Table of contents

  1. December 2014
  2. November 2014
  3. October 2014
  4. September 2014
  5. August 2014
  6. July 2014
  7. June 2014
  8. May 2014
  9. April 2014
  10. March 2014
  11. February 2014
  12. January 2014

December 2014

December 30, 2014

Bob Price found 2 near-repdigit PRPs.

Unprovable near-repdigit PRPs
 digitsflabelwlabelexpressionwhenwho
106773235777757w(52·1077322-7)/9December 30, 2014Bob Price
111750285777757w(52·1075027-7)/9December 30, 2014Bob Price

December 27, 2014

Serge Batalov found three near-repdigit PRPs. Three small primes of the form (10n+269)/9; n=2, 8 and 56 had been known. The next PRP was found at n=675470 after a long gap.

Unprovable near-repdigit PRPs
 digitsflabelwlabelexpressionwhenwho
2718580111411w41(10718580+269)/9December 27, 2014Serge Batalov
3685224111211w21(10685224+89)/9December 27, 2014Serge Batalov
4675470111411w41(10675470+269)/9December 27, 2014Serge Batalov

Bob Price found 2 near-repdigit PRPs.

Unprovable near-repdigit PRPs
 digitsflabelwlabelexpressionwhenwho
91878647333373w(22·1087863-1)/3December 27, 2014Bob Price
109753697333373w(22·1075368-1)/3December 27, 2014Bob Price

December 26, 2014

Serge Batalov found 3 near-repdigit PRPs.

Unprovable near-repdigit PRPs
 digitsflabelwlabelexpressionwhenwho
2427912111211w21(10427912+89)/9December 26, 2014Serge Batalov
7249010999799w7910249010-21December 26, 2014Serge Batalov
10230706111311w31(10230706+179)/9December 26, 2014Serge Batalov

December 25, 2014

Serge Batalov found 78 near-repdigit PRPs.

Unprovable near-repdigit PRPs
 digitsflabelwlabelexpressionwhenwho
822406317111171w(154·10224061-1)/9December 25, 2014Serge Batalov
9221654111311w31(10221654+179)/9December 25, 2014Serge Batalov
1121736212111121w(109·10217360-1)/9December 25, 2014Serge Batalov
1221278118111181w(163·10212779-1)/9December 25, 2014Serge Batalov
13211610111011w01(10211610-91)/9December 25, 2014Serge Batalov
1420150616111161w(145·10201504-1)/9December 25, 2014Serge Batalov
1520074819111191w(172·10200746-1)/9December 25, 2014Serge Batalov
16200001333833w83(10200001+149)/3December 25, 2014Serge Batalov
1719548034333343w(103·10195478-1)/3December 25, 2014Serge Batalov
1819415237333373w(112·10194150-1)/3December 25, 2014Serge Batalov
19189385333133w13(10189385-61)/3December 25, 2014Serge Batalov
20188164111511w51(10188164+359)/9December 25, 2014Serge Batalov
2218322918111181w(163·10183227-1)/9December 25, 2014Serge Batalov
23181182999799w7910181182-21December 25, 2014Serge Batalov
24180979999899w8910180979-11December 25, 2014Serge Batalov
25178695999299w2910178695-71December 25, 2014Serge Batalov
2617775615111151w(136·10177754-1)/9December 25, 2014Serge Batalov
2717286438333383w(115·10172862-1)/3December 25, 2014Serge Batalov
2816933917111171w(154·10169337-1)/9December 25, 2014Serge Batalov
3016215538333383w(115·10162153-1)/3December 25, 2014Serge Batalov
3115973815111151w(136·10159736-1)/9December 25, 2014Serge Batalov
32157792111511w51(10157792+359)/9December 25, 2014Serge Batalov
3315487138333383w(115·10154869-1)/3December 25, 2014Serge Batalov
3415381217111171w(154·10153810-1)/9December 25, 2014Serge Batalov
3515302737333373w(112·10153025-1)/3December 25, 2014Serge Batalov
36150029999599w5910150029-41December 25, 2014Serge Batalov
39142699111511w51(10142699+359)/9December 25, 2014Serge Batalov
40142425111511w51(10142425+359)/9December 25, 2014Serge Batalov
4114035937333373w(112·10140357-1)/3December 25, 2014Serge Batalov
42135011111911w91(10135011+719)/9December 25, 2014Serge Batalov
43134385111911w91(10134385+719)/9December 25, 2014Serge Batalov
4513233937333373w(112·10132337-1)/3December 25, 2014Serge Batalov
46129051333233w23(10129051-31)/3December 25, 2014Serge Batalov
4712786032333323w(97·10127858-1)/3December 25, 2014Serge Batalov
4812684135333353w(106·10126839-1)/3December 25, 2014Serge Batalov
49125792111011w01(10125792-91)/9December 25, 2014Serge Batalov
50125706333833w83(10125706+149)/3December 25, 2014Serge Batalov
5112529419111191w(172·10125292-1)/9December 25, 2014Serge Batalov
53120782333433w43(10120782+29)/3December 25, 2014Serge Batalov
54120574111511w51(10120574+359)/9December 25, 2014Serge Batalov
5512039737333373w(112·10120395-1)/3December 25, 2014Serge Batalov
56119880111311w31(10119880+179)/9December 25, 2014Serge Batalov
57118324111511w51(10118324+359)/9December 25, 2014Serge Batalov
58117059999299w2910117059-71December 25, 2014Serge Batalov
5911661216111161w(145·10116610-1)/9December 25, 2014Serge Batalov
6011579632333323w(97·10115794-1)/3December 25, 2014Serge Batalov
6111422816111161w(145·10114226-1)/9December 25, 2014Serge Batalov
66104212999299w2910104212-71December 25, 2014Serge Batalov
7198890333833w83(1098890+149)/3December 25, 2014Serge Batalov
8189160333433w43(1089160+29)/3December 25, 2014Serge Batalov
9083916111611w61(1083916+449)/9December 25, 2014Serge Batalov
9281363111911w91(1081363+719)/9December 25, 2014Serge Batalov
9381353111611w61(1081353+449)/9December 25, 2014Serge Batalov
9877637111511w51(1077637+359)/9December 25, 2014Serge Batalov
10672097333833w83(1072097+149)/3December 25, 2014Serge Batalov
11071223333533w53(1071223+59)/3December 25, 2014Serge Batalov
11468078333533w53(1068078+59)/3December 25, 2014Serge Batalov
11767404111311w31(1067404+179)/9December 25, 2014Serge Batalov
11966650333833w83(1066650+149)/3December 25, 2014Serge Batalov
13062451333733w73(1062451+119)/3December 25, 2014Serge Batalov
13756781333233w23(1056781-31)/3December 25, 2014Serge Batalov
14454038333233w23(1054038-31)/3December 25, 2014Serge Batalov
14553991111311w31(1053991+179)/9December 25, 2014Serge Batalov
14653859333833w83(1053859+149)/3December 25, 2014Serge Batalov
15651652333233w23(1051652-31)/3December 25, 2014Serge Batalov
15851364333733w73(1051364+119)/3December 25, 2014Serge Batalov
16549806333733w73(1049806+119)/3December 25, 2014Serge Batalov
17148604333233w23(1048604-31)/3December 25, 2014Serge Batalov
18441908333233w23(1041908-31)/3December 25, 2014Serge Batalov
18541756333433w43(1041756+29)/3December 25, 2014Serge Batalov
19140984333733w73(1040984+119)/3December 25, 2014Serge Batalov
19340038333233w23(1040038-31)/3December 25, 2014Serge Batalov
20737473333733w73(1037473+119)/3December 25, 2014Serge Batalov
22034613111311w31(1034613+179)/9December 25, 2014Serge Batalov
22233886111711w71(1033886+539)/9December 25, 2014Serge Batalov
22433102111011w01(1033102-91)/9December 25, 2014Serge Batalov
23031574333733w73(1031574+119)/3December 25, 2014Serge Batalov
23230384333133w13(1030384-61)/3December 25, 2014Serge Batalov

December 24, 2014

Serge Batalov found 26 near-repdigit PRPs.

Unprovable near-repdigit PRPs
 digitsflabelwlabelexpressionwhenwho
1711040737333373w(112·10110405-1)/3December 24, 2014Serge Batalov
2010347615111151w(136·10103474-1)/9December 24, 2014Serge Batalov
309015732333323w(97·1090155-1)/3December 24, 2014Serge Batalov
348846135333353w(106·1088459-1)/3December 24, 2014Serge Batalov
368698416111161w(145·1086982-1)/9December 24, 2014Serge Batalov
398413632333323w(97·1084134-1)/3December 24, 2014Serge Batalov
527176216111161w(145·1071760-1)/9December 24, 2014Serge Batalov
606675717111171w(154·1066755-1)/9December 24, 2014Serge Batalov
636604538333383w(115·1066043-1)/3December 24, 2014Serge Batalov
696320419111191w(172·1063202-1)/9December 24, 2014Serge Batalov
716207538333383w(115·1062073-1)/3December 24, 2014Serge Batalov
755741634333343w(103·1057414-1)/3December 24, 2014Serge Batalov
825472918111181w(163·1054727-1)/9December 24, 2014Serge Batalov
985003735333353w(106·1050035-1)/3December 24, 2014Serge Batalov
994977615111151w(136·1049774-1)/9December 24, 2014Serge Batalov
1054802835333353w(106·1048026-1)/3December 24, 2014Serge Batalov
1094399735333353w(106·1043995-1)/3December 24, 2014Serge Batalov
1144290634333343w(103·1042904-1)/3December 24, 2014Serge Batalov
1164161016111161w(145·1041608-1)/9December 24, 2014Serge Batalov
1303796212111121w(109·1037960-1)/9December 24, 2014Serge Batalov
1333786634333343w(103·1037864-1)/3December 24, 2014Serge Batalov
1413590131333313w(94·1035899-1)/3December 24, 2014Serge Batalov
1453515919111191w(172·1035157-1)/9December 24, 2014Serge Batalov
1483330538333383w(115·1033303-1)/3December 24, 2014Serge Batalov
1513227735333353w(106·1032275-1)/3December 24, 2014Serge Batalov
1573001334333343w(103·1030011-1)/3December 24, 2014Serge Batalov

December 22, 2014

Bob Price found a near-repdigit PRP.

Unprovable near-repdigit PRPs
 digitsflabelwlabelexpressionwhenwho
41754994777747w(43·1075498-7)/9December 22, 2014Bob Price

December 21, 2014

Bob Price found a near-repdigit PRP.

Unprovable near-repdigit PRPs
 digitsflabelwlabelexpressionwhenwho
78515124333343w(13·1051511-1)/3December 21, 2014Bob Price

December 19, 2014

Prime factorization tables of the following 12 near-repdigit sequences were added. All composite factors on the tables had passed the level 35 of ECM 118 times. Most unknown factors are supposed to be larger than 1030.

December 17, 2014

Bob Price found a near-repdigit PRP.

Unprovable near-repdigit PRPs
 digitsflabelwlabelexpressionwhenwho
22955752777727w(25·1095574-7)/9December 17, 2014Bob Price

December 6, 2014

Prime factorization tables of the following 18 near-repdigit sequences were added. All composite factors on the tables had passed the level 35 of ECM 118 times. Most unknown factors are supposed to be larger than 1030.

December 5, 2014

Bob Price found 11 near-repdigit PRPs.

Unprovable near-repdigit PRPs
 digitsflabelwlabelexpressionwhenwho
2789189444494w9(4·1089189+41)/9December 5, 2014Bob Price
2888680333373w7(1088680+11)/3December 5, 2014Bob Price
35786369111191w(82·1078635-1)/9December 5, 2014Bob Price
37782439777797w(88·1078242-7)/9December 5, 2014Bob Price
4074350333373w7(1074350+11)/3December 5, 2014Bob Price
4372821111191w9(1072821+71)/9December 5, 2014Bob Price
4769674888838w3(8·1069674-53)/9December 5, 2014Bob Price
5067796444474w7(4·1067796+23)/9December 5, 2014Bob Price
5266284444474w7(4·1066284+23)/9December 5, 2014Bob Price
5464715555535w3(5·1064715-23)/9December 5, 2014Bob Price
7552740444494w9(4·1052740+41)/9December 5, 2014Bob Price

November 2014

November 17, 2014

Prime factorization tables of the following 12 near-repdigit sequences were added. All composite factors on the tables had passed the level 35 of ECM 118 times. Most unknown factors are supposed to be larger than 1030.

November 8, 2014

Serge Batalov found 2 near-repdigit prime numbers. The larger one is the largest known near-repdigit prime number that was proved with CHG. Congratulations! CHG proof certificate is available.

Proven near-repdigit primes
 digitsflabelwlabelexpressionwhenwho
9388080 9v89w10388080-10112433-1November 8, 2014Serge Batalov
10388080 9v89w10388080-10180868-1November 8, 2014Serge Batalov

November 6, 2014

P.Kurtovic found 3 near-repdigit PRPs.

Unprovable near-repdigit PRPs
 digitsflabelwlabelexpressionwhenwho
4465009 9w89991065009-1001November 6, 2014P.Kurtovic
5655596 9w89991055596-1001November 6, 2014P.Kurtovic
7745205 9w89991045205-1001November 6, 2014P.Kurtovic

November 3, 2014

P.Kurtovic found 1 near-repdigit PRP.

Unprovable near-repdigit PRPs
 digitsflabelwlabelexpressionwhenwho
62481468111181w(73·10248145-1)/9November 3, 2014P.Kurtovic

November 2, 2014

P.Kurtovic found 1 near-repdigit PRP.

Unprovable near-repdigit PRPs
 digitsflabelwlabelexpressionwhenwho
161049438111181w(73·10104942-1)/9November 2, 2014P.Kurtovic

October 2014

October 31, 2014

Serge Batalov found the largest known unprovable quasi-repdigit PRP (except platequ and depression PRPs). Congratulations!

Unprovable quasi-repdigit PRPs (except pd)
 digitsflabelwlabelexpressionwhenwho
12807111666716w7(5·10280710+1)/3October 31, 2014Serge Batalov

October 29, 2014

P.Kurtovic found 1 near-repdigit PRP and 1 quasi-repdigit PRP.

Unprovable near-repdigit PRPs
 digitsflabelwlabelexpressionwhenwho
1411210010111101w(91·10112098-1)/9October 29, 2014P.Kurtovic
Unprovable quasi-repdigit PRPs (except pd)
 digitsflabelwlabelexpressionwhenwho
22133585 551w(496·1033583-1)/9October 29, 2014P.Kurtovic

October 28, 2014

P.Kurtovic found 1 near-repdigit PRP.

Unprovable near-repdigit PRPs
 digitsflabelwlabelexpressionwhenwho
161007819111191w(82·10100780-1)/9October 28, 2014P.Kurtovic

Serge Batalov found 3 near-repdigit PRPs.

Unprovable near-repdigit PRPs
 digitsflabelwlabelexpressionwhenwho
81837613111131w(28·10183760-1)/9October 28, 2014Serge Batalov
91653593111131w(28·10165358-1)/9October 28, 2014Serge Batalov
121341233111131w(28·10134122-1)/9October 28, 2014Serge Batalov

October 27, 2014

P.Kurtovic found 2 near-repdigit PRPs.

Unprovable near-repdigit PRPs
 digitsflabelwlabelexpressionwhenwho
101225938111181w(73·10122592-1)/9October 27, 2014P.Kurtovic
30737159111191w(82·1073714-1)/9October 27, 2014P.Kurtovic

Serge Batalov found 4 near-repdigit PRPs.

Unprovable near-repdigit PRPs
 digitsflabelwlabelexpressionwhenwho
13991445111151w(46·1099143-1)/9October 27, 2014Serge Batalov
14967995111151w(46·1096798-1)/9October 27, 2014Serge Batalov
58511125111151w(46·1051111-1)/9October 27, 2014Serge Batalov
79400343111131w(28·1040033-1)/9October 27, 2014Serge Batalov

October 26, 2014

P.Kurtovic found 3 near-repdigit PRPs.

Unprovable near-repdigit PRPs
 digitsflabelwlabelexpressionwhenwho
23785778111181w(73·1078576-1)/9October 26, 2014P.Kurtovic
27716718111181w(73·1071670-1)/9October 26, 2014P.Kurtovic
53511638111181w(73·1051162-1)/9October 26, 2014P.Kurtovic

October 19, 2014

Bob Price found 3 near-repdigit PRPs.

Unprovable near-repdigit PRPs
 digitsflabelwlabelexpressionwhenwho
2770727777737w3(7·1070727-43)/9October 19, 2014Bob Price
3164568777737w3(7·1064568-43)/9October 19, 2014Bob Price
4155851777737w3(7·1055851-43)/9October 19, 2014Bob Price

October 16, 2014

P.Kurtovic found 3 near-repdigit-related primes.

Proven near-repdigit-related primes (except ru/nr/pd/qr)
 digitsflabelwlabelexpressionwhenwho
4181459251992519w252·1081456-1October 16, 2014P.Kurtovic
13548839251992519w252·1048836-1October 16, 2014P.Kurtovic
42030093251992519w252·1030090-1October 16, 2014P.Kurtovic

October 12, 2014

Bob Price found 1 near-repdigit PRP.

Unprovable near-repdigit PRPs
 digitsflabelwlabelexpressionwhenwho
4851054111131w3(1051054+17)/9October 12, 2014Bob Price

September 2014

September 22, 2014

Serge Batalov found the largest known unprovable near-repdigit PRP. Congratulations!

Unprovable near-repdigit PRPs
 digitsflabelwlabelexpressionwhenwho
17628127111171w(64·10762811-1)/9September 22, 2014Serge Batalov

September 21, 2014

Serge Batalov found the largest known unprovable plateau and depression PRP. Congratulations!

Unprovable plateau and depression PRPs
 digitsflabelwlabelexpressionwhenwho
14115919888998w9(89·10411590+1)/9September 21, 2014Serge Batalov

September 8, 2014

Erik Branger found 6 quasi-repdigit PRPs.

Unprovable quasi-repdigit PRPs (except pd)
 digitsflabelwlabelexpressionwhenwho
14994759666196w1(29·1099474-17)/3September 8, 2014Erik Branger
26900979666196w1(29·1090096-17)/3September 8, 2014Erik Branger
34835267333173w1(22·1083525-7)/3September 8, 2014Erik Branger
36817684666346w3(14·1081767-11)/3September 8, 2014Erik Branger
64637484666346w3(14·1063747-11)/3September 8, 2014Erik Branger
89530347333173w1(22·1053033-7)/3September 8, 2014Erik Branger

August 2014

August 17, 2014

Bob Price found 4 near-repdigit PRPs.

Unprovable near-repdigit PRPs
 digitsflabelwlabelexpressionwhenwho
1195072666616w1(2·1095072-17)/3August 17, 2014Bob Price
1392976666616w1(2·1092976-17)/3August 17, 2014Bob Price
1884904666616w1(2·1084904-17)/3August 17, 2014Bob Price
3064041666616w1(2·1064041-17)/3August 17, 2014Bob Price

July 2014

July 1, 2014

Factorizations of near-repdigit-related numbers has been moved.

June 2014

June 8, 2014

"Covering sets of sequences with 0.00% difficulty" was added to the bottom of primedifficulty.txt. "n mod 6" box shows how the sequence is covered by small prime factors and algebraic factors.

May 2014

May 19, 2014

Predrag Kurtovic found the 5th largest known near-repdigit prime. Congratulations!

Proven near-repdigit primes
 digitsflabelwlabelexpressionwhenwho
546600494999949w95·10466002-1May 19, 2014Predrag Kurtovic

May 12, 2014

Edward Trice found the 2nd largest known quasi-repdigit prime. Congratulations!

Proven quasi-repdigit primes (except pd)
 digitsflabelwlabelexpressionwhenwho
28308667000170w17·10830865+1May 12, 2014Edward Trice

May 8, 2014

Near-repdigit-related (probable) prime numbers has been moved.

P.Kurtovic found 1 quasi-repdigit prime.

Proven quasi-repdigit primes (except pd)
 digitsflabelwlabelexpressionwhenwho
168856317999179w18·1088561-1May 8, 2014P.Kurtovic

April 2014

April 12, 2014

P.Kurtovic found 1 quasi-repdigit prime.

Proven quasi-repdigit primes (except pd)
 digitsflabelwlabelexpressionwhenwho
216180667999679w68·1061804-1April 12, 2014P.Kurtovic

April 7, 2014

Factorizations of 11...11 (Repunit) and Primality certifications have been moved.

March 2014

March 24, 2014

I intend to move web pages, related to near-repdigit-related numbers, to mada.la.coocan.jp. Pages under Contributions and Graphs have been moved as a trial.

March 17, 2014

Erik Branger found 3 near-repdigit PRPs and 6 quasi-repdigit PRPs.

Unprovable near-repdigit PRPs
 digitsflabelwlabelexpressionwhenwho
29597972333323w(7·1059796-1)/3March 17, 2014Erik Branger
39531862333323w(7·1053185-1)/3March 17, 2014Erik Branger
44507032333323w(7·1050702-1)/3March 17, 2014Erik Branger
Unprovable quasi-repdigit PRPs (except pd)
 digitsflabelwlabelexpressionwhenwho
19959771666916w9(5·1095976+7)/3March 17, 2014Erik Branger
35810302666326w3(8·1081029-11)/3March 17, 2014Erik Branger
57648082333923w9(7·1064807+17)/3March 17, 2014Erik Branger
75552553666736w7(11·1055254+1)/3March 17, 2014Erik Branger
81532882333923w9(7·1053287+17)/3March 17, 2014Erik Branger
82532753666136w1(11·1053274-17)/3March 17, 2014Erik Branger

March 14, 2014

P.Kurtovic found 4 near-repdigit-related primes.

Proven near-repdigit-related primes (except ru/nr/pd/qr)
 digitsflabelwlabelexpressionwhenwho
2334098575001750w175·1040983+1March 14, 2014P.Kurtovic
23740840 550w155·1040838+1March 14, 2014P.Kurtovic
3423424475001750w175·1034242+1March 14, 2014P.Kurtovic
3693278675001750w175·1032784+1March 14, 2014P.Kurtovic

March 7, 2014

P.Kurtovic found 2 near-repdigit-related primes.

Proven near-repdigit-related primes (except ru/nr/pd/qr)
 digitsflabelwlabelexpressionwhenwho
1914424397001970w197·1044241+1March 7, 2014P.Kurtovic
3133609097001970w197·1036088+1March 7, 2014P.Kurtovic

February 2014

February 26, 2014

Factorizations of 399...991, Factorizations of 533...33, Factorizations of 799...99, Factorizations of 833...33, Factorizations of 88...889, Factorizations of 899...99 and Factorizations of 99...991 have been extended up to n=300. Added composite numbers had passed ECM iterations 118 times at the level 35. Most unknown factors are supposed to be greater than 1030.

February 19, 2014

Kenji Ibusuki successfully factored a 254-digit composite number (6·10256-1)/1483 into two prime factors, c254 = P81 · P174. It"s the biggest SNFS factorization in our tables so far. Congratulations!

January 2014

January 16, 2014

David Broadhurst found the record-breaking 69th prime number of the form 1903523558927331964461080487·10n-1. Congratulations!

Prime numbers of the form k·10n-1 (including 45 known prime numbers at least)
 digitsflabelwlabelexpressionwhenwho
3073609 19035235589273319644610804869w1903523558927331964461080487·1073581-1January 14, 2014David Broadhurst
3370538 19035235589273319644610804869w1903523558927331964461080487·1070510-1January 14, 2014David Broadhurst
4256844 19035235589273319644610804869w1903523558927331964461080487·1056816-1January 13, 2014David Broadhurst
4354984 19035235589273319644610804869w1903523558927331964461080487·1054956-1January 13, 2014David Broadhurst

January 8, 2014

Predrag Kurtovic found 1 near-repdigit-related prime.

Proven near-repdigit-related primes (except ru/nr/pd/qr)
 digitsflabelwlabelexpressionwhenwho
1804483481001810w181·1044832+1January 8, 2014Predrag Kurtovic

January 6, 2014

Stefano D"Urso found the 9th largest known near-repdigit prime. Congratulations!

Proven near-repdigit primes
 digitsflabelwlabelexpressionwhenwho
9369712 99999979w9999998·10369705-1January 6, 2014Stefano D"Urso
  1. The Prime Database: 9999998*10^369705-1 (Chris K. Caldwell)
  2. The Top Twenty: Near-repdigit (Chris K. Caldwell)