+31)/9 = 1(5)201759<20177> is PRP.
  13. (5·1012546-11)/3 = 1(6)125453<12547> is PRP.
  14. (5·1022443-11)/3 = 1(6)224423<22444> is PRP.
  15. (5·1017765+1)/3 = 1(6)177647<17766> is PRP.
  16. (5·1019305+7)/3 = 1(6)193049<19306> is PRP.
  17. (16·1026000+11)/9 = 1(7)259999<26001> is PRP.
  18. (17·1022666-53)/9 = 1(8)226653<22667> is PRP.
  19. (17·1029292-53)/9 = 1(8)292913<29293> is PRP.
  20. (17·1029508-53)/9 = 1(8)295073<29509> is PRP.

March 20, 2010

Factorizations of 811...119, Factorizations of 822...221 and Factorizations of 822...223 have been extended up to n=200. Composite numbers that appeared newly have passed 118 times ECM runs at level 35. Unknown factors have probably 30 digits or more.

March 18, 2010

RSALS and Jeff Gilchrist factored (16·10246-7)/9: c243 = P112 · P132. It's the largest SNFS factorization and P112 is the largest prime factor in our tables so far. Congratulations!

March 15, 2010

Factorizations of 599...99 have been extended up to n=300. Composite numbers that appeared newly have passed 118 times ECM runs at level 35. Unknown factors have probably 30 digits or more.

March 10, 2010

Information of ECM efforts is available in the Contributions page.

March 8, 2010

Dmitry Domanov found 4 primes and 68 PRPs by using Prime95 v25.11 and pfgw. 2·10113941+9 is the largest unprovable quasi-repdigit PRP in our tables so far. Congratulations!

  1. 6·1086287+1 = 6(0)862861<86288> is prime.
  2. 7·1020310+1 = 7(0)203091<20311> is prime.
  3. 7·1020360+1 = 7(0)203591<20361> is prime.
  4. 9·1091836+1 = 9(0)918351<91837> is prime.
  5. 2·1042762-7 = 1(9)427613<42763> is PRP.
  6. 2·1090597-7 = 1(9)905963<90598> is PRP.
  7. 2·1010856-3 = 1(9)108557<10857> is PRP.
  8. 2·1025959-3 = 1(9)259587<25960> is PRP.
  9. 2·1064882-3 = 1(9)648817<64883> is PRP.
  10. 2·1027217+3 = 2(0)272163<27218> is PRP.
  11. 2·1027693+3 = 2(0)276923<27694> is PRP.
  12. 2·1026669+9 = 2(0)266689<26670> is PRP.
  13. 2·10113941+9 = 2(0)1139409<113942> is PRP.
  14. 5·1020718-7 = 4(9)207173<20719> is PRP.
  15. 5·1051163-7 = 4(9)511623<51164> is PRP.
  16. 5·1035326-3 = 4(9)353257<35327> is PRP.
  17. 5·1036991-3 = 4(9)369907<36992> is PRP.
  18. 5·1059586-3 = 4(9)595857<59587> is PRP.
  19. 5·1088261-3 = 4(9)882607<88262> is PRP.
  20. 5·1019737+3 = 5(0)197363<19738> is PRP.
  21. 5·1032197+3 = 5(0)321963<32198> is PRP.
  22. 5·1051508+3 = 5(0)515073<51509> is PRP.
  23. 5·1058275+3 = 5(0)582743<58276> is PRP.
  24. 5·1062233+3 = 5(0)622323<62234> is PRP.
  25. 5·1090033+3 = 5(0)900323<90034> is PRP.
  26. 5·1024853+9 = 5(0)248529<24854> is PRP.
  27. 5·1039629+9 = 5(0)396289<39630> is PRP.
  28. 5·1053492+9 = 5(0)534919<53493> is PRP.
  29. 5·1071237+9 = 5(0)712369<71238> is PRP.
  30. 5·1072302+9 = 5(0)723019<72303> is PRP.
  31. 5·1081653+9 = 5(0)816529<81654> is PRP.
  32. 6·1013936-7 = 5(9)139353<13937> is PRP.
  33. 6·1016486-7 = 5(9)164853<16487> is PRP.
  34. 6·1085910-7 = 5(9)859093<85911> is PRP.
  35. 6·1014927+7 = 6(0)149267<14928> is PRP.
  36. 6·1034562+7 = 6(0)345617<34563> is PRP.
  37. 6·1064387+7 = 6(0)643867<64388> is PRP.
  38. 6·1071299+7 = 6(0)712987<71300> is PRP.
  39. 6·1071951+7 = 6(0)719507<71952> is PRP.
  40. 7·1034943-9 = 6(9)349421<34944> is PRP.
  41. 7·1037652-9 = 6(9)376511<37653> is PRP.
  42. 7·1038108-9 = 6(9)381071<38109> is PRP.
  43. 7·1038686-9 = 6(9)386851<38687> is PRP.
  44. 7·1039384-9 = 6(9)393831<39385> is PRP.
  45. 7·1043393-9 = 6(9)433921<43394> is PRP.
  46. 7·1047280-9 = 6(9)472791<47281> is PRP.
  47. 7·1055030-9 = 6(9)550291<55031> is PRP.
  48. 7·1010491-3 = 6(9)104907<10492> is PRP.
  49. 7·1011199-3 = 6(9)111987<11200> is PRP.
  50. 7·1012190-3 = 6(9)121897<12191> is PRP.
  51. 7·1033594-3 = 6(9)335937<33595> is PRP.
  52. 7·1038256-3 = 6(9)382557<38257> is PRP.
  53. 7·1089169-3 = 6(9)891687<89170> is PRP.
  54. 7·1063351+9 = 7(0)633509<63352> is PRP.
  55. 8·1048081-9 = 7(9)480801<48082> is PRP.
  56. 8·1015789-7 = 7(9)157883<15790> is PRP.
  57. 8·1023074-7 = 7(9)230733<23075> is PRP.
  58. 8·1038466-7 = 7(9)384653<38467> is PRP.
  59. 8·1068400-7 = 7(9)683993<68401> is PRP.
  60. 8·1020911+9 = 8(0)209109<20912> is PRP.
  61. 8·1024345+9 = 8(0)243449<24346> is PRP.
  62. 8·1031964+9 = 8(0)319639<31965> is PRP.
  63. 8·1067742+9 = 8(0)677419<67743> is PRP.
  64. 9·1023640-7 = 8(9)236393<23641> is PRP.
  65. 9·1031440-7 = 8(9)314393<31441> is PRP.
  66. 9·1031839-7 = 8(9)318383<31840> is PRP.
  67. 9·1032287-7 = 8(9)322863<32288> is PRP.
  68. 9·1021604+7 = 9(0)216037<21605> is PRP.
  69. 9·1025891+7 = 9(0)258907<25892> is PRP.
  70. 9·1026725+7 = 9(0)267247<26726> is PRP.
  71. 9·1034838+7 = 9(0)348377<34839> is PRP.
  72. 9·1067468+7 = 9(0)674677<67469> is PRP.

March 5, 2010

Robert Backstrom factored (71·10189+1)/9: c186 = P93 · P93. It's the second largest nice split so far in our tables. Congratulations!

March 4, 2010

Factorizations of 811...113 and Factorizations of 811...117 have been extended up to n=200. Composite numbers that appeared newly have passed 118 times ECM runs at level 35. Unknown factors have probably 30 digits or more.

February 2010

February 25, 2010

Erik Branger found the following 22 PRPs.

  1. (7·1018895-1)/3 = 2(3)18895<18896> is PRP.
  2. (25·1015795-7)/9 = 2(7)15795<15796> is PRP.
  3. (25·1022535-7)/9 = 2(7)22535<22536> is PRP.
  4. (25·1027752-7)/9 = 2(7)27752<27753> is PRP.
  5. (28·1015892-1)/9 = 3(1)15892<15893> is PRP.
  6. (28·1024022-1)/9 = 3(1)24022<24023> is PRP.
  7. (28·1027041-1)/9 = 3(1)27041<27042> is PRP.
  8. (13·1015206-1)/3 = 4(3)15206<15207> is PRP.
  9. (13·1024041-1)/3 = 4(3)24041<24042> is PRP.
  10. (13·1025321-1)/3 = 4(3)25321<25322> is PRP.
  11. (43·1021823-7)/9 = 4(7)21823<21824> is PRP.
  12. (46·1012390-1)/9 = 5(1)12390<12391> is PRP.
  13. (46·1028608-1)/9 = 5(1)28608<28609> is PRP.
  14. (52·1013344-7)/9 = 5(7)13344<13345> is PRP.
  15. (22·1011039-1)/3 = 7(3)11039<11040> is PRP.
  16. (22·1011247-1)/3 = 7(3)11247<11248> is PRP.
  17. (22·1013275-1)/3 = 7(3)13275<13276> is PRP.
  18. (22·1016781-1)/3 = 7(3)16781<16782> is PRP.
  19. (22·1020138-1)/3 = 7(3)20138<20139> is PRP.
  20. (79·1015210-7)/9 = 8(7)15210<15211> is PRP.
  21. (82·1018592-1)/9 = 9(1)18592<18593> is PRP.
  22. (88·1011395-7)/9 = 9(7)11395<11396> is PRP.

February 24, 2010

Factorizations of 166...667 have been extended up to n=300. Composite numbers that appeared newly have passed 118 times ECM runs at level 35. Unknown factors have probably 30 digits or more.

February 22, 2010

The Factorizations of Phi_n(10) had been updated. Click numbers followed by three dots to view all digits of Φn(10) (n≤100000) and those factors. This function uses JavaScript and Java applet.

February 21, 2010

Factorizations of 866...669, Factorizations of 877...771, Factorizations of 877...773 and Factorizations of 877...779 have been extended up to n=150. Composite numbers that appeared newly have passed 118 times ECM runs at level 35. Unknown factors have probably 30 digits or more.

February 15, 2010

Factorizations of 499...99 have been extended up to n=300. Composite numbers that appeared newly have passed 118 times ECM runs at level 35. Unknown factors have probably 30 digits or more.

Factorizations of 855...551, Factorizations of 855...553, Factorizations of 855...557 and Factorizations of 855...559 have been extended up to n=150. Composite numbers that appeared newly have passed 118 times ECM runs at level 35. Unknown factors have probably 30 digits or more.

February 8, 2010

Markus Tervooren factored 8·10244-1 : c164 = P60 · P104 by gnfs. It's the largest number factored by gnfs in our table so far. Congratulations!

February 5, 2010

Factorizations of 788...883 and Factorizations of 788...889 have been extended up to n=200. Composite numbers that appeared newly have passed 118 times ECM runs at level 35. Unknown factors have probably 30 digits or more.

February 4, 2010

JPascoa factored (73·10218-1)/9 : c156 = P58 · P99 by gnfs. It's the largest number factored by gnfs in our table so far. Congratulations!

February 1, 2010

Erik Branger reported 20 PRPs. (2·1015617+7)/9 = (2)156163<15617>, (2·1026459+7)/9 = (2)264583<26459>, (2·1010391+61)/9 = (2)103909<10391>, (2·1012105+61)/9 = (2)121049<12105>, (2·1019616+61)/9 = (2)196159<19616>, (4·1012338-31)/9 = (4)123371<12338>, (4·1020194-31)/9 = (4)201931<20194>, (4·1028934+23)/9 = (4)289337<28934>, (4·1020208+41)/9 = (4)202079<20208>, (5·1018522+13)/9 = (5)185217<18522>, (2·1010392-17)/3 = (6)103911<10392>, (2·1012458-17)/3 = (6)124571<12458>, (2·1021057-17)/3 = (6)210561<21057>, (2·1026223-17)/3 = (6)262221<26223>, (7·1021167-43)/9 = (7)211663<21167>, (8·1027811-71)/9 = (8)278101<27811>, (8·1029188-71)/9 = (8)291871<29188>, (8·1018173-53)/9 = (8)181723<18173>, (8·1018971-53)/9 = (8)189703<18971>, (8·1021906-17)/9 = (8)219057<21906>.

January 2010

January 27, 2010

Factorizations of 766...661, Factorizations of 766...663 and Factorizations of 766...669 have been extended up to n=200. Composite numbers that appeared newly have passed 118 times ECM runs at level 35. Unknown factors have probably 30 digits or more.

January 25, 2010

Records were changed. Top 100 big SNFS factorizations are not sorted by the composite number but sorted by the value of the polynomial.

January 22, 2010

RSALS + Jeff Gilchrist factored 2·10229+9 = c230 = P109 · P121. c230 is the third largest number factored by snfs in our tables so far. And also, P109 is the second largest prime factor found by snfs in our tables so far. Congratulations! P109 is almost the number one. Markus Tervooren's P110 has been submitted only 28 hours ago.

January 20, 2010

Markus Tervooren factored 6·10242+1 = c243 = P110 · P134. c243 is the largest number factored by snfs in our tables so far. And also, P110 is the largest prime factor found by snfs in our tables so far. Congratulations!

January 14, 2010

Factorizations of 844...441, Factorizations of 844...443, Factorizations of 844...447 and Factorizations of 844...449 have been extended up to n=150. Composite numbers that appeared newly have passed 118 times ECM runs at level 35. Unknown factors have probably 30 digits or more.

January 7, 2010

Factorizations of 822...229 and Factorizations of 833...339 have been extended up to n=150. Composite numbers that appeared newly have passed 118 times ECM runs at level 35. Unknown factors have probably 30 digits or more.

Factorizations of 755...559 have been extended up to n=200. Composite numbers that appeared newly have passed 118 times ECM runs at level 35. Unknown factors have probably 30 digits or more.

January 4, 2010

Factorizations of 822...227 have been extended up to n=150. Composite numbers that appeared newly have passed 118 times ECM runs at level 35. Unknown factors have probably 30 digits or more.

Factorizations of 755...551 and Factorizations of 755...553 have been extended up to n=200. Composite numbers that appeared newly have passed 118 times ECM runs at level 35. Unknown factors have probably 30 digits or more.

January 3, 2010

Robert Backstrom factored c241 = P65 · P66 · P111. c241 is the largest number factored by snfs in our tables so far. Congratulations!