Table of contents

  1. December 2012
  2. November 2012
  3. October 2012
  4. September 2012
  5. August 2012
  6. July 2012
  7. June 2012
  8. May 2012
  9. April 2012
  10. March 2012
  11. February 2012
  12. January 2012

December 2012

December 31, 2012

Factorizations of 744...441 have been extended up to n=250. Added composite numbers had passed ECM iterations 118 times at the level 35. Most unknown factors are supposed to be greater than 1030.

December 29, 2012

Maksym Voznyy certificated the primality of the quasi-repdigit prime number 4·103131+3 by Primo. Certification is available.

Proven quasi-repdigit primes (except pd)
 digitsflabelwlabelexpressionwhenwho
29031324000340w34·103131+3December 29, 2012Maksym Voznyy

December 27, 2012

Factorizations of 733...339 have been extended up to n=250. Added composite numbers had passed ECM iterations 118 times at the level 35. Most unknown factors are supposed to be greater than 1030.

December 26, 2012

Maksym Voznyy certificated the primality of the quasi-repdigit prime number 6·103016+7 by Primo. Certification is available.

Proven quasi-repdigit primes (except pd)
 digitsflabelwlabelexpressionwhenwho
29730176000760w76·103016+7December 26, 2012Maksym Voznyy

December 24, 2012

Ray Chandler certificated 4 near-repdigit prime numbers, 40 quasi-repdigit prime numbers and 122 near-repdigit-related prime numbers by Primo. Certifications are available.

Proven near-repdigit primes
 digitsflabelwlabelexpressionwhenwho
4952676777877w87(7·102676+83)/9December 24, 2012Ray Chandler
4962671777877w87(7·102671+83)/9December 24, 2012Ray Chandler
4992622333133w13(102622-61)/3December 24, 2012Ray Chandler
5012610333433w43(102610+29)/3December 24, 2012Ray Chandler
Proven quasi-repdigit primes (except pd)
 digitsflabelwlabelexpressionwhenwho
33426871999719w72·102686-3December 24, 2012Ray Chandler
335268597111971w(874·102683-1)/9December 24, 2012Ray Chandler
3372684888238w23(8·102684-593)/9December 24, 2012Ray Chandler
3382681 8w11(8·102681-701)/9December 24, 2012Ray Chandler
340267940111401w(361·102677-1)/9December 24, 2012Ray Chandler
3412678888318w31(8·102678-521)/9December 24, 2012Ray Chandler
342267843441434w1(391·102676-31)/9December 24, 2012Ray Chandler
3432677999019w01102677-99December 24, 2012Ray Chandler
34426775779757w97(52·102676+173)/9December 24, 2012Ray Chandler
34526763000730w73·102675+7December 24, 2012Ray Chandler
34626759666796w7(29·102674+1)/3December 24, 2012Ray Chandler
347266945449454w9(409·102667+41)/9December 24, 2012Ray Chandler
3492669222072w07(2·102669-137)/9December 24, 2012Ray Chandler
351266261669616w9(185·102660+7)/3December 24, 2012Ray Chandler
3522661 4w99(4·102661+491)/9December 24, 2012Ray Chandler
353266061669616w9(185·102658+7)/3December 24, 2012Ray Chandler
354266056557565w7(509·102658+13)/9December 24, 2012Ray Chandler
355265982333823w(247·102657-1)/3December 24, 2012Ray Chandler
35626545444954w9(49·102653+41)/9December 24, 2012Ray Chandler
35726507666176w1(23·102649-17)/3December 24, 2012Ray Chandler
358265042447424w7(382·102648+23)/9December 24, 2012Ray Chandler
3592642444194w19(4·102642-229)/9December 24, 2012Ray Chandler
36126387115171w51(64·102637+359)/9December 24, 2012Ray Chandler
362263757557575w7(518·102635+13)/9December 24, 2012Ray Chandler
36326337110171w01(64·102632-91)/9December 24, 2012Ray Chandler
3652631 6w77(2·102631+31)/3December 24, 2012Ray Chandler
366263125221252w1(227·102629-11)/9December 24, 2012Ray Chandler
367263123223232w3(209·102629+7)/9December 24, 2012Ray Chandler
37026297339373w93(22·102628+179)/3December 24, 2012Ray Chandler
372262559559595w9(536·102623+31)/9December 24, 2012Ray Chandler
37526227997979w798·102621-21December 24, 2012Ray Chandler
378262086333863w(259·102618-1)/3December 24, 2012Ray Chandler
37926198992989w299·102618-71December 24, 2012Ray Chandler
3802619111271w27(102619+143)/9December 24, 2012Ray Chandler
381261658551585w1(527·102614-41)/9December 24, 2012Ray Chandler
382261628111281w(253·102614-1)/9December 24, 2012Ray Chandler
383261340111401w(361·102611-1)/9December 24, 2012Ray Chandler
384261156333563w(169·102609-1)/3December 24, 2012Ray Chandler
3852611 113w(34·102609-1)/3December 24, 2012Ray Chandler
386260850553505w3(455·102606-23)/9December 24, 2012Ray Chandler
Proven near-repdigit-related primes (except ru/nr/pd/qr)
 digitsflabelwlabelexpressionwhenwho
223826845227352w73(47·102683+457)/9December 24, 2012Ray Chandler
223926835880158w01(53·102682-791)/9December 24, 2012Ray Chandler
22402683 448w9(404·102681+1)/9December 24, 2012Ray Chandler
224126831001910w19102682+19December 24, 2012Ray Chandler
224426827663776w37(23·102681-89)/3December 24, 2012Ray Chandler
224626819773997w39(88·102680-349)/9December 24, 2012Ray Chandler
22472681 85w77(77·102680+193)/9December 24, 2012Ray Chandler
224826815770357w03(52·102680-673)/9December 24, 2012Ray Chandler
225026809885998w59(89·102679-269)/9December 24, 2012Ray Chandler
225326796881368w13(62·102678-683)/9December 24, 2012Ray Chandler
225426794558745w87(41·102678+283)/9December 24, 2012Ray Chandler
225526785663956w39(17·102677-83)/3December 24, 2012Ray Chandler
22562678 228w9(206·102676+1)/9December 24, 2012Ray Chandler
225726776770367w03(61·102676-673)/9December 24, 2012Ray Chandler
225926759002390w239·102674+23December 24, 2012Ray Chandler
226026749886998w69(89·102673-179)/9December 24, 2012Ray Chandler
22612674 445w3(401·102672-23)/9December 24, 2012Ray Chandler
226226744005740w574·102673+57December 24, 2012Ray Chandler
226426738660986w09(26·102672-173)/3December 24, 2012Ray Chandler
22652673 776w3(233·102671-11)/3December 24, 2012Ray Chandler
226826701886118w61(17·102669-251)/9December 24, 2012Ray Chandler
22702668 883w1(265·102666-7)/3December 24, 2012Ray Chandler
22712668 442w3(398·102666+7)/9December 24, 2012Ray Chandler
22722668 336w1(101·102666-17)/3December 24, 2012Ray Chandler
22742667 998w7(899·102665-17)/9December 24, 2012Ray Chandler
227626673991339w134·102666-87December 24, 2012Ray Chandler
22782666 559w756·102664-3December 24, 2012Ray Chandler
228026656771367w13(61·102664-583)/9December 24, 2012Ray Chandler
228126645225952w59(47·102663+331)/9December 24, 2012Ray Chandler
228226642662126w21(8·102663-137)/3December 24, 2012Ray Chandler
22832664 228w7(206·102662-17)/9December 24, 2012Ray Chandler
228526625228752w87(47·102661+583)/9December 24, 2012Ray Chandler
228626618332983w29(25·102660-13)/3December 24, 2012Ray Chandler
228726597887178w71(71·102658-161)/9December 24, 2012Ray Chandler
22882659 663w1(199·102657-7)/3December 24, 2012Ray Chandler
22892659 30w773·102658+77December 24, 2012Ray Chandler
229126577882378w23(71·102656-593)/9December 24, 2012Ray Chandler
229226569227192w71(83·102655+439)/9December 24, 2012Ray Chandler
229326559449794w97(85·102654+473)/9December 24, 2012Ray Chandler
229426555660956w09(17·102654-173)/3December 24, 2012Ray Chandler
229526553227932w79(29·102654+511)/9December 24, 2012Ray Chandler
229626552442924w29(22·102654-139)/9December 24, 2012Ray Chandler
229726543778137w81(34·102653+29)/9December 24, 2012Ray Chandler
229826543007930w793·102653+79December 24, 2012Ray Chandler
22992654 10w33102653+33December 24, 2012Ray Chandler
23002653 880w388·102651+3December 24, 2012Ray Chandler
230126536882168w21(62·102652-611)/9December 24, 2012Ray Chandler
230226535008950w895·102652+89December 24, 2012Ray Chandler
230326529883798w37(89·102651-467)/9December 24, 2012Ray Chandler
23042652 884w1(796·102650-31)/9December 24, 2012Ray Chandler
230726505882758w27(53·102649-557)/9December 24, 2012Ray Chandler
230926491447314w73(13·102648+257)/9December 24, 2012Ray Chandler
231026486112961w29(55·102647+161)/9December 24, 2012Ray Chandler
231126483446334w63(31·102647+167)/9December 24, 2012Ray Chandler
231226475774357w43(52·102646-313)/9December 24, 2012Ray Chandler
23132646 87w11(79·102645-601)/9December 24, 2012Ray Chandler
231426458665786w57(26·102644-29)/3December 24, 2012Ray Chandler
231526449773997w39(88·102643-349)/9December 24, 2012Ray Chandler
23162644 56w33(17·102643-101)/3December 24, 2012Ray Chandler
23172643 889w789·102641-3December 24, 2012Ray Chandler
23182643 883w7(265·102641+11)/3December 24, 2012Ray Chandler
231926433446134w61(31·102642+149)/9December 24, 2012Ray Chandler
232026432116321w63(19·102642+467)/9December 24, 2012Ray Chandler
232126427663776w37(23·102641-89)/3December 24, 2012Ray Chandler
232326406996169w617·102639-39December 24, 2012Ray Chandler
232426404331943w19(13·102639-43)/3December 24, 2012Ray Chandler
232526391997319w732·102638-27December 24, 2012Ray Chandler
232626381445714w57(13·102637+113)/9December 24, 2012Ray Chandler
232826369112991w29(82·102635+161)/9December 24, 2012Ray Chandler
23292636 56w33(17·102635-101)/3December 24, 2012Ray Chandler
233126356003760w376·102634+37December 24, 2012Ray Chandler
23332634 559w156·102632-9December 24, 2012Ray Chandler
233426343114731w47(28·102633+323)/9December 24, 2012Ray Chandler
233526342558125w81(23·102633+229)/9December 24, 2012Ray Chandler
233626342448724w87(22·102633+383)/9December 24, 2012Ray Chandler
23382633 74w11(67·102632-301)/9December 24, 2012Ray Chandler
233926333557935w79(32·102632+211)/9December 24, 2012Ray Chandler
234026332990329w033·102632-97December 24, 2012Ray Chandler
234226316551965w19(59·102630-329)/9December 24, 2012Ray Chandler
234326311227312w73(11·102630+457)/9December 24, 2012Ray Chandler
234426308559785w97(77·102629+373)/9December 24, 2012Ray Chandler
234526305887158w71(53·102629-161)/9December 24, 2012Ray Chandler
23472630 12w99(11·102629+691)/9December 24, 2012Ray Chandler
23492629 86w99(26·102628+97)/3December 24, 2012Ray Chandler
235026295773157w31(52·102628-421)/9December 24, 2012Ray Chandler
23512629 448w1(404·102627-71)/9December 24, 2012Ray Chandler
235226271442314w23(13·102626-193)/9December 24, 2012Ray Chandler
235326271223912w39(11·102626+151)/9December 24, 2012Ray Chandler
235526266886368w63(62·102625-233)/9December 24, 2012Ray Chandler
235626241778917w89(16·102623+101)/9December 24, 2012Ray Chandler
235726238997189w719·102622-29December 24, 2012Ray Chandler
235826235995359w536·102622-47December 24, 2012Ray Chandler
236026232002720w272·102622+27December 24, 2012Ray Chandler
236126227336773w67(22·102621+101)/3December 24, 2012Ray Chandler
236326219339193w91(28·102620+173)/3December 24, 2012Ray Chandler
236426209110391w03(82·102619-73)/9December 24, 2012Ray Chandler
236526208554985w49(77·102619-59)/9December 24, 2012Ray Chandler
23692619 224w7(202·102617+23)/9December 24, 2012Ray Chandler
237026188553185w31(77·102617-221)/9December 24, 2012Ray Chandler
23712618 331w9(298·102616+71)/9December 24, 2012Ray Chandler
237226182669326w93(8·102617+79)/3December 24, 2012Ray Chandler
23732617 229w323·102615-7December 24, 2012Ray Chandler
237426167886378w63(71·102615-233)/9December 24, 2012Ray Chandler
23752616 56w33(17·102615-101)/3December 24, 2012Ray Chandler
237626154009340w934·102614+93December 24, 2012Ray Chandler
23782614 59w336·102613-67December 24, 2012Ray Chandler
237926145882158w21(53·102613-611)/9December 24, 2012Ray Chandler
238026135004150w415·102612+41December 24, 2012Ray Chandler
238126131221312w13(11·102612-83)/9December 24, 2012Ray Chandler
238226127447174w71(67·102611+239)/9December 24, 2012Ray Chandler
238326126445364w53(58·102611+77)/9December 24, 2012Ray Chandler
238426125110351w03(46·102611-73)/9December 24, 2012Ray Chandler
238526122668726w87(8·102611+61)/3December 24, 2012Ray Chandler
238626107221372w13(65·102609-83)/9December 24, 2012Ray Chandler
238826071003710w37102606+37December 24, 2012Ray Chandler
238926061552315w23(14·102605-293)/9December 24, 2012Ray Chandler
239126049884998w49(89·102603-359)/9December 24, 2012Ray Chandler
239226049557195w71(86·102603+139)/9December 24, 2012Ray Chandler
23952603 28w77(26·102602-107)/9December 24, 2012Ray Chandler
239626023223932w39(29·102601+151)/9December 24, 2012Ray Chandler
23972600 76w99(23·102599+97)/3December 24, 2012Ray Chandler
239826006334963w49(19·102599+47)/3December 24, 2012Ray Chandler

Factorizations of 733...33 have been extended up to n=250. Added composite numbers had passed ECM iterations 118 times at the level 35. Most unknown factors are supposed to be greater than 1030.

December 23, 2012

Ray Chandler successfully proved the primality of a 10625-digit prime number Phi(26570,10) by Primo. Congratulations! Certification is available.

December 20, 2012

Ray Chandler certificated 5 near-repdigit prime numbers, 41 quasi-repdigit prime numbers and 131 near-repdigit-related prime numbers by Primo. Certifications are available.

Proven near-repdigit primes
 digitsflabelwlabelexpressionwhenwho
5042557 9w49999102557-50001December 20, 2012Ray Chandler
505255535333353w(106·102553-1)/3December 20, 2012Ray Chandler
5062546 9w299999999102546-700000001December 20, 2012Ray Chandler
5082526 9w79999102526-20001December 20, 2012Ray Chandler
510251415111151w(136·102512-1)/9December 20, 2012Ray Chandler
Proven quasi-repdigit primes (except pd)
 digitsflabelwlabelexpressionwhenwho
34025982115121w51(19·102597+359)/9December 20, 2012Ray Chandler
34225944991949w195·102593-81December 20, 2012Ray Chandler
3432594444234w23(4·102594-193)/9December 20, 2012Ray Chandler
344259345443454w3(409·102591-13)/9December 20, 2012Ray Chandler
34525926444764w7(58·102591+23)/9December 20, 2012Ray Chandler
346259079779797w9(718·102588+11)/9December 20, 2012Ray Chandler
348258617113171w3(154·102584+17)/9December 20, 2012Ray Chandler
34925838775787w57(79·102582-187)/9December 20, 2012Ray Chandler
3502581999019w01102581-99December 20, 2012Ray Chandler
352258123777237w(214·102579-7)/9December 20, 2012Ray Chandler
3532573222472w47(2·102573+223)/9December 20, 2012Ray Chandler
3542571666016w01(2·102571-197)/3December 20, 2012Ray Chandler
355257125777257w(232·102569-7)/9December 20, 2012Ray Chandler
3572565444314w31(4·102565-121)/9December 20, 2012Ray Chandler
35825644999149w15·102563-9December 20, 2012Ray Chandler
36025639222192w1(83·102562-11)/9December 20, 2012Ray Chandler
36225568335383w53(25·102555+59)/3December 20, 2012Ray Chandler
36325557444974w9(67·102554+41)/9December 20, 2012Ray Chandler
36425545339353w93(16·102553+179)/3December 20, 2012Ray Chandler
365255410119101w9(91·102552+71)/9December 20, 2012Ray Chandler
36625477555175w1(68·102546-41)/9December 20, 2012Ray Chandler
367254654559545w9(491·102544+31)/9December 20, 2012Ray Chandler
368254595111951w(856·102543-1)/9December 20, 2012Ray Chandler
369254297333973w(292·102540-1)/3December 20, 2012Ray Chandler
37025406337363w73(19·102539+119)/3December 20, 2012Ray Chandler
372253370333703w(211·102531-1)/3December 20, 2012Ray Chandler
3732533555215w21(5·102533-311)/9December 20, 2012Ray Chandler
374253263661636w1(191·102530-17)/3December 20, 2012Ray Chandler
375253240449404w9(364·102530+41)/9December 20, 2012Ray Chandler
3762529111371w37(102529+233)/9December 20, 2012Ray Chandler
377252416113161w3(145·102522+17)/9December 20, 2012Ray Chandler
37825195990959w096·102518-91December 20, 2012Ray Chandler
379251931777317w(286·102517-7)/9December 20, 2012Ray Chandler
38025168555985w9(77·102515+31)/9December 20, 2012Ray Chandler
38125142772727w27(25·102513-457)/9December 20, 2012Ray Chandler
38425086444364w3(58·102507-13)/9December 20, 2012Ray Chandler
385250848777487w(439·102506-7)/9December 20, 2012Ray Chandler
3862506222312w31(2·102506+79)/9December 20, 2012Ray Chandler
38725033770737w07(34·102502-637)/9December 20, 2012Ray Chandler
38825027112171w21(64·102501+89)/9December 20, 2012Ray Chandler
389250020229202w9(182·102498+61)/9December 20, 2012Ray Chandler
Proven near-repdigit-related primes (except ru/nr/pd/qr)
 digitsflabelwlabelexpressionwhenwho
22552598 48w33(44·102597-503)/9December 20, 2012Ray Chandler
225625977883978w39(71·102596-449)/9December 20, 2012Ray Chandler
225725976448364w83(58·102596+347)/9December 20, 2012Ray Chandler
225825964889748w97(44·102595+73)/9December 20, 2012Ray Chandler
225925959005390w539·102594+53December 20, 2012Ray Chandler
226025958770987w09(79·102594-619)/9December 20, 2012Ray Chandler
226125956001760w176·102594+17December 20, 2012Ray Chandler
22632595 48w99(44·102594+91)/9December 20, 2012Ray Chandler
22652594 52w11(47·102593-101)/9December 20, 2012Ray Chandler
226725939776397w63(88·102592-133)/9December 20, 2012Ray Chandler
226825939443794w37(85·102592-67)/9December 20, 2012Ray Chandler
226925937446974w69(67·102592+221)/9December 20, 2012Ray Chandler
227025937112771w27(64·102592+143)/9December 20, 2012Ray Chandler
227125936007360w736·102592+73December 20, 2012Ray Chandler
22722592 117w9(106·102590+11)/9December 20, 2012Ray Chandler
227325917992779w278·102590-73December 20, 2012Ray Chandler
227425917882978w29(71·102590-539)/9December 20, 2012Ray Chandler
227525914668746w87(14·102590+61)/3December 20, 2012Ray Chandler
227625909441994w19(85·102589-229)/9December 20, 2012Ray Chandler
227725907557175w71(68·102589+139)/9December 20, 2012Ray Chandler
227825898335783w57(25·102588+71)/3December 20, 2012Ray Chandler
227925897881378w13(71·102588-683)/9December 20, 2012Ray Chandler
228025893441734w17(31·102588-247)/9December 20, 2012Ray Chandler
22812589 28w77(26·102588-107)/9December 20, 2012Ray Chandler
228425867449374w93(67·102585+437)/9December 20, 2012Ray Chandler
228525853990139w014·102584-99December 20, 2012Ray Chandler
228725846228962w89(56·102583+601)/9December 20, 2012Ray Chandler
228925838995789w579·102582-43December 20, 2012Ray Chandler
229025833113731w37(28·102582+233)/9December 20, 2012Ray Chandler
229125823110931w09(28·102581-19)/9December 20, 2012Ray Chandler
229325814229142w91(38·102580+619)/9December 20, 2012Ray Chandler
229425811992719w272·102580-73December 20, 2012Ray Chandler
229725787008170w817·102577+81December 20, 2012Ray Chandler
229825784556745w67(41·102577+103)/9December 20, 2012Ray Chandler
229925781776317w63(16·102577-133)/9December 20, 2012Ray Chandler
230025781448914w89(13·102577+401)/9December 20, 2012Ray Chandler
230125781006110w61102577+61December 20, 2012Ray Chandler
23022577 36w11(11·102576-167)/3December 20, 2012Ray Chandler
230425769775197w51(88·102575-241)/9December 20, 2012Ray Chandler
230625741557915w79(14·102573+211)/9December 20, 2012Ray Chandler
230825725008150w815·102571+81December 20, 2012Ray Chandler
230925723554735w47(32·102571-77)/9December 20, 2012Ray Chandler
231225703991339w134·102569-87December 20, 2012Ray Chandler
23132570 34w99(31·102569+491)/9December 20, 2012Ray Chandler
231425695668156w81(17·102568+43)/3December 20, 2012Ray Chandler
231525685885958w59(53·102567-269)/9December 20, 2012Ray Chandler
231825679885198w51(89·102566-341)/9December 20, 2012Ray Chandler
232025665335153w51(16·102565+53)/3December 20, 2012Ray Chandler
23222566 25w33(23·102565-203)/9December 20, 2012Ray Chandler
232325662448924w89(22·102565+401)/9December 20, 2012Ray Chandler
232425659001990w199·102564+19December 20, 2012Ray Chandler
232525649008990w899·102563+89December 20, 2012Ray Chandler
232725611886918w69(17·102560-179)/9December 20, 2012Ray Chandler
232925604551945w19(41·102559-329)/9December 20, 2012Ray Chandler
233225593220732w07(29·102558-137)/9December 20, 2012Ray Chandler
233425584338743w87(13·102557+161)/3December 20, 2012Ray Chandler
233525577990379w038·102556-97December 20, 2012Ray Chandler
233625567669376w93(23·102555+79)/3December 20, 2012Ray Chandler
233725566115961w59(55·102555+431)/9December 20, 2012Ray Chandler
23382555 94w99(85·102554+491)/9December 20, 2012Ray Chandler
23392554 996w7(299·102552+1)/3December 20, 2012Ray Chandler
23402554 89w779·102553-23December 20, 2012Ray Chandler
23412554 52w33(47·102553+97)/9December 20, 2012Ray Chandler
234225543003730w373·102553+37December 20, 2012Ray Chandler
23432553 448w3(404·102551-53)/9December 20, 2012Ray Chandler
23452549 334w3(301·102547-13)/9December 20, 2012Ray Chandler
23472548 94w33(85·102547-103)/9December 20, 2012Ray Chandler
234825483440134w01(31·102547-391)/9December 20, 2012Ray Chandler
23492548 227w3(205·102546-43)/9December 20, 2012Ray Chandler
235025481336113w61(4·102547+83)/3December 20, 2012Ray Chandler
235125479664196w41(29·102546-77)/3December 20, 2012Ray Chandler
235225474550945w09(41·102546-419)/9December 20, 2012Ray Chandler
235325473443734w37(31·102546-67)/9December 20, 2012Ray Chandler
235525466556965w69(59·102545+121)/9December 20, 2012Ray Chandler
235725457880178w01(71·102544-791)/9December 20, 2012Ray Chandler
235825451337913w79(4·102544+137)/3December 20, 2012Ray Chandler
235925441558715w87(14·102543+283)/9December 20, 2012Ray Chandler
236025439112991w29(82·102542+161)/9December 20, 2012Ray Chandler
236125426335963w59(19·102541+77)/3December 20, 2012Ray Chandler
236325418558385w83(77·102540+247)/9December 20, 2012Ray Chandler
236425413557335w73(32·102540+157)/9December 20, 2012Ray Chandler
236525412008920w892·102540+89December 20, 2012Ray Chandler
23662539 772w7(695·102537+43)/9December 20, 2012Ray Chandler
236725392334723w47(7·102538+41)/3December 20, 2012Ray Chandler
236925385229352w93(47·102537+637)/9December 20, 2012Ray Chandler
237025384226942w69(38·102537+421)/9December 20, 2012Ray Chandler
237125364554745w47(41·102535-77)/9December 20, 2012Ray Chandler
237225351770317w03(16·102534-673)/9December 20, 2012Ray Chandler
237325351449314w93(13·102534+437)/9December 20, 2012Ray Chandler
237425349551395w13(86·102533-383)/9December 20, 2012Ray Chandler
237525343991339w134·102533-87December 20, 2012Ray Chandler
237625338005980w598·102532+59December 20, 2012Ray Chandler
23772533 771w7(694·102531+53)/9December 20, 2012Ray Chandler
237925317556375w63(68·102530+67)/9December 20, 2012Ray Chandler
238025282885928w59(26·102527-269)/9December 20, 2012Ray Chandler
238125275664156w41(17·102526-77)/3December 20, 2012Ray Chandler
23822527 110w911·102525+9December 20, 2012Ray Chandler
238325268992389w239·102525-77December 20, 2012Ray Chandler
238425267220172w01(65·102525-191)/9December 20, 2012Ray Chandler
238525265885158w51(53·102525-341)/9December 20, 2012Ray Chandler
238625254336143w61(13·102524+83)/3December 20, 2012Ray Chandler
23872524 53w99(16·102523+197)/3December 20, 2012Ray Chandler
23882523 336w7(101·102521+1)/3December 20, 2012Ray Chandler
238925228224382w43(74·102521+187)/9December 20, 2012Ray Chandler
239125222114921w49(19·102521+341)/9December 20, 2012Ray Chandler
239325214221342w13(38·102520-83)/9December 20, 2012Ray Chandler
239425213445734w57(31·102520+113)/9December 20, 2012Ray Chandler
239525207005770w577·102519+57December 20, 2012Ray Chandler
239625183771337w13(34·102517-583)/9December 20, 2012Ray Chandler
23972516 97w11(88·102515-601)/9December 20, 2012Ray Chandler
239825153775137w51(34·102514-241)/9December 20, 2012Ray Chandler
239925139779397w93(88·102512+137)/9December 20, 2012Ray Chandler
240025135887958w79(53·102512-89)/9December 20, 2012Ray Chandler
240125131442914w29(13·102512-139)/9December 20, 2012Ray Chandler
24022512 95w11(86·102511-401)/9December 20, 2012Ray Chandler
240325127335173w51(22·102511+53)/3December 20, 2012Ray Chandler
240425127224372w43(65·102511+187)/9December 20, 2012Ray Chandler
24052511 83w99(25·102510+197)/3December 20, 2012Ray Chandler
240625117441974w19(67·102510-229)/9December 20, 2012Ray Chandler
240725116225362w53(56·102510+277)/9December 20, 2012Ray Chandler
240825108776387w63(79·102509-133)/9December 20, 2012Ray Chandler
24092510 440w344·102508+3December 20, 2012Ray Chandler
24122508 664w1(598·102506-31)/9December 20, 2012Ray Chandler
241325084335743w57(13·102507+71)/3December 20, 2012Ray Chandler
241425073996739w674·102506-33December 20, 2012Ray Chandler
241525042778127w81(25·102503+29)/9December 20, 2012Ray Chandler
241625037884178w41(71·102502-431)/9December 20, 2012Ray Chandler
24172503 50w775·102502+77December 20, 2012Ray Chandler
241925016008360w836·102500+83December 20, 2012Ray Chandler
242025011339713w97(4·102500+191)/3December 20, 2012Ray Chandler
242225001330713w07(4·102499-79)/3December 20, 2012Ray Chandler

Factorizations of 722...227 have been extended up to n=250. Added composite numbers had passed ECM iterations 118 times at the level 35. Most unknown factors are supposed to be greater than 1030.

December 17, 2012

Ray Chandler certificated 7 near-repdigit prime numbers, 42 quasi-repdigit prime numbers and 111 near-repdigit-related prime numbers by Primo. Certifications are available.

Proven near-repdigit primes
 digitsflabelwlabelexpressionwhenwho
5122495 9w59999999102495-40000001December 17, 2012Ray Chandler
5132494777577w57(7·102494-187)/9December 17, 2012Ray Chandler
5162475 9w599102475-401December 17, 2012Ray Chandler
5182444 9w59999102444-40001December 17, 2012Ray Chandler
5202438 9w7999102438-2001December 17, 2012Ray Chandler
5212420 9w79999999102420-20000001December 17, 2012Ray Chandler
5232400 9w5999999102400-4000001December 17, 2012Ray Chandler
Proven quasi-repdigit primes (except pd)
 digitsflabelwlabelexpressionwhenwho
3492497 4w11(4·102497-301)/9December 17, 2012Ray Chandler
350249654111541w(487·102494-1)/9December 17, 2012Ray Chandler
351249561661616w1(185·102493-17)/3December 17, 2012Ray Chandler
35224947888378w3(71·102493-53)/9December 17, 2012Ray Chandler
35324926444164w1(58·102491-31)/9December 17, 2012Ray Chandler
355248684883848w3(764·102484-53)/9December 17, 2012Ray Chandler
356248662777627w(565·102484-7)/9December 17, 2012Ray Chandler
357248585887858w7(773·102483-17)/9December 17, 2012Ray Chandler
3592482333493w49(102482+47)/3December 17, 2012Ray Chandler
3602479333493w49(102479+47)/3December 17, 2012Ray Chandler
36124787336373w63(22·102477+89)/3December 17, 2012Ray Chandler
3642476666896w89(2·102476+67)/3December 17, 2012Ray Chandler
366247220229202w9(182·102470+61)/9December 17, 2012Ray Chandler
367246982887828w7(746·102467-17)/9December 17, 2012Ray Chandler
368246712117121w7(109·102465+53)/9December 17, 2012Ray Chandler
371246430111301w(271·102462-1)/9December 17, 2012Ray Chandler
3722461 771w(694·102459-1)/9December 17, 2012Ray Chandler
373246052777527w(475·102458-7)/9December 17, 2012Ray Chandler
375245736777367w(331·102455-7)/9December 17, 2012Ray Chandler
376245664777647w(583·102454-7)/9December 17, 2012Ray Chandler
37824475998959w896·102446-11December 17, 2012Ray Chandler
3792445555935w93(5·102445+337)/9December 17, 2012Ray Chandler
38124431991919w192·102442-81December 17, 2012Ray Chandler
38224427118171w81(64·102441+629)/9December 17, 2012Ray Chandler
383244236777367w(331·102440-7)/9December 17, 2012Ray Chandler
3842442222512w51(2·102442+259)/9December 17, 2012Ray Chandler
385243931331313w1(94·102437-7)/3December 17, 2012Ray Chandler
3862437 1w001(102437-991)/9December 17, 2012Ray Chandler
3882433555935w93(5·102433+337)/9December 17, 2012Ray Chandler
3902432222672w67(2·102432+403)/9December 17, 2012Ray Chandler
3912430666196w19(2·102430-143)/3December 17, 2012Ray Chandler
392242995993959w396·102427-7December 17, 2012Ray Chandler
393242917113171w3(154·102427+17)/9December 17, 2012Ray Chandler
39624256995969w597·102424-41December 17, 2012Ray Chandler
39824232995929w593·102422-41December 17, 2012Ray Chandler
3992419 667w(601·102417-7)/9December 17, 2012Ray Chandler
4012418111931w93(102418+737)/9December 17, 2012Ray Chandler
40224165771757w17(52·102415-547)/9December 17, 2012Ray Chandler
40324147994979w498·102413-51December 17, 2012Ray Chandler
40624036776767w67(61·102402-97)/9December 17, 2012Ray Chandler
407240170773707w3(637·102399-43)/9December 17, 2012Ray Chandler
408240085883858w3(773·102398-53)/9December 17, 2012Ray Chandler
Proven near-repdigit-related primes (except ru/nr/pd/qr)
 digitsflabelwlabelexpressionwhenwho
22922499 662w7(596·102497+43)/9December 17, 2012Ray Chandler
22932499 552w7(497·102497+43)/9December 17, 2012Ray Chandler
229424988440784w07(76·102497-337)/9December 17, 2012Ray Chandler
22962498 330w733·102496+7December 17, 2012Ray Chandler
229824974885348w53(44·102496-323)/9December 17, 2012Ray Chandler
229924962115721w57(19·102495+413)/9December 17, 2012Ray Chandler
230124958557385w73(77·102494+157)/9December 17, 2012Ray Chandler
230224941228912w89(11·102493+601)/9December 17, 2012Ray Chandler
230324929778997w89(88·102491+101)/9December 17, 2012Ray Chandler
230424924001340w134·102491+13December 17, 2012Ray Chandler
230524915449754w97(49·102490+473)/9December 17, 2012Ray Chandler
230624892002120w212·102488+21December 17, 2012Ray Chandler
230724872445724w57(22·102486+113)/9December 17, 2012Ray Chandler
230824872116321w63(19·102486+467)/9December 17, 2012Ray Chandler
230924862665726w57(8·102485-29)/3December 17, 2012Ray Chandler
231024857660176w01(23·102484-197)/3December 17, 2012Ray Chandler
231124856007360w736·102484+73December 17, 2012Ray Chandler
231224853993739w374·102484-63December 17, 2012Ray Chandler
23132484 883w1(265·102482-7)/3December 17, 2012Ray Chandler
231424843667336w73(11·102483+19)/3December 17, 2012Ray Chandler
231524818668386w83(26·102480+49)/3December 17, 2012Ray Chandler
23162480 94w11(85·102479-301)/9December 17, 2012Ray Chandler
231824798226782w67(74·102478+403)/9December 17, 2012Ray Chandler
232024783551735w17(32·102477-347)/9December 17, 2012Ray Chandler
232124776994169w417·102476-59December 17, 2012Ray Chandler
232224769119791w97(82·102475+773)/9December 17, 2012Ray Chandler
23242475 559w756·102473-3December 17, 2012Ray Chandler
232524755002150w215·102474+21December 17, 2012Ray Chandler
232624749448194w81(85·102473+329)/9December 17, 2012Ray Chandler
232724747550975w09(68·102473-419)/9December 17, 2012Ray Chandler
233024722441724w17(22·102471-247)/9December 17, 2012Ray Chandler
233124719553995w39(86·102470-149)/9December 17, 2012Ray Chandler
23332471 117w9(106·102469+11)/9December 17, 2012Ray Chandler
233424705118951w89(46·102469+701)/9December 17, 2012Ray Chandler
233524696117361w73(55·102468+557)/9December 17, 2012Ray Chandler
233724689556795w67(86·102467+103)/9December 17, 2012Ray Chandler
233824687228772w87(65·102467+583)/9December 17, 2012Ray Chandler
23392468 446w9(134·102466+7)/3December 17, 2012Ray Chandler
234124664884948w49(44·102465-359)/9December 17, 2012Ray Chandler
23422466 115w3(104·102464-23)/9December 17, 2012Ray Chandler
234424638008380w838·102462+83December 17, 2012Ray Chandler
234724624114341w43(37·102461+287)/9December 17, 2012Ray Chandler
23482461 61w99(55·102460+791)/9December 17, 2012Ray Chandler
23492460 112w3(101·102458+7)/9December 17, 2012Ray Chandler
235124599667196w71(29·102458+13)/3December 17, 2012Ray Chandler
23522459 445w7(401·102457+13)/9December 17, 2012Ray Chandler
235324587009370w937·102457+93December 17, 2012Ray Chandler
235424583006730w673·102457+67December 17, 2012Ray Chandler
235824562440324w03(22·102455-373)/9December 17, 2012Ray Chandler
235924561330113w01(4·102455-97)/3December 17, 2012Ray Chandler
23602455 23w77(7·102454+131)/3December 17, 2012Ray Chandler
236224549447394w73(85·102453+257)/9December 17, 2012Ray Chandler
236324547008170w817·102453+81December 17, 2012Ray Chandler
236424539448394w83(85·102452+347)/9December 17, 2012Ray Chandler
236524538116781w67(73·102452+503)/9December 17, 2012Ray Chandler
236624534660946w09(14·102452-173)/3December 17, 2012Ray Chandler
23682452 17w33(16·102451-403)/9December 17, 2012Ray Chandler
236924521336713w67(4·102451+101)/3December 17, 2012Ray Chandler
237024508110981w09(73·102449-19)/9December 17, 2012Ray Chandler
237124508007180w718·102449+71December 17, 2012Ray Chandler
237224507996179w618·102449-39December 17, 2012Ray Chandler
23732449 86w11(26·102448-167)/3December 17, 2012Ray Chandler
237424497005770w577·102448+57December 17, 2012Ray Chandler
23752448 30w773·102447+77December 17, 2012Ray Chandler
23762447 35w99(32·102446+391)/9December 17, 2012Ray Chandler
237924445668356w83(17·102443+49)/3December 17, 2012Ray Chandler
238024437332773w27(22·102442-19)/3December 17, 2012Ray Chandler
238124436448164w81(58·102442+329)/9December 17, 2012Ray Chandler
23832441 61w33(55·102440+197)/9December 17, 2012Ray Chandler
238424415662156w21(17·102440-137)/3December 17, 2012Ray Chandler
238524412440324w03(22·102440-373)/9December 17, 2012Ray Chandler
238724395226352w63(47·102438+367)/9December 17, 2012Ray Chandler
23882439 38w11(35·102438-701)/9December 17, 2012Ray Chandler
238924387119771w97(64·102437+773)/9December 17, 2012Ray Chandler
239224378228182w81(74·102436+529)/9December 17, 2012Ray Chandler
239524357990179w018·102434-99December 17, 2012Ray Chandler
239624352668126w81(8·102434+43)/3December 17, 2012Ray Chandler
23982434 74w77(67·102433+293)/9December 17, 2012Ray Chandler
239924344337943w79(13·102433+137)/3December 17, 2012Ray Chandler
240324329889798w97(89·102431+73)/9December 17, 2012Ray Chandler
240424329661796w17(29·102431-149)/3December 17, 2012Ray Chandler
240524328665386w53(26·102431-41)/3December 17, 2012Ray Chandler
240724317119371w93(64·102430+737)/9December 17, 2012Ray Chandler
24082431 29w773·102430-23December 17, 2012Ray Chandler
241024288552785w27(77·102427-257)/9December 17, 2012Ray Chandler
241124278552785w27(77·102426-257)/9December 17, 2012Ray Chandler
241224271662716w27(5·102426-119)/3December 17, 2012Ray Chandler
241324269664996w49(29·102425-53)/3December 17, 2012Ray Chandler
24152426 76w33(23·102425-101)/3December 17, 2012Ray Chandler
241724252661726w17(8·102424-149)/3December 17, 2012Ray Chandler
241824246771367w13(61·102423-583)/9December 17, 2012Ray Chandler
24202422 882w1(794·102420-11)/9December 17, 2012Ray Chandler
242124218660986w09(26·102420-173)/3December 17, 2012Ray Chandler
242224217665776w57(23·102420-29)/3December 17, 2012Ray Chandler
242324172448724w87(22·102416+383)/9December 17, 2012Ray Chandler
24242415 53w77(16·102414+131)/3December 17, 2012Ray Chandler
242624148662786w27(26·102413-119)/3December 17, 2012Ray Chandler
242724146330163w01(19·102413-97)/3December 17, 2012Ray Chandler
24282412 37w11(34·102411-601)/9December 17, 2012Ray Chandler
243124109885798w57(89·102409-287)/9December 17, 2012Ray Chandler
243224098445984w59(76·102408+131)/9December 17, 2012Ray Chandler
243324091443914w39(13·102408-49)/9December 17, 2012Ray Chandler
243524078221382w13(74·102406-83)/9December 17, 2012Ray Chandler
24362407 76w99(23·102406+97)/3December 17, 2012Ray Chandler
24392405 90w119·102404+11December 17, 2012Ray Chandler
244124028770987w09(79·102401-619)/9December 17, 2012Ray Chandler
244224024778947w89(43·102401+101)/9December 17, 2012Ray Chandler
244324022887928w79(26·102401-89)/9December 17, 2012Ray Chandler
24442402 13w99(4·102401+197)/3December 17, 2012Ray Chandler
244524007556975w69(68·102399+121)/9December 17, 2012Ray Chandler
244624007115771w57(64·102399+413)/9December 17, 2012Ray Chandler

Factorizations of 700...009 have been extended up to n=250. Added composite numbers had passed ECM iterations 118 times at the level 35. Most unknown factors are supposed to be greater than 1030.

December 15, 2012

Ray Chandler certificated 8 near-repdigit prime numbers, 44 quasi-repdigit prime numbers and 117 near-repdigit-related prime numbers by Primo. Certifications are available.

Proven near-repdigit primes
 digitsflabelwlabelexpressionwhenwho
5172388 9w199102388-801December 15, 2012Ray Chandler
5182388 9w19999102388-80001December 15, 2012Ray Chandler
5242350 9w799999999102350-200000001December 15, 2012Ray Chandler
525233115111151w(136·102329-1)/9December 15, 2012Ray Chandler
5262329777177w17(7·102329-547)/9December 15, 2012Ray Chandler
5272328999799w79102328-21December 15, 2012Ray Chandler
528232434333343w(103·102322-1)/3December 15, 2012Ray Chandler
5292311 9w1999102311-8001December 15, 2012Ray Chandler
Proven quasi-repdigit primes (except pd)
 digitsflabelwlabelexpressionwhenwho
3682399222132w13(2·102399-83)/9December 15, 2012Ray Chandler
369239854559545w9(491·102396+31)/9December 15, 2012Ray Chandler
3702397666076w07(2·102397-179)/3December 15, 2012Ray Chandler
371239578773787w3(709·102393-43)/9December 15, 2012Ray Chandler
37223954339343w93(13·102394+179)/3December 15, 2012Ray Chandler
37323935335353w53(16·102392+59)/3December 15, 2012Ray Chandler
3742387 4w77(4·102387+293)/9December 15, 2012Ray Chandler
37623809778797w87(88·102379+83)/9December 15, 2012Ray Chandler
377238046333463w(139·102378-1)/3December 15, 2012Ray Chandler
3802374555675w67(5·102374+103)/9December 15, 2012Ray Chandler
38123734339343w93(13·102372+179)/3December 15, 2012Ray Chandler
382237261669616w9(185·102370+7)/3December 15, 2012Ray Chandler
383237054111541w(487·102368-1)/9December 15, 2012Ray Chandler
3842368999139w13102368-87December 15, 2012Ray Chandler
38523683118131w81(28·102367+629)/9December 15, 2012Ray Chandler
38623657994979w498·102364-51December 15, 2012Ray Chandler
387236458551585w1(527·102362-41)/9December 15, 2012Ray Chandler
388235385887858w7(773·102351-17)/9December 15, 2012Ray Chandler
389235246449464w9(418·102350+41)/9December 15, 2012Ray Chandler
3912349 9w11102349-89December 15, 2012Ray Chandler
39223488330383w03(25·102347-91)/3December 15, 2012Ray Chandler
393234691993919w392·102344-7December 15, 2012Ray Chandler
394234591991919w192·102343-9December 15, 2012Ray Chandler
397234052777527w(475·102338-7)/9December 15, 2012Ray Chandler
39823379770797w07(88·102336-637)/9December 15, 2012Ray Chandler
3992337111571w57(102337+413)/9December 15, 2012Ray Chandler
4002333999079w07102333-93December 15, 2012Ray Chandler
401232924223242w3(218·102327+7)/9December 15, 2012Ray Chandler
4022327222732w73(2·102327+457)/9December 15, 2012Ray Chandler
4032324666296w29(2·102324-113)/3December 15, 2012Ray Chandler
405232429777297w(268·102322-7)/9December 15, 2012Ray Chandler
406232291333913w(274·102320-1)/3December 15, 2012Ray Chandler
4072322222632w63(2·102322+367)/9December 15, 2012Ray Chandler
40823214331343w13(13·102320-61)/3December 15, 2012Ray Chandler
409231946447464w7(418·102317+23)/9December 15, 2012Ray Chandler
4102319111731w73(102319+557)/9December 15, 2012Ray Chandler
4112317888498w49(8·102317-359)/9December 15, 2012Ray Chandler
413231731331313w1(94·102315-7)/3December 15, 2012Ray Chandler
414231150333503w(151·102309-1)/3December 15, 2012Ray Chandler
41623087118171w81(64·102307+629)/9December 15, 2012Ray Chandler
41723072118121w81(19·102306+629)/9December 15, 2012Ray Chandler
41823035110151w01(46·102302-91)/9December 15, 2012Ray Chandler
42023028992989w299·102301-71December 15, 2012Ray Chandler
421230089777897w(808·102298-7)/9December 15, 2012Ray Chandler
Proven near-repdigit-related primes (except ru/nr/pd/qr)
 digitsflabelwlabelexpressionwhenwho
23362399 89w779·102398-23December 15, 2012Ray Chandler
233923982773127w31(25·102397-421)/9December 15, 2012Ray Chandler
234123969889398w93(89·102395+37)/9December 15, 2012Ray Chandler
23422396 775w1(698·102394-41)/9December 15, 2012Ray Chandler
234323965116951w69(46·102395+521)/9December 15, 2012Ray Chandler
234423961990119w012·102395-99December 15, 2012Ray Chandler
234523937001970w197·102392+19December 15, 2012Ray Chandler
234723928446784w67(76·102391+203)/9December 15, 2012Ray Chandler
23482392 80w338·102391+33December 15, 2012Ray Chandler
234923919667196w71(29·102390+13)/3December 15, 2012Ray Chandler
235323902770927w09(25·102389-619)/9December 15, 2012Ray Chandler
235423893440934w09(31·102388-319)/9December 15, 2012Ray Chandler
235623887221972w19(65·102387-29)/9December 15, 2012Ray Chandler
235923873667936w79(11·102386+37)/3December 15, 2012Ray Chandler
23602386 880w788·102384+7December 15, 2012Ray Chandler
236123867112371w23(64·102385+107)/9December 15, 2012Ray Chandler
236623834883748w37(44·102382-467)/9December 15, 2012Ray Chandler
236723831335713w57(4·102382+71)/3December 15, 2012Ray Chandler
23702381 229w323·102379-7December 15, 2012Ray Chandler
237123805223752w37(47·102379+133)/9December 15, 2012Ray Chandler
237323802665726w57(8·102379-29)/3December 15, 2012Ray Chandler
237423798008180w818·102378+81December 15, 2012Ray Chandler
237623788779387w93(79·102377+137)/9December 15, 2012Ray Chandler
237723773448134w81(31·102376+329)/9December 15, 2012Ray Chandler
23792376 58w11(53·102375-701)/9December 15, 2012Ray Chandler
238123764886748w67(44·102375-197)/9December 15, 2012Ray Chandler
238423745330953w09(16·102373-73)/3December 15, 2012Ray Chandler
238523742775327w53(25·102373-223)/9December 15, 2012Ray Chandler
238623733669736w97(11·102372+91)/3December 15, 2012Ray Chandler
238723726557365w73(59·102371+157)/9December 15, 2012Ray Chandler
23892371 17w99(16·102370+191)/9December 15, 2012Ray Chandler
239023709440794w07(85·102369-337)/9December 15, 2012Ray Chandler
239123703775937w59(34·102369-169)/9December 15, 2012Ray Chandler
239523671556715w67(14·102366+103)/9December 15, 2012Ray Chandler
239623669440394w03(85·102365-373)/9December 15, 2012Ray Chandler
23972363 52w77(47·102362+493)/9December 15, 2012Ray Chandler
239923609556995w69(86·102359+121)/9December 15, 2012Ray Chandler
240023603886738w67(35·102359-197)/9December 15, 2012Ray Chandler
240123603005930w593·102359+59December 15, 2012Ray Chandler
240223599881798w17(89·102358-647)/9December 15, 2012Ray Chandler
240423598008980w898·102358+89December 15, 2012Ray Chandler
240523594886148w61(44·102358-251)/9December 15, 2012Ray Chandler
240623583229732w97(29·102357+673)/9December 15, 2012Ray Chandler
240723577990179w018·102356-99December 15, 2012Ray Chandler
240823577882378w23(71·102356-593)/9December 15, 2012Ray Chandler
240923575881958w19(53·102356-629)/9December 15, 2012Ray Chandler
241023567445774w57(67·102355+113)/9December 15, 2012Ray Chandler
24112356 36w11(11·102355-167)/3December 15, 2012Ray Chandler
241223562889728w97(26·102355+73)/9December 15, 2012Ray Chandler
241323559448394w83(85·102354+347)/9December 15, 2012Ray Chandler
24142355 668w1(602·102353-71)/9December 15, 2012Ray Chandler
241623529001390w139·102351+13December 15, 2012Ray Chandler
241723518557385w73(77·102350+157)/9December 15, 2012Ray Chandler
241923513226732w67(29·102350+403)/9December 15, 2012Ray Chandler
242023504009740w974·102349+97December 15, 2012Ray Chandler
242123495665756w57(17·102348-29)/3December 15, 2012Ray Chandler
24222348 98w99(89·102347+91)/9December 15, 2012Ray Chandler
242423485886158w61(53·102347-251)/9December 15, 2012Ray Chandler
242623469115391w53(82·102345+377)/9December 15, 2012Ray Chandler
242823452440724w07(22·102344-337)/9December 15, 2012Ray Chandler
24292344 447w1(403·102342-61)/9December 15, 2012Ray Chandler
243123432552325w23(23·102342-293)/9December 15, 2012Ray Chandler
243323417665776w57(23·102340-29)/3December 15, 2012Ray Chandler
243523398998789w879·102338-13December 15, 2012Ray Chandler
243623397338773w87(22·102338+161)/3December 15, 2012Ray Chandler
243723395008750w875·102338+87December 15, 2012Ray Chandler
243823392662326w23(8·102338-131)/3December 15, 2012Ray Chandler
243923382992729w273·102337-73December 15, 2012Ray Chandler
24402337 220w322·102335+3December 15, 2012Ray Chandler
244123367006770w677·102335+67December 15, 2012Ray Chandler
244323355992359w236·102334-77December 15, 2012Ray Chandler
24452334 776w3(233·102332-11)/3December 15, 2012Ray Chandler
244623345445754w57(49·102333+113)/9December 15, 2012Ray Chandler
244723324998149w815·102331-19December 15, 2012Ray Chandler
24482331 559w156·102329-9December 15, 2012Ray Chandler
24492331 47w99(43·102330+191)/9December 15, 2012Ray Chandler
245023312006920w692·102330+69December 15, 2012Ray Chandler
245123304008740w874·102329+87December 15, 2012Ray Chandler
245223292884328w43(26·102328-413)/9December 15, 2012Ray Chandler
245323291990319w032·102328-97December 15, 2012Ray Chandler
245523268006980w698·102325+69December 15, 2012Ray Chandler
245723254773947w39(43·102324-349)/9December 15, 2012Ray Chandler
24582325 339w734·102323-3December 15, 2012Ray Chandler
246123237445374w53(67·102322+77)/9December 15, 2012Ray Chandler
246223234227142w71(38·102322+439)/9December 15, 2012Ray Chandler
246323216226962w69(56·102320+421)/9December 15, 2012Ray Chandler
246423213551335w13(32·102320-383)/9December 15, 2012Ray Chandler
24652320 889w189·102318-9December 15, 2012Ray Chandler
246723191225112w51(11·102318+259)/9December 15, 2012Ray Chandler
246923185669356w93(17·102317+79)/3December 15, 2012Ray Chandler
247023178774987w49(79·102316-259)/9December 15, 2012Ray Chandler
24712317 336w1(101·102315-17)/3December 15, 2012Ray Chandler
24722317 227w3(205·102315-43)/9December 15, 2012Ray Chandler
247323169661396w13(29·102315-161)/3December 15, 2012Ray Chandler
247423167889778w97(71·102315+73)/9December 15, 2012Ray Chandler
247523166227362w73(56·102315+457)/9December 15, 2012Ray Chandler
24762315 75w77(68·102314+193)/9December 15, 2012Ray Chandler
247723154669146w91(14·102314+73)/3December 15, 2012Ray Chandler
247823129884398w43(89·102311-413)/9December 15, 2012Ray Chandler
24792312 83w11(25·102311-67)/3December 15, 2012Ray Chandler
248023127114971w49(64·102311+341)/9December 15, 2012Ray Chandler
24822310 668w1(602·102308-71)/9December 15, 2012Ray Chandler
248423081770917w09(16·102307-619)/9December 15, 2012Ray Chandler
248523081660716w07(5·102307-179)/3December 15, 2012Ray Chandler
248623079228992w89(83·102306+601)/9December 15, 2012Ray Chandler
248723077440174w01(67·102306-391)/9December 15, 2012Ray Chandler
24892305 61w99(55·102304+791)/9December 15, 2012Ray Chandler
249023051224112w41(11·102304+169)/9December 15, 2012Ray Chandler
24912304 58w11(53·102303-701)/9December 15, 2012Ray Chandler
24932304 43w99(13·102303+197)/3December 15, 2012Ray Chandler
24942304 24w11(22·102303-301)/9December 15, 2012Ray Chandler
249523034559345w93(41·102302+337)/9December 15, 2012Ray Chandler
249623034115941w59(37·102302+431)/9December 15, 2012Ray Chandler
249723031667316w73(5·102302+19)/3December 15, 2012Ray Chandler
249823023442734w27(31·102301-157)/9December 15, 2012Ray Chandler
249923013117931w79(28·102300+611)/9December 15, 2012Ray Chandler
250223004771347w13(43·102299-583)/9December 15, 2012Ray Chandler

Factorizations of 677...779 have been extended up to n=250. Added composite numbers had passed ECM iterations 118 times at the level 35. Most unknown factors are supposed to be greater than 1030.

December 14, 2012

Ray Chandler successfully proved the primality of a 9505-digit prime number Phi(20644,10) by Primo. Congratulations! Certification is available.

December 13, 2012

Ray Chandler certificated 7 near-repdigit prime numbers, 45 quasi-repdigit prime numbers and 148 near-repdigit-related prime numbers by Primo. Certifications are available.

Proven near-repdigit primes
 digitsflabelwlabelexpressionwhenwho
522229532333323w(97·102293-1)/3December 13, 2012Ray Chandler
524227718111181w(163·102275-1)/9December 13, 2012Ray Chandler
5262269 9w5999999102269-4000001December 13, 2012Ray Chandler
5272268999799w79102268-21December 13, 2012Ray Chandler
5292238 9w79999102238-20001December 13, 2012Ray Chandler
5322221 9w19999999102221-80000001December 13, 2012Ray Chandler
5352204 9w799999999102204-200000001December 13, 2012Ray Chandler
Proven quasi-repdigit primes (except pd)
 digitsflabelwlabelexpressionwhenwho
3772297 4w77(4·102297+293)/9December 13, 2012Ray Chandler
378229685881858w1(773·102294-71)/9December 13, 2012Ray Chandler
381228841333413w(124·102286-1)/3December 13, 2012Ray Chandler
38222881334313w43(4·102287+29)/3December 13, 2012Ray Chandler
383228657551575w1(518·102284-41)/9December 13, 2012Ray Chandler
3842283 661w(595·102281-1)/9December 13, 2012Ray Chandler
385228356553565w3(509·102281-23)/9December 13, 2012Ray Chandler
38622827337373w73(22·102281+119)/3December 13, 2012Ray Chandler
3872282666596w59(2·102282-23)/3December 13, 2012Ray Chandler
3882281 1w99(102281+791)/9December 13, 2012Ray Chandler
3892280888938w93(8·102280+37)/9December 13, 2012Ray Chandler
390228049333493w(148·102278-1)/3December 13, 2012Ray Chandler
3922275111291w29(102275+161)/9December 13, 2012Ray Chandler
393226992333923w(277·102267-1)/3December 13, 2012Ray Chandler
3942267333473w47(102267+41)/3December 13, 2012Ray Chandler
395226494777947w(853·102262-7)/9December 13, 2012Ray Chandler
39622626331363w13(19·102261-61)/3December 13, 2012Ray Chandler
398226127227272w7(245·102259+43)/9December 13, 2012Ray Chandler
399226041333413w(124·102258-1)/3December 13, 2012Ray Chandler
400225728227282w7(254·102255+43)/9December 13, 2012Ray Chandler
401225241443414w3(373·102250-13)/9December 13, 2012Ray Chandler
403225054777547w(493·102248-7)/9December 13, 2012Ray Chandler
4042246555715w71(5·102246+139)/9December 13, 2012Ray Chandler
4062243222732w73(2·102243+457)/9December 13, 2012Ray Chandler
40722384778747w87(43·102237+83)/9December 13, 2012Ray Chandler
40922363776737w67(34·102235-97)/9December 13, 2012Ray Chandler
41022354336343w63(13·102234+89)/3December 13, 2012Ray Chandler
411223017333173w(52·102228-1)/3December 13, 2012Ray Chandler
4122229888098w09(8·102229-719)/9December 13, 2012Ray Chandler
413222776779767w9(691·102225+11)/9December 13, 2012Ray Chandler
414222336111361w(325·102221-1)/9December 13, 2012Ray Chandler
41522231779717w97(16·102222+173)/9December 13, 2012Ray Chandler
417222219333193w(58·102220-1)/3December 13, 2012Ray Chandler
418221987887878w7(791·102217-17)/9December 13, 2012Ray Chandler
4192216999719w71102216-29December 13, 2012Ray Chandler
42022167994979w498·102215-51December 13, 2012Ray Chandler
42222157994979w498·102214-51December 13, 2012Ray Chandler
4232215666296w29(2·102215-113)/3December 13, 2012Ray Chandler
4252213444234w23(4·102213-193)/9December 13, 2012Ray Chandler
427221215777157w(142·102210-7)/9December 13, 2012Ray Chandler
428221061777617w(556·102208-7)/9December 13, 2012Ray Chandler
42922101994919w492·102209-51December 13, 2012Ray Chandler
431220815117151w7(136·102206+53)/9December 13, 2012Ray Chandler
432220641777417w(376·102204-7)/9December 13, 2012Ray Chandler
433220626221262w1(236·102204-11)/9December 13, 2012Ray Chandler
Proven near-repdigit-related primes (except ru/nr/pd/qr)
 digitsflabelwlabelexpressionwhenwho
238522998668786w87(26·102298+61)/3December 13, 2012Ray Chandler
23872299 556w3(167·102297-11)/3December 13, 2012Ray Chandler
23882298 81w33(73·102297+197)/9December 13, 2012Ray Chandler
239122974886348w63(44·102296-233)/9December 13, 2012Ray Chandler
239322964667946w79(14·102295+37)/3December 13, 2012Ray Chandler
239422964334943w49(13·102295+47)/3December 13, 2012Ray Chandler
23972294 889w189·102292-9December 13, 2012Ray Chandler
239822947880978w09(71·102293-719)/9December 13, 2012Ray Chandler
239922946113961w39(55·102293+251)/9December 13, 2012Ray Chandler
240022939339193w91(28·102292+173)/3December 13, 2012Ray Chandler
240122937998779w878·102292-13December 13, 2012Ray Chandler
240422921774317w43(16·102291-313)/9December 13, 2012Ray Chandler
240522915665756w57(17·102290-29)/3December 13, 2012Ray Chandler
240622906336763w67(19·102289+101)/3December 13, 2012Ray Chandler
240722889662996w29(29·102287-113)/3December 13, 2012Ray Chandler
240822885221352w13(47·102287-83)/9December 13, 2012Ray Chandler
24092288 335w3(302·102286-23)/9December 13, 2012Ray Chandler
24102287 51w77(46·102286+593)/9December 13, 2012Ray Chandler
241222872886128w61(26·102286-251)/9December 13, 2012Ray Chandler
241422847664976w49(23·102283-53)/3December 13, 2012Ray Chandler
241522845664156w41(17·102283-77)/3December 13, 2012Ray Chandler
241722833889138w91(35·102282+19)/9December 13, 2012Ray Chandler
241822826886368w63(62·102281-233)/9December 13, 2012Ray Chandler
24192281 62w33(56·102280+97)/9December 13, 2012Ray Chandler
242022814001340w134·102280+13December 13, 2012Ray Chandler
242222805883958w39(53·102279-449)/9December 13, 2012Ray Chandler
24242279 84w99(76·102278+491)/9December 13, 2012Ray Chandler
242522798116781w67(73·102278+503)/9December 13, 2012Ray Chandler
242622791885918w59(17·102278-269)/9December 13, 2012Ray Chandler
242722791448914w89(13·102278+401)/9December 13, 2012Ray Chandler
242822779887198w71(89·102276-161)/9December 13, 2012Ray Chandler
243222771663916w39(5·102276-83)/3December 13, 2012Ray Chandler
243322768449784w97(76·102275+473)/9December 13, 2012Ray Chandler
243422744336143w61(13·102273+83)/3December 13, 2012Ray Chandler
243522737550375w03(68·102272-473)/9December 13, 2012Ray Chandler
243622735771357w13(52·102272-583)/9December 13, 2012Ray Chandler
243722707331973w19(22·102269-43)/3December 13, 2012Ray Chandler
243822705448754w87(49·102269+383)/9December 13, 2012Ray Chandler
243922698337183w71(25·102268+113)/3December 13, 2012Ray Chandler
244022689552395w23(86·102267-293)/9December 13, 2012Ray Chandler
244122689445994w59(85·102267+131)/9December 13, 2012Ray Chandler
24422268 330w733·102266+7December 13, 2012Ray Chandler
244422678557385w73(77·102266+157)/9December 13, 2012Ray Chandler
244522666227162w71(56·102265+439)/9December 13, 2012Ray Chandler
244622658442784w27(76·102264-157)/9December 13, 2012Ray Chandler
244722655669356w93(17·102264+79)/3December 13, 2012Ray Chandler
244922646337163w71(19·102263+113)/3December 13, 2012Ray Chandler
245022643556135w61(32·102263+49)/9December 13, 2012Ray Chandler
245122641338113w81(4·102263+143)/3December 13, 2012Ray Chandler
245322635332753w27(16·102262-19)/3December 13, 2012Ray Chandler
245522631775117w51(16·102262-241)/9December 13, 2012Ray Chandler
245622622334723w47(7·102261+41)/3December 13, 2012Ray Chandler
245722618225982w59(74·102260+331)/9December 13, 2012Ray Chandler
246022589226992w69(83·102257+421)/9December 13, 2012Ray Chandler
246122587003970w397·102257+39December 13, 2012Ray Chandler
246222584002140w214·102257+21December 13, 2012Ray Chandler
246422567441374w13(67·102255-283)/9December 13, 2012Ray Chandler
24652256 335w7(302·102254+13)/9December 13, 2012Ray Chandler
246822556775967w59(61·102254-169)/9December 13, 2012Ray Chandler
246922554229342w93(38·102254+637)/9December 13, 2012Ray Chandler
247022551008110w81102254+81December 13, 2012Ray Chandler
247122549119391w93(82·102253+737)/9December 13, 2012Ray Chandler
24732254 45w77(41·102253+193)/9December 13, 2012Ray Chandler
247422544005140w514·102253+51December 13, 2012Ray Chandler
247622538112781w27(73·102252+143)/9December 13, 2012Ray Chandler
247722532558125w81(23·102252+229)/9December 13, 2012Ray Chandler
247822522118721w87(19·102251+683)/9December 13, 2012Ray Chandler
248022516119761w97(55·102250+773)/9December 13, 2012Ray Chandler
248122511663116w31(5·102250-107)/3December 13, 2012Ray Chandler
248222509667396w73(29·102249+19)/3December 13, 2012Ray Chandler
24832250 64w77(58·102249+293)/9December 13, 2012Ray Chandler
248422502004720w472·102249+47December 13, 2012Ray Chandler
248522486884168w41(62·102247-431)/9December 13, 2012Ray Chandler
24862248 10w33102247+33December 13, 2012Ray Chandler
248722478552985w29(77·102246-239)/9December 13, 2012Ray Chandler
24892247 556w1(167·102245-17)/3December 13, 2012Ray Chandler
249022467993779w378·102245-63December 13, 2012Ray Chandler
249122464229342w93(38·102245+637)/9December 13, 2012Ray Chandler
249222455889358w93(53·102244+37)/9December 13, 2012Ray Chandler
249322453223932w39(29·102244+151)/9December 13, 2012Ray Chandler
249422453117931w79(28·102244+611)/9December 13, 2012Ray Chandler
249522452110721w07(19·102244-37)/9December 13, 2012Ray Chandler
24962244 89w339·102243-67December 13, 2012Ray Chandler
249722447003970w397·102243+39December 13, 2012Ray Chandler
24982244 663w1(199·102242-7)/3December 13, 2012Ray Chandler
249922438662786w27(26·102242-119)/3December 13, 2012Ray Chandler
250022436991769w177·102242-83December 13, 2012Ray Chandler
250222413442334w23(31·102240-193)/9December 13, 2012Ray Chandler
250322395992759w276·102238-73December 13, 2012Ray Chandler
250422391003710w37102238+37December 13, 2012Ray Chandler
250522389667396w73(29·102237+19)/3December 13, 2012Ray Chandler
250622388552785w27(77·102237-257)/9December 13, 2012Ray Chandler
250722386224762w47(56·102237+223)/9December 13, 2012Ray Chandler
250822385440954w09(49·102237-319)/9December 13, 2012Ray Chandler
250922378223782w37(74·102236+133)/9December 13, 2012Ray Chandler
251022372992129w213·102236-79December 13, 2012Ray Chandler
251122365004150w415·102235+41December 13, 2012Ray Chandler
251222358668186w81(26·102234+43)/3December 13, 2012Ray Chandler
251422351776317w63(16·102234-133)/9December 13, 2012Ray Chandler
251522347556375w63(68·102233+67)/9December 13, 2012Ray Chandler
251722336005360w536·102232+53December 13, 2012Ray Chandler
251822312664726w47(8·102230-59)/3December 13, 2012Ray Chandler
252022307009770w977·102229+97December 13, 2012Ray Chandler
252122299336193w61(28·102228+83)/3December 13, 2012Ray Chandler
252222298228382w83(74·102228+547)/9December 13, 2012Ray Chandler
252422286883768w37(62·102227-467)/9December 13, 2012Ray Chandler
252522283225132w51(29·102227+259)/9December 13, 2012Ray Chandler
252722267443974w39(67·102225-49)/9December 13, 2012Ray Chandler
252822263550135w01(32·102225-491)/9December 13, 2012Ray Chandler
252922261006910w69102225+69December 13, 2012Ray Chandler
25312225 64w99(58·102224+491)/9December 13, 2012Ray Chandler
25322224 880w988·102222+9December 13, 2012Ray Chandler
253522236551965w19(59·102222-329)/9December 13, 2012Ray Chandler
253622216007360w736·102220+73December 13, 2012Ray Chandler
253822203119731w97(28·102219+773)/9December 13, 2012Ray Chandler
254022189558795w87(86·102217+283)/9December 13, 2012Ray Chandler
254222187334973w49(22·102217+47)/3December 13, 2012Ray Chandler
254322184004940w494·102217+49December 13, 2012Ray Chandler
254522176449764w97(58·102216+473)/9December 13, 2012Ray Chandler
254622173225332w53(29·102216+277)/9December 13, 2012Ray Chandler
25472217 119w312·102215-7December 13, 2012Ray Chandler
254822168116981w69(73·102215+521)/9December 13, 2012Ray Chandler
25492216 556w9(167·102214+7)/3December 13, 2012Ray Chandler
255022153667136w71(11·102214+13)/3December 13, 2012Ray Chandler
255122145112351w23(46·102213+107)/9December 13, 2012Ray Chandler
255222134115941w59(37·102212+431)/9December 13, 2012Ray Chandler
25532213 26w99(8·102212+97)/3December 13, 2012Ray Chandler
255422129559395w93(86·102211+337)/9December 13, 2012Ray Chandler
255522123882338w23(35·102211-593)/9December 13, 2012Ray Chandler
255622116225962w59(56·102210+331)/9December 13, 2012Ray Chandler
255822093779337w93(34·102208+137)/9December 13, 2012Ray Chandler
255922091330913w09(4·102208-73)/3December 13, 2012Ray Chandler
256022088227182w71(74·102207+439)/9December 13, 2012Ray Chandler
25612208 26w33(8·102207-101)/3December 13, 2012Ray Chandler
256222079005990w599·102206+59December 13, 2012Ray Chandler
25632207 42w99(38·102206+691)/9December 13, 2012Ray Chandler
256422073660736w07(11·102206-179)/3December 13, 2012Ray Chandler
256522068448384w83(76·102205+347)/9December 13, 2012Ray Chandler
25672206 72w11(65·102205-101)/9December 13, 2012Ray Chandler
256822065992759w276·102205-73December 13, 2012Ray Chandler
257022059448394w83(85·102204+347)/9December 13, 2012Ray Chandler
257122053552335w23(32·102204-293)/9December 13, 2012Ray Chandler
257322051557315w73(14·102204+157)/9December 13, 2012Ray Chandler
25752204 64w11(58·102203-301)/9December 13, 2012Ray Chandler
257622043003730w373·102203+37December 13, 2012Ray Chandler
25772204 117w1(106·102202-61)/9December 13, 2012Ray Chandler
257922022776927w69(25·102201-79)/9December 13, 2012Ray Chandler
258022014882748w27(44·102200-557)/9December 13, 2012Ray Chandler

December 12, 2012

Factorizations of 677...77 have been extended up to n=250. Added composite numbers had passed ECM iterations 118 times at the level 35. Most unknown factors are supposed to be greater than 1030.

December 11, 2012

Ray Chandler certificated 9 near-repdigit prime numbers, 39 quasi-repdigit prime numbers and 129 near-repdigit-related prime numbers by Primo. Certifications are available.

Proven near-repdigit primes
 digitsflabelwlabelexpressionwhenwho
5292192 9w1999999999102192-8000000001December 11, 2012Ray Chandler
5302189 9w79999102189-20001December 11, 2012Ray Chandler
5322175 9w79999102175-20001December 11, 2012Ray Chandler
5342169 9w5999999102169-4000001December 11, 2012Ray Chandler
5352168 9w4999999102168-5000001December 11, 2012Ray Chandler
5382151 9w8999999102151-1000001December 11, 2012Ray Chandler
5392146999299w29102146-71December 11, 2012Ray Chandler
5402140333233w23(102140-31)/3December 11, 2012Ray Chandler
5412130 9w499999102130-500001December 11, 2012Ray Chandler
Proven quasi-repdigit primes (except pd)
 digitsflabelwlabelexpressionwhenwho
3932196111431w43(102196+287)/9December 11, 2012Ray Chandler
395219553111531w(478·102193-1)/9December 11, 2012Ray Chandler
396219527221272w1(245·102193-11)/9December 11, 2012Ray Chandler
397219410113101w3(91·102192+17)/9December 11, 2012Ray Chandler
398219390777907w(817·102191-7)/9December 11, 2012Ray Chandler
400218959557595w7(536·102187+13)/9December 11, 2012Ray Chandler
401218838777387w(349·102186-7)/9December 11, 2012Ray Chandler
4022187 337w(304·102185-7)/9December 11, 2012Ray Chandler
403218324229242w9(218·102181+61)/9December 11, 2012Ray Chandler
404218150559505w9(455·102179+31)/9December 11, 2012Ray Chandler
4062180222412w41(2·102180+169)/9December 11, 2012Ray Chandler
40821758339383w93(25·102174+179)/3December 11, 2012Ray Chandler
40921738995989w599·102172-41December 11, 2012Ray Chandler
4112170777417w41(7·102170-331)/9December 11, 2012Ray Chandler
412216910333103w(31·102167-1)/3December 11, 2012Ray Chandler
41321657993979w398·102164-61December 11, 2012Ray Chandler
414216550111501w(451·102163-1)/9December 11, 2012Ray Chandler
4172161444834w83(4·102161+347)/9December 11, 2012Ray Chandler
420215861669616w9(185·102156+7)/3December 11, 2012Ray Chandler
4232150888678w67(8·102150-197)/9December 11, 2012Ray Chandler
4242149555975w97(5·102149+373)/9December 11, 2012Ray Chandler
427214720333203w(61·102145-1)/3December 11, 2012Ray Chandler
428214117119171w9(154·102139+71)/9December 11, 2012Ray Chandler
43121385995959w596·102137-41December 11, 2012Ray Chandler
4332134666376w37(2·102134-89)/3December 11, 2012Ray Chandler
435213214113141w3(127·102130+17)/9December 11, 2012Ray Chandler
43621281334313w43(4·102127+29)/3December 11, 2012Ray Chandler
4372127555695w69(5·102127+121)/9December 11, 2012Ray Chandler
438212468663686w3(206·102122-11)/3December 11, 2012Ray Chandler
4392123555135w13(5·102123-383)/9December 11, 2012Ray Chandler
44221186113161w31(55·102117+179)/9December 11, 2012Ray Chandler
4432117888078w07(8·102117-737)/9December 11, 2012Ray Chandler
4452115666016w01(2·102115-197)/3December 11, 2012Ray Chandler
446211546447464w7(418·102113+23)/9December 11, 2012Ray Chandler
447211459111591w(532·102112-1)/9December 11, 2012Ray Chandler
44821121330313w03(4·102111-91)/3December 11, 2012Ray Chandler
449211161667616w7(185·102109+1)/3December 11, 2012Ray Chandler
450211128229282w9(254·102109+61)/9December 11, 2012Ray Chandler
453210641443414w3(373·102104-13)/9December 11, 2012Ray Chandler
Proven near-repdigit-related primes (except ru/nr/pd/qr)
 digitsflabelwlabelexpressionwhenwho
243321993997339w734·102198-27December 11, 2012Ray Chandler
243421989330793w07(28·102197-79)/3December 11, 2012Ray Chandler
243521983118931w89(28·102197+701)/9December 11, 2012Ray Chandler
24362197 663w7(199·102195+11)/3December 11, 2012Ray Chandler
243721976110361w03(55·102196-73)/9December 11, 2012Ray Chandler
243921962550925w09(23·102195-419)/9December 11, 2012Ray Chandler
24402195 64w99(58·102194+491)/9December 11, 2012Ray Chandler
244121952881728w17(26·102194-647)/9December 11, 2012Ray Chandler
244221931553115w31(14·102192-221)/9December 11, 2012Ray Chandler
244421924886948w69(44·102191-179)/9December 11, 2012Ray Chandler
244521904332743w27(13·102189-19)/3December 11, 2012Ray Chandler
244621899556995w69(86·102188+121)/9December 11, 2012Ray Chandler
244721896116961w69(55·102188+521)/9December 11, 2012Ray Chandler
244821886991369w137·102187-87December 11, 2012Ray Chandler
244921886550965w09(59·102187-419)/9December 11, 2012Ray Chandler
245021885229752w97(47·102187+673)/9December 11, 2012Ray Chandler
245121881662716w27(5·102187-119)/3December 11, 2012Ray Chandler
245221872446924w69(22·102186+221)/9December 11, 2012Ray Chandler
245421866115361w53(55·102185+377)/9December 11, 2012Ray Chandler
245521848338983w89(25·102183+167)/3December 11, 2012Ray Chandler
24562184 58w77(53·102183-107)/9December 11, 2012Ray Chandler
245721843440134w01(31·102183-391)/9December 11, 2012Ray Chandler
245821841449714w97(13·102183+473)/9December 11, 2012Ray Chandler
24602181 81w99(73·102180+791)/9December 11, 2012Ray Chandler
246221804778347w83(43·102179+47)/9December 11, 2012Ray Chandler
246421802445124w51(22·102179+59)/9December 11, 2012Ray Chandler
246521801557115w71(14·102179+139)/9December 11, 2012Ray Chandler
246621798001780w178·102178+17December 11, 2012Ray Chandler
24672179 770w377·102177+3December 11, 2012Ray Chandler
246821796998369w837·102178-17December 11, 2012Ray Chandler
247021772332123w21(7·102176-37)/3December 11, 2012Ray Chandler
247221759886198w61(89·102174-251)/9December 11, 2012Ray Chandler
247421754882148w21(44·102174-611)/9December 11, 2012Ray Chandler
247521749445994w59(85·102173+131)/9December 11, 2012Ray Chandler
247621741336113w61(4·102173+83)/3December 11, 2012Ray Chandler
247721735665756w57(17·102172-29)/3December 11, 2012Ray Chandler
247821719885198w51(89·102170-341)/9December 11, 2012Ray Chandler
247921709661796w17(29·102169-149)/3December 11, 2012Ray Chandler
24822169 883w1(265·102167-7)/3December 11, 2012Ray Chandler
248421694004340w434·102168+43December 11, 2012Ray Chandler
248521672883928w39(26·102166-449)/9December 11, 2012Ray Chandler
248621669112991w29(82·102165+161)/9December 11, 2012Ray Chandler
248721666995369w537·102165-47December 11, 2012Ray Chandler
248821664557945w79(41·102165+211)/9December 11, 2012Ray Chandler
248921657445374w53(67·102164+77)/9December 11, 2012Ray Chandler
24902165 50w775·102164+77December 11, 2012Ray Chandler
249121644665746w57(14·102163-29)/3December 11, 2012Ray Chandler
249221643884738w47(35·102163-377)/9December 11, 2012Ray Chandler
24932163 668w7(602·102161-17)/9December 11, 2012Ray Chandler
249521626112961w29(55·102161+161)/9December 11, 2012Ray Chandler
249821599667196w71(29·102158+13)/3December 11, 2012Ray Chandler
249921596994169w417·102158-59December 11, 2012Ray Chandler
250021591774917w49(16·102158-259)/9December 11, 2012Ray Chandler
250121587995179w518·102157-49December 11, 2012Ray Chandler
250321572776927w69(25·102156-79)/9December 11, 2012Ray Chandler
25042156 62w33(56·102155+97)/9December 11, 2012Ray Chandler
250521561226912w69(11·102155+421)/9December 11, 2012Ray Chandler
250921551552315w23(14·102154-293)/9December 11, 2012Ray Chandler
251221531663116w31(5·102152-107)/3December 11, 2012Ray Chandler
251421531332713w27(4·102152-19)/3December 11, 2012Ray Chandler
251621528992389w239·102151-77December 11, 2012Ray Chandler
251721522773127w31(25·102151-421)/9December 11, 2012Ray Chandler
251821513887938w79(35·102150-89)/9December 11, 2012Ray Chandler
25192151 34w11(31·102150-301)/9December 11, 2012Ray Chandler
252021512884128w41(26·102150-431)/9December 11, 2012Ray Chandler
252121512445724w57(22·102150+113)/9December 11, 2012Ray Chandler
252321503003730w373·102149+37December 11, 2012Ray Chandler
252421501005710w57102149+57December 11, 2012Ray Chandler
252521492550325w03(23·102148-473)/9December 11, 2012Ray Chandler
252621492447124w71(22·102148+239)/9December 11, 2012Ray Chandler
252721488662386w23(26·102147-131)/3December 11, 2012Ray Chandler
252921458668186w81(26·102144+43)/3December 11, 2012Ray Chandler
253021454339143w91(13·102144+173)/3December 11, 2012Ray Chandler
25312145 118w3(107·102143-53)/9December 11, 2012Ray Chandler
25332143 449w345·102141-7December 11, 2012Ray Chandler
253421428442184w21(76·102141-211)/9December 11, 2012Ray Chandler
25352142 82w33(74·102141+97)/9December 11, 2012Ray Chandler
253721427663776w37(23·102141-89)/3December 11, 2012Ray Chandler
253821424550145w01(41·102141-491)/9December 11, 2012Ray Chandler
253921422662126w21(8·102141-137)/3December 11, 2012Ray Chandler
254021419550995w09(86·102140-419)/9December 11, 2012Ray Chandler
25412141 880w388·102139+3December 11, 2012Ray Chandler
254221418114381w43(73·102140+287)/9December 11, 2012Ray Chandler
254421413551335w13(32·102140-383)/9December 11, 2012Ray Chandler
25452140 93w77(28·102139+131)/3December 11, 2012Ray Chandler
254621404664946w49(14·102139-53)/3December 11, 2012Ray Chandler
25472140 19w332·102139-67December 11, 2012Ray Chandler
254821401664316w43(5·102139-71)/3December 11, 2012Ray Chandler
254921394774947w49(43·102138-259)/9December 11, 2012Ray Chandler
255021393665336w53(11·102138-41)/3December 11, 2012Ray Chandler
255121389667996w79(29·102137+37)/3December 11, 2012Ray Chandler
25522138 64w33(58·102137-103)/9December 11, 2012Ray Chandler
25532138 37w11(34·102137-601)/9December 11, 2012Ray Chandler
255421382995129w513·102137-49December 11, 2012Ray Chandler
255521375338753w87(16·102136+161)/3December 11, 2012Ray Chandler
255921345223752w37(47·102133+133)/9December 11, 2012Ray Chandler
25602134 223w7(67·102132+11)/3December 11, 2012Ray Chandler
256121336884768w47(62·102132-377)/9December 11, 2012Ray Chandler
25622133 54w99(49·102132+491)/9December 11, 2012Ray Chandler
256421327882978w29(71·102131-539)/9December 11, 2012Ray Chandler
256521326448764w87(58·102131+383)/9December 11, 2012Ray Chandler
25672130 552w1(497·102128-11)/9December 11, 2012Ray Chandler
25682130 15w99(14·102129+391)/9December 11, 2012Ray Chandler
25692129 64w33(58·102128-103)/9December 11, 2012Ray Chandler
257021291447914w79(13·102128+311)/9December 11, 2012Ray Chandler
257121283770937w09(34·102127-619)/9December 11, 2012Ray Chandler
257221272552325w23(23·102126-293)/9December 11, 2012Ray Chandler
257521256882968w29(62·102124-539)/9December 11, 2012Ray Chandler
257621246117361w73(55·102123+557)/9December 11, 2012Ray Chandler
257721243771937w19(34·102123-529)/9December 11, 2012Ray Chandler
257921239227392w73(83·102122+457)/9December 11, 2012Ray Chandler
258021227441774w17(67·102121-247)/9December 11, 2012Ray Chandler
258121226223962w39(56·102121+151)/9December 11, 2012Ray Chandler
258221217448774w87(67·102120+383)/9December 11, 2012Ray Chandler
258421207338773w87(22·102119+161)/3December 11, 2012Ray Chandler
258821159772997w29(88·102114-439)/9December 11, 2012Ray Chandler
25892115 883w7(265·102113+11)/3December 11, 2012Ray Chandler
259021156228362w83(56·102114+547)/9December 11, 2012Ray Chandler
259121155882158w21(53·102114-611)/9December 11, 2012Ray Chandler
259221155449354w93(49·102114+437)/9December 11, 2012Ray Chandler
259521132665926w59(8·102112-23)/3December 11, 2012Ray Chandler
259621128662386w23(26·102111-131)/3December 11, 2012Ray Chandler
259921114220942w09(38·102110-119)/9December 11, 2012Ray Chandler
26002110 72w11(65·102109-101)/9December 11, 2012Ray Chandler
260121106991369w137·102109-87December 11, 2012Ray Chandler
260221094115741w57(37·102108+413)/9December 11, 2012Ray Chandler
260321093221332w13(29·102108-83)/9December 11, 2012Ray Chandler
260421087112371w23(64·102107+107)/9December 11, 2012Ray Chandler
261121027225372w53(65·102101+277)/9December 11, 2012Ray Chandler

December 10, 2012

Ray Chandler certificated 5 near-repdigit prime numbers, 39 quasi-repdigit prime numbers and 121 near-repdigit-related prime numbers by Primo. Certifications are available.

Proven near-repdigit primes
 digitsflabelwlabelexpressionwhenwho
538205131333313w(94·102049-1)/3December 10, 2012Ray Chandler
5392048 9w59999999102048-40000001December 10, 2012Ray Chandler
5432021 9w299999999102021-700000001December 10, 2012Ray Chandler
5502006 9w8999999999102006-1000000001December 10, 2012Ray Chandler
5512006333233w23(102006-31)/3December 10, 2012Ray Chandler
Proven quasi-repdigit primes (except pd)
 digitsflabelwlabelexpressionwhenwho
416209859553595w3(536·102096-23)/9December 10, 2012Ray Chandler
4192092444814w81(4·102092+329)/9December 10, 2012Ray Chandler
42120922990929w093·102091-91December 10, 2012Ray Chandler
42220913773737w37(34·102090-367)/9December 10, 2012Ray Chandler
4232086888078w07(8·102086-737)/9December 10, 2012Ray Chandler
4252083444694w69(4·102083+221)/9December 10, 2012Ray Chandler
4292072888298w29(8·102072-539)/9December 10, 2012Ray Chandler
4332068666796w79(2·102068+37)/3December 10, 2012Ray Chandler
434206794777947w(853·102065-7)/9December 10, 2012Ray Chandler
436206719333193w(58·102065-1)/3December 10, 2012Ray Chandler
438206528221282w1(254·102063-11)/9December 10, 2012Ray Chandler
440206360667606w7(182·102061+1)/3December 10, 2012Ray Chandler
44120624991949w195·102061-81December 10, 2012Ray Chandler
442206182881828w1(746·102059-71)/9December 10, 2012Ray Chandler
44320615998959w896·102060-11December 10, 2012Ray Chandler
4442060888678w67(8·102060-197)/9December 10, 2012Ray Chandler
4452060777537w53(7·102060-223)/9December 10, 2012Ray Chandler
446205983881838w1(755·102057-71)/9December 10, 2012Ray Chandler
44720595332353w23(16·102058-31)/3December 10, 2012Ray Chandler
4482056444214w21(4·102056-211)/9December 10, 2012Ray Chandler
4492055777317w31(7·102055-421)/9December 10, 2012Ray Chandler
45120533115131w51(28·102052+359)/9December 10, 2012Ray Chandler
452205257111571w(514·102050-1)/9December 10, 2012Ray Chandler
4532052444914w91(4·102052+419)/9December 10, 2012Ray Chandler
4542050555635w63(5·102050+67)/9December 10, 2012Ray Chandler
455204816777167w(151·102046-7)/9December 10, 2012Ray Chandler
4562044666796w79(2·102044+37)/3December 10, 2012Ray Chandler
458204087881878w1(791·102038-71)/9December 10, 2012Ray Chandler
45920407336373w63(22·102039+89)/3December 10, 2012Ray Chandler
46220366338363w83(19·102035+149)/3December 10, 2012Ray Chandler
463203568777687w(619·102033-7)/9December 10, 2012Ray Chandler
464203458111581w(523·102032-1)/9December 10, 2012Ray Chandler
46720326334363w43(19·102031+29)/3December 10, 2012Ray Chandler
468202569777697w(628·102023-7)/9December 10, 2012Ray Chandler
469202458333583w(175·102022-1)/3December 10, 2012Ray Chandler
4702024222972w97(2·102024+673)/9December 10, 2012Ray Chandler
47120195330353w03(16·102018-91)/3December 10, 2012Ray Chandler
483200659777597w(538·102004-7)/9December 10, 2012Ray Chandler
4842005 6w77(2·102005+31)/3December 10, 2012Ray Chandler
Proven near-repdigit-related primes (except ru/nr/pd/qr)
 digitsflabelwlabelexpressionwhenwho
248220989228192w81(83·102097+529)/9December 10, 2012Ray Chandler
248420982559325w93(23·102097+337)/9December 10, 2012Ray Chandler
248520979334793w47(28·102096+41)/3December 10, 2012Ray Chandler
24862097 13w99(4·102096+197)/3December 10, 2012Ray Chandler
248720969887398w73(89·102095-143)/9December 10, 2012Ray Chandler
248920961445314w53(13·102095+77)/9December 10, 2012Ray Chandler
249120949882998w29(89·102093-539)/9December 10, 2012Ray Chandler
249220941336913w69(4·102093+107)/3December 10, 2012Ray Chandler
249420933557335w73(32·102092+157)/9December 10, 2012Ray Chandler
24952092 557w3(502·102090-43)/9December 10, 2012Ray Chandler
249720907665176w51(23·102089-47)/3December 10, 2012Ray Chandler
249820894551945w19(41·102088-329)/9December 10, 2012Ray Chandler
249920893661736w17(11·102088-149)/3December 10, 2012Ray Chandler
250020893448134w81(31·102088+329)/9December 10, 2012Ray Chandler
250120871669316w93(5·102086+79)/3December 10, 2012Ray Chandler
250220869226392w63(83·102085+367)/9December 10, 2012Ray Chandler
250320865442954w29(49·102085-139)/9December 10, 2012Ray Chandler
250620851990319w032·102084-97December 10, 2012Ray Chandler
250720846778167w81(61·102083+29)/9December 10, 2012Ray Chandler
250920842886128w61(26·102083-251)/9December 10, 2012Ray Chandler
251020841774317w43(16·102083-313)/9December 10, 2012Ray Chandler
251120841226312w63(11·102083+367)/9December 10, 2012Ray Chandler
251220831227112w71(11·102082+439)/9December 10, 2012Ray Chandler
251320823114731w47(28·102081+323)/9December 10, 2012Ray Chandler
251420816556765w67(59·102080+103)/9December 10, 2012Ray Chandler
251520809448794w87(85·102079+383)/9December 10, 2012Ray Chandler
251620807554175w41(68·102079-131)/9December 10, 2012Ray Chandler
251720803116931w69(28·102079+521)/9December 10, 2012Ray Chandler
252020786558765w87(59·102077+283)/9December 10, 2012Ray Chandler
252120784116741w67(37·102077+503)/9December 10, 2012Ray Chandler
252220778223782w37(74·102076+133)/9December 10, 2012Ray Chandler
252520768225982w59(74·102075+331)/9December 10, 2012Ray Chandler
25272074 993w1(298·102072-7)/3December 10, 2012Ray Chandler
252820747110371w03(64·102073-73)/9December 10, 2012Ray Chandler
252920733883738w37(35·102072-467)/9December 10, 2012Ray Chandler
25302073 32w11(29·102072-101)/9December 10, 2012Ray Chandler
253120728228982w89(74·102071+601)/9December 10, 2012Ray Chandler
253220711558315w83(14·102070+247)/9December 10, 2012Ray Chandler
253320707335773w57(22·102069+71)/3December 10, 2012Ray Chandler
253420694660346w03(14·102068-191)/3December 10, 2012Ray Chandler
253520692115721w57(19·102068+413)/9December 10, 2012Ray Chandler
25362068 880w388·102066+3December 10, 2012Ray Chandler
253720686990769w077·102067-93December 10, 2012Ray Chandler
25392065 71w33(64·102064+197)/9December 10, 2012Ray Chandler
254020656886368w63(62·102064-233)/9December 10, 2012Ray Chandler
25422064 776w9(233·102062+7)/3December 10, 2012Ray Chandler
254320641770117w01(16·102063-691)/9December 10, 2012Ray Chandler
254620638559785w97(77·102062+373)/9December 10, 2012Ray Chandler
254720637556375w63(68·102062+67)/9December 10, 2012Ray Chandler
254820635997159w716·102062-29December 10, 2012Ray Chandler
255220621551315w13(14·102061-383)/9December 10, 2012Ray Chandler
25542060 220w922·102058+9December 10, 2012Ray Chandler
255520597003970w397·102058+39December 10, 2012Ray Chandler
25572058 993w7(298·102056+11)/3December 10, 2012Ray Chandler
255920558118781w87(73·102054+683)/9December 10, 2012Ray Chandler
256020556005360w536·102054+53December 10, 2012Ray Chandler
256120548774987w49(79·102053-259)/9December 10, 2012Ray Chandler
256220547669776w97(23·102053+91)/3December 10, 2012Ray Chandler
25632053 779w378·102051-7December 10, 2012Ray Chandler
256420535662956w29(17·102052-113)/3December 10, 2012Ray Chandler
256520534993149w315·102052-69December 10, 2012Ray Chandler
256620532002720w272·102052+27December 10, 2012Ray Chandler
25672052 62w77(56·102051+493)/9December 10, 2012Ray Chandler
25712051 338w9(305·102049+1)/9December 10, 2012Ray Chandler
257220512880728w07(26·102050-737)/9December 10, 2012Ray Chandler
25732051 118w1(107·102049-71)/9December 10, 2012Ray Chandler
25742049 775w3(698·102047-23)/9December 10, 2012Ray Chandler
257520494330143w01(13·102048-97)/3December 10, 2012Ray Chandler
257620485998359w836·102047-17December 10, 2012Ray Chandler
257920476007360w736·102046+73December 10, 2012Ray Chandler
258020474002140w214·102046+21December 10, 2012Ray Chandler
25812045 883w7(265·102043+11)/3December 10, 2012Ray Chandler
258220452110721w07(19·102044-37)/9December 10, 2012Ray Chandler
258320446447364w73(58·102043+257)/9December 10, 2012Ray Chandler
25842043 557w1(502·102041-61)/9December 10, 2012Ray Chandler
25852043 16w99(5·102042+97)/3December 10, 2012Ray Chandler
258820415665356w53(17·102040-41)/3December 10, 2012Ray Chandler
25912040 991w7(892·102038+53)/9December 10, 2012Ray Chandler
259220406774167w41(61·102039-331)/9December 10, 2012Ray Chandler
259420399775997w59(88·102038-169)/9December 10, 2012Ray Chandler
259520395448754w87(49·102038+383)/9December 10, 2012Ray Chandler
259620393116931w69(28·102038+521)/9December 10, 2012Ray Chandler
25982038 69w777·102037-23December 10, 2012Ray Chandler
259920368663986w39(26·102035-83)/3December 10, 2012Ray Chandler
260320351009310w93102034+93December 10, 2012Ray Chandler
260420344779147w91(43·102033+119)/9December 10, 2012Ray Chandler
260620329223992w39(83·102031+151)/9December 10, 2012Ray Chandler
260720322662126w21(8·102031-137)/3December 10, 2012Ray Chandler
26082031 76w99(23·102030+97)/3December 10, 2012Ray Chandler
260920311227912w79(11·102030+511)/9December 10, 2012Ray Chandler
26112027 50w775·102026+77December 10, 2012Ray Chandler
261220272554925w49(23·102026-59)/9December 10, 2012Ray Chandler
26132026 770w377·102024+3December 10, 2012Ray Chandler
261420265664156w41(17·102025-77)/3December 10, 2012Ray Chandler
261520263448134w81(31·102025+329)/9December 10, 2012Ray Chandler
261620259228392w83(83·102024+547)/9December 10, 2012Ray Chandler
261820252556325w63(23·102024+67)/9December 10, 2012Ray Chandler
261920252445724w57(22·102024+113)/9December 10, 2012Ray Chandler
262320238557985w79(77·102022+211)/9December 10, 2012Ray Chandler
262420228665386w53(26·102021-41)/3December 10, 2012Ray Chandler
26252021 92w33(83·102020+97)/9December 10, 2012Ray Chandler
262720217330173w01(22·102020-97)/3December 10, 2012Ray Chandler
262920201991319w132·102019-87December 10, 2012Ray Chandler
26302019 84w11(76·102018-301)/9December 10, 2012Ray Chandler
263120192885728w57(26·102018-287)/9December 10, 2012Ray Chandler
263220191449314w93(13·102018+437)/9December 10, 2012Ray Chandler
263320176550365w03(59·102016-473)/9December 10, 2012Ray Chandler
263420175886358w63(53·102016-233)/9December 10, 2012Ray Chandler
26382015 667w9(601·102013+11)/9December 10, 2012Ray Chandler
263920154885748w57(44·102014-287)/9December 10, 2012Ray Chandler
264420098114981w49(73·102008+341)/9December 10, 2012Ray Chandler
264920057330173w01(22·102004-97)/3December 10, 2012Ray Chandler
265220047886778w67(71·102003-197)/9December 10, 2012Ray Chandler
265320046994369w437·102003-57December 10, 2012Ray Chandler
265420043990139w014·102003-99December 10, 2012Ray Chandler
265520043662336w23(11·102003-131)/3December 10, 2012Ray Chandler
265620032995729w573·102002-43December 10, 2012Ray Chandler
265720032776127w61(25·102002-151)/9December 10, 2012Ray Chandler
26592002 23w99(7·102001+197)/3December 10, 2012Ray Chandler
266020017446974w69(67·102000+221)/9December 10, 2012Ray Chandler
266320011886318w63(17·102000-233)/9December 10, 2012Ray Chandler

December 9, 2012

Factorizations of 600...007 have been extended up to n=250. Added composite numbers had passed ECM iterations 118 times at the level 35. Most unknown factors are supposed to be greater than 1030.

December 6, 2012

Factorizations of 577...77 have been extended up to n=250. Added composite numbers had passed ECM iterations 118 times at the level 35. Most unknown factors are supposed to be greater than 1030.

December 4, 2012

Factorizations of 499...991 have been extended up to n=250. Added composite numbers had passed ECM iterations 118 times at the level 35. Most unknown factors are supposed to be greater than 1030.

December 2, 2012

Factorizations of 866...663 have been extended up to n=250. Added composite numbers had passed ECM iterations 118 times at the level 35. Most unknown factors are supposed to be greater than 1030.

November 2012

November 30, 2012

Factorizations of 722...223 have been extended up to n=250. Added composite numbers had passed ECM iterations 118 times at the level 35. Most unknown factors are supposed to be greater than 1030.

November 27, 2012

Factorizations of 44...441 have been extended up to n=250. Added composite numbers had passed ECM iterations 118 times at the level 35. Most unknown factors are supposed to be greater than 1030.

November 25, 2012

Factorizations of 400...007 have been extended up to n=250. Added composite numbers had passed ECM iterations 118 times at the level 35. Most unknown factors are supposed to be greater than 1030.

November 24, 2012

Factorizations of 166...661 have been extended up to n=250. Added composite numbers had passed ECM iterations 118 times at the level 35. Most unknown factors are supposed to be greater than 1030.

November 22, 2012

Factorizations of 155...559 have been extended up to n=250. Added composite numbers had passed ECM iterations 118 times at the level 35. Most unknown factors are supposed to be greater than 1030.

November 21, 2012

Factorizations of 588...889 have been extended up to n=250. Added composite numbers had passed ECM iterations 118 times at the level 35. Most unknown factors are supposed to be greater than 1030.

November 20, 2012

Factorizations of 355...559 have been extended up to n=250. Added composite numbers had passed ECM iterations 118 times at the level 35. Most unknown factors are supposed to be greater than 1030.

November 19, 2012

Factorizations of 99...997 have been extended up to n=250. Added composite numbers had passed ECM iterations 118 times at the level 35. Most unknown factors are supposed to be greater than 1030.

November 18, 2012

Factorizations of 844...449 have been extended up to n=250. Added composite numbers had passed ECM iterations 118 times at the level 35. Most unknown factors are supposed to be greater than 1030.

November 16, 2012

Factorizations of 488...881 have been extended up to n=250. Added composite numbers had passed ECM iterations 118 times at the level 35. Most unknown factors are supposed to be greater than 1030.

November 15, 2012

Factorizations of 22...221 have been extended up to n=250. Added composite numbers had passed ECM iterations 118 times at the level 35. Most unknown factors are supposed to be greater than 1030.

November 13, 2012

Factorizations of 422...227 have been extended up to n=250. Added composite numbers had passed ECM iterations 118 times at the level 35. Most unknown factors are supposed to be greater than 1030.

November 12, 2012

Factorizations of 400...003 have been extended up to n=250. Added composite numbers had passed ECM iterations 118 times at the level 35. Most unknown factors are supposed to be greater than 1030.

November 1, 2012

Factorizations of 988...881 have been extended up to n=250. Added composite numbers had passed ECM iterations 118 times at the level 35. Most unknown factors are supposed to be greater than 1030.

October 2012

October 27, 2012

Factorizations of 155...551 have been extended up to n=250. Added composite numbers had passed ECM iterations 118 times at the level 35. Most unknown factors are supposed to be greater than 1030.

October 22, 2012

Factorizations of 822...229 have been extended up to n=250. Added composite numbers had passed ECM iterations 118 times at the level 35. Most unknown factors are supposed to be greater than 1030.

October 15, 2012

Factorizations of 799...997 have been extended up to n=250. Added composite numbers had passed ECM iterations 118 times at the level 35. Most unknown factors are supposed to be greater than 1030.

October 9, 2012

Factorizations of 855...553 have been extended up to n=250. Added composite numbers had passed ECM iterations 118 times at the level 35. Most unknown factors are supposed to be greater than 1030.

October 4, 2012

Factorizations of 388...883 have been extended up to n=250. Added composite numbers had passed ECM iterations 118 times at the level 35. Most unknown factors are supposed to be greater than 1030.

September 2012

September 27, 2012

Markus Tervooren proved primality of 107668+3 by ECPP. Certification is available.

Proven quasi-repdigit primes (except pd)
 digitsflabelwlabelexpressionwhenwho
17676691000310w3107668+3September 27, 2012Markus Tervooren

September 26, 2012

Factorizations of 177...773 have been extended up to n=250. Added composite numbers had passed ECM iterations 118 times at the level 35. Most unknown factors are supposed to be greater than 1030.

September 21, 2012

Factorizations of 88...883 have been extended up to n=250. Added composite numbers had passed ECM iterations 118 times at the level 35. Most unknown factors are supposed to be greater than 1030.

September 15, 2012

Factorizations of 322...223 have been extended up to n=250. Added composite numbers had passed ECM iterations 118 times at the level 35. Most unknown factors are supposed to be greater than 1030.

September 13, 2012

Alexander Gramolin found the largest known quasi-repdit prime number. Congratulations!

Proven quasi-repdigit primes (except pd)
 digitsflabelwlabelexpressionwhenwho
16658303000130w13·10665829+1September 13, 2012Alexander Gramolin

September 9, 2012

Factorizations of 233...339 have been extended up to n=250. Added composite numbers had passed ECM iterations 118 times at the level 35. Most unknown factors are supposed to be greater than 1030.

September 5, 2012

Stefano D'Urso found the 46th prime number of the form 1003205·10n-1. It's also the largest known prime number of the form k·10n-1 where k generates 45 known prime numbers at least. Congratulations!

Prime numbers of the form k·10n-1 (including 45 known prime numbers at least)
 digitsflabelwlabelexpressionwhenwho
1314712 10032049w1003205·10314705-1September 5, 2012Stefano D'Urso

September 2, 2012

Factorizations of 22...227 have been extended up to n=250. Added composite numbers had passed ECM iterations 118 times at the level 35. Most unknown factors are supposed to be greater than 1030.

August 2012

August 28, 2012

Factorizations of 211...11 have been extended up to n=250. Added composite numbers had passed ECM iterations 118 times at the level 35. Most unknown factors are supposed to be greater than 1030.

August 24, 2012

Stefano D'Urso found the 45th prime number of the form 1003205·10n-1. It's also the largest known prime number of the form k·10n-1 where k generates 45 known prime numbers at least. Congratulations!

Prime numbers of the form k·10n-1 (including 45 known prime numbers at least)
 digitsflabelwlabelexpressionwhenwho
1291684 10032049w1003205·10291677-1August 24, 2012Stefano D'Urso
2258342 10032049w1003205·10258335-1May 4, 2012Stefano D'Urso
8217813 10032049w1003205·10217806-1January 8, 2012Stefano D'Urso

August 22, 2012

Factorizations of 133...331 have been extended up to n=250. Added composite numbers had passed ECM iterations 118 times at the level 35. Most unknown factors are supposed to be greater than 1030.

August 17, 2012

Factorizations of 100...007 have been extended up to n=250. Added composite numbers had passed ECM iterations 118 times at the level 35. Most unknown factors are supposed to be greater than 1030.

August 14, 2012

Mathew proved 2 near-repdigit primes and 4 quasi-repdigit primes by Primo. Certifications are available.

Proven near-repdigit primes
 digitsflabelwlabelexpressionwhenwho
4024709335333w53w(104709+6·102354-1)/3August 10, 2012Mathew
4363641335333w53w(103641+6·101820-1)/3August 5, 2012Mathew
Proven quasi-repdigit primes (except pd)
 digitsflabelwlabelexpressionwhenwho
24341234999349w35·104122-7August 12, 2012Mathew
26834738444384w3(76·103472-13)/9August 14, 2012Mathew
27533264999349w35·103325-7August 12, 2012Mathew
28531648444384w3(76·103163-13)/9August 13, 2012Mathew

August 12, 2012

Factorizations of 133...33 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.

August 8, 2012

Factorizations of 411...119 have been extended up to n=250. Added composite numbers had passed ECM iterations 118 times at the level 35. Most unknown factors are supposed to be greater than 1030.

August 5, 2012

Alexander Gramolin found the largest proven quasi-repdit prime (except pd). Congratulations!

Proven quasi-repdigit primes (except pd)
 digitsflabelwlabelexpressionwhenwho
16188543000130w13·10618853+1August 5, 2012Alexander Gramolin

August 1, 2012

Factorizations of 355...557 have been extended up to n=250. Added composite numbers had passed ECM iterations 118 times at the level 35. Most unknown factors are supposed to be greater than 1030.

July 2012

July 29, 2012

Mathew proved a quasi-repdigit prime by Primo. Certifications are available.

Proven quasi-repdigit primes (except pd)
 digitsflabelwlabelexpressionwhenwho
28531111666716w7(5·103110+1)/3July 29, 2012Mathew

July 27, 2012

Factorizations of 322...229 have been extended up to n=250. Added composite numbers had passed ECM iterations 118 times at the level 35. Most unknown factors are supposed to be greater than 1030.

July 23, 2012

Factorizations of 155...557 have been extended up to n=250. Added composite numbers had passed ECM iterations 118 times at the level 35. Most unknown factors are supposed to be greater than 1030.

July 18, 2012

Factorizations of 911...119 have been extended up to n=250. Added composite numbers had passed ECM iterations 118 times at the level 35. Most unknown factors are supposed to be greater than 1030.

July 14, 2012

Factorizations of 133...337 have been extended up to n=250. Added composite numbers had passed ECM iterations 118 times at the level 35. Most unknown factors are supposed to be greater than 1030.

July 10, 2012

Factorizations of 733...331 have been extended up to n=250. Added composite numbers had passed ECM iterations 118 times at the level 35. Most unknown factors are supposed to be greater than 1030.

July 4, 2012

Factorizations of 955...559 have been extended up to n=250. Added composite numbers had passed ECM iterations 118 times at the level 35. Most unknown factors are supposed to be greater than 1030.

June 2012

June 28, 2012

Factorizations of 77...77477...77 have been extended up to n=150. Added composite numbers had passed ECM iterations 118 times at the level 35. Most unknown factors are supposed to be greater than 1030.

June 26, 2012

Erik Branger pointed out that the Murphy_E score of some SNFS polynomials can be greatly improved by multiplied by a small number. So, I changed the polynomial selection method to new one based on the Murphy_E score. For example, SNFS polynomial of 77677_119 was changed from 700000·(1039)6-900·(1039)3-7 to 7·(1040)6-9·(1040)3-70. Its Murphy_E score was increased from 3.597e-13 to 5.537e-13. Sieving time may be shortened but I'm not sure whether the change always brings positive effects.

June 20, 2012

Factorizations of 377...77 have been extended up to n=250. Added composite numbers had passed ECM iterations 118 times at the level 35. Most unknown factors are supposed to be greater than 1030.

June 14, 2012

Factorizations of 922...221 have been extended up to n=250. Added composite numbers had passed ECM iterations 118 times at the level 35. Most unknown factors are supposed to be greater than 1030.

June 11, 2012

Ray Chandler reported that no additional prime number of the form 7347764627675020164·10n-1 up to n=200000 was found.

June 8, 2012

Factorizations of 211...117 have been extended up to n=250. Added composite numbers had passed ECM iterations 118 times at the level 35. Most unknown factors are supposed to be greater than 1030.

June 4, 2012

The threshold of the wanted list 3, composite numbers which are longer than 97 percent of the corresponding SNFS polynomial, has been raised from 95 percent at the suggestion of Serge Batalov.

June 3, 2012

Please make sure of your mail address before making reservations. Thank you.

June 2, 2012

Factorizations of 966...667 have been extended up to n=250. Added composite numbers had passed ECM iterations 118 times at the level 35. Most unknown factors are supposed to be greater than 1030.

May 2012

May 27, 2012

Factorizations of 944...447 have been extended up to n=250. Added composite numbers had passed ECM iterations 118 times at the level 35. Most unknown factors are supposed to be greater than 1030.

May 22, 2012

Factorizations of 855...557 have been extended up to n=250. Added composite numbers had passed ECM iterations 118 times at the level 35. Most unknown factors are supposed to be greater than 1030.

May 16, 2012

Factorizations of 155...553 have been extended up to n=250. Added composite numbers had passed ECM iterations 118 times at the level 35. Most unknown factors are supposed to be greater than 1030.

May 14, 2012

Erik Branger has finished searching prime numbers of the form 711...11 until 200000 digits.

May 11, 2012

Factorizations of 144...441 have been extended up to n=250. Added composite numbers had passed ECM iterations 118 times at the level 35. Most unknown factors are supposed to be greater than 1030.

May 5, 2012

Factorizations of 122...227 have been extended up to n=250. Added composite numbers had passed ECM iterations 118 times at the level 35. Most unknown factors are supposed to be greater than 1030.

May 1, 2012

Factorizations of 522...223 have been extended up to n=250. Added composite numbers had passed ECM iterations 118 times at the level 35. Most unknown factors are supposed to be greater than 1030.

April 2012

April 24, 2012

Factorizations of 199...997 have been extended up to n=250. Added composite numbers had passed ECM iterations 118 times at the level 35. Most unknown factors are supposed to be greater than 1030.

April 19, 2012

Factorizations of 99...99799...99 have been extended up to n=150. Added composite numbers had passed ECM iterations 118 times at the level 35. Most unknown factors are supposed to be greater than 1030.

April 16, 2012

History of searching prime numbers of each form is available. e.g. History of searching prime numbers of the form 77...771

April 15, 2012

Erik Branger has finished searching prime numbers of the form 77...771 until 300000 digits.

April 13, 2012

Factorizations of 511...117 have been extended up to n=250. Added composite numbers had passed ECM iterations 118 times at the level 35. Most unknown factors are supposed to be greater than 1030.

April 11, 2012

Darren Bedwell found the largest known near-repdigit-palindrome prime number. Congratulations!

Proven near-repdigit-palindrome primes
 digitsflabelwlabelexpressionwhenwho
1290253997999w79w10290253-2·10145126-1April 11, 2012Darren Bedwell

April 9, 2012

Factorizations of 699...991 have been extended up to n=250. Added composite numbers had passed ECM iterations 118 times at the level 35. Most unknown factors are supposed to be greater than 1030.

April 5, 2012

Factorizations of 911...11 have been extended up to n=250. Added composite numbers had passed ECM iterations 118 times at the level 35. Most unknown factors are supposed to be greater than 1030.

April 2, 2012

Factorizations of 433...331 have been extended up to n=250. Added composite numbers had passed ECM iterations 118 times at the level 35. Most unknown factors are supposed to be greater than 1030.

Ray Chandler found the 62nd prime number of the form 7347764627675020164·10n-1.

Prime numbers of the form k·10n-1 (including 45 known prime numbers at least)
 digitsflabelwlabelexpressionwhenwho
11145198 73477646276750201639w7347764627675020164·10145179-1April 2, 2012Ray Chandler

March 2012

March 30, 2012

Factorizations of 977...773 have been extended up to n=250. Added composite numbers had passed ECM iterations 118 times at the level 35. Most unknown factors are supposed to be greater than 1030.

March 29, 2012

Erik Branger proved 114 prime cofactors of Phin(10) by ECPP. See Primality certifications.

March 27, 2012

Ray Chandler found the 61st prime number of the form 7347764627675020164·10n-1.

Prime numbers of the form k·10n-1 (including 45 known prime numbers at least)
 digitsflabelwlabelexpressionwhenwho
12136281 73477646276750201639w7347764627675020164·10136262-1March 27, 2012Ray Chandler

March 26, 2012

Factorizations of 766...661 have been extended up to n=250. Added composite numbers had passed ECM iterations 118 times at the level 35. Most unknown factors are supposed to be greater than 1030.

March 21, 2012

Factorizations of 77...77877...77 have been extended up to n=150. Added composite numbers had passed ECM iterations 118 times at the level 35. Most unknown factors are supposed to be greater than 1030.

March 15, 2012

Factorizations of 255...557 have been extended up to n=250. Added composite numbers had passed ECM iterations 118 times at the level 35. Most unknown factors are supposed to be greater than 1030.

March 12, 2012

Ray Chandler found 15 prime numbers of the form k·10n-1 (including 45 known prime numbers at least). 46th-47th of n=1199620156415569595, 48th of n=24255533047620308, 49th of n=248108640286930808, 51st of n=330640210602617363, 46th of n=4155941632109082935, 48th of n=5189395769656459445, 47th of n=529220357182862954, 47th of n=5410621003833542777, 49th of n=5906181743052623648, 50th of n=8058799722014140442, 53rd of n=8861036989751958627 and 50th-52nd of n=9334983988275764.

Prime numbers of the form k·10n-1 (including 45 known prime numbers at least)
 digitsflabelwlabelexpressionwhenwho
3649659 93349839882757639w9334983988275764·1049643-1March 12, 2012Ray Chandler
3949360 93349839882757639w9334983988275764·1049344-1March 12, 2012Ray Chandler
4249236 51893957696564594449w5189395769656459445·1049217-1March 12, 2012Ray Chandler
5947345 80587997220141404419w8058799722014140442·1047326-1March 12, 2012Ray Chandler
7745701 2481086402869308079w248108640286930808·1045683-1March 12, 2012Ray Chandler
7945490 93349839882757639w9334983988275764·1045474-1March 12, 2012Ray Chandler
8045473 59061817430526236479w5906181743052623648·1045454-1March 12, 2012Ray Chandler
8445137 41559416321090829349w4155941632109082935·1045118-1March 12, 2012Ray Chandler
8744799 5292203571828629539w529220357182862954·1044781-1March 12, 2012Ray Chandler
8944758 11996201564155695949w1199620156415569595·1044739-1March 12, 2012Ray Chandler
9044649 11996201564155695949w1199620156415569595·1044630-1March 12, 2012Ray Chandler
9943416 242555330476203079w24255533047620308·1043399-1March 12, 2012Ray Chandler
10542851 54106210038335427769w5410621003833542777·1042832-1March 12, 2012Ray Chandler
10742668 3306402106026173629w330640210602617363·1042650-1March 12, 2012Ray Chandler
10842548 88610369897519586269w8861036989751958627·1042529-1March 12, 2012Ray Chandler

Factorizations of 88...881 have been extended up to n=250. Added composite numbers had passed ECM iterations 118 times at the level 35. Most unknown factors are supposed to be greater than 1030.

March 7, 2012

Factorizations of 844...441 have been extended up to n=250. Added composite numbers had passed ECM iterations 118 times at the level 35. Most unknown factors are supposed to be greater than 1030.

March 5, 2012

Erik Branger found the third largest known unprovable near-repdigit PRP. Congratulations!

Unprovable near-repdigit PRPs
 digitsflabelwlabelexpressionwhenwho
3271757777717w1(7·10271757-61)/9March 5, 2012Erik Branger

March 4, 2012

Factorizations of 744...443 have been extended up to n=250. Added composite numbers had passed ECM iterations 118 times at the level 35. Most unknown factors are supposed to be greater than 1030.

February 2012

February 29, 2012

Darren Bedwell found the largest known near-repdigit-palindrome prime number. Congratulations!

Proven near-repdigit-palindrome primes
 digitsflabelwlabelexpressionwhenwho
1269479992999w29w10269479-7·10134739-1February 29, 2012Darren Bedwell

February 28, 2012

Ray Chandler found the 60th prime number of the form 7347764627675020164·10n-1. Congratulations!

Prime numbers of the form k·10n-1 (including 45 known prime numbers at least)
 digitsflabelwlabelexpressionwhenwho
13103129 73477646276750201639w7347764627675020164·10103110-1February 28, 2012Ray Chandler

Factorizations of 755...559 have been extended up to n=250. Added composite numbers had passed ECM iterations 118 times at the level 35. Most unknown factors are supposed to be greater than 1030.

February 24, 2012

Alexander Gramolin found the second largest proven quasi-repdit prime (except pd). Congratulations!

Proven quasi-repdigit primes (except pd)
 digitsflabelwlabelexpressionwhenwho
21119893000130w13·10111988+1February 24, 2012Alexander Gramolin

Factorizations of 933...337 have been extended up to n=250. Added composite numbers had passed ECM iterations 118 times at the level 35. Most unknown factors are supposed to be greater than 1030.

February 22, 2012

Ray Chandler found 24 prime numbers of the form k·10n-1 (including 45 known prime numbers at least). 45th-46th of n=8461887092138837, 48th-49th of n=9334983988275764, 45th-47th of n=15600468793880159, 48th of n=16337430201479681, 46th-47th of n=24255533047620308, 47th-48th of n=29472578289080199, 48th of n=30895035496936877, 44th of n=35627728454703812, 48th of n=248108640286930808, 50th of n=330640210602617363, 44th of n=1089887362034810066, 52nd-53rd of n=3688107672047143961, 48th of n=3745413626697133958, 46th of n=5410621003833542777, 48th of n=5906181743052623648, 48th-49th of n=8058799722014140442 and 46th-47th of n=8124529194875611707.

Prime numbers of the form k·10n-1 (including 45 known prime numbers at least)
 digitsflabelwlabelexpressionwhenwho
10641913 54106210038335427769w5410621003833542777·1041894-1February 22, 2012Ray Chandler
11341145 36881076720471439609w3688107672047143961·1041126-1February 22, 2012Ray Chandler
11840844 294725782890801989w29472578289080199·1040827-1February 22, 2012Ray Chandler
11940829 84618870921388369w8461887092138837·1040813-1February 22, 2012Ray Chandler
12340273 156004687938801589w15600468793880159·1040256-1February 22, 2012Ray Chandler
13139537 84618870921388369w8461887092138837·1039521-1February 22, 2012Ray Chandler
13239534 2481086402869308079w248108640286930808·1039516-1February 22, 2012Ray Chandler
13739365 93349839882757639w9334983988275764·1039349-1February 22, 2012Ray Chandler
13939293 242555330476203079w24255533047620308·1039276-1February 22, 2012Ray Chandler
14039227 81245291948756117069w8124529194875611707·1039208-1February 22, 2012Ray Chandler
14139068 93349839882757639w9334983988275764·1039052-1February 22, 2012Ray Chandler
14538699 80587997220141404419w8058799722014140442·1038680-1February 22, 2012Ray Chandler
14738691 156004687938801589w15600468793880159·1038674-1February 22, 2012Ray Chandler
15538100 242555330476203079w24255533047620308·1038083-1February 22, 2012Ray Chandler
15638049 156004687938801589w15600468793880159·1038032-1February 22, 2012Ray Chandler
16737331 59061817430526236479w5906181743052623648·1037312-1February 22, 2012Ray Chandler
17237060 294725782890801989w29472578289080199·1037043-1February 22, 2012Ray Chandler
18536230 80587997220141404419w8058799722014140442·1036211-1February 22, 2012Ray Chandler
18736124 37454136266971339579w3745413626697133958·1036105-1February 22, 2012Ray Chandler
18936058 308950354969368769w30895035496936877·1036041-1February 22, 2012Ray Chandler
19335527 81245291948756117069w8124529194875611707·1035508-1February 22, 2012Ray Chandler
19535416 163374302014796809w16337430201479681·1035399-1February 22, 2012Ray Chandler
20534928 3306402106026173629w330640210602617363·1034910-1February 22, 2012Ray Chandler
23033279 36881076720471439609w3688107672047143961·1033260-1February 22, 2012Ray Chandler

February 21, 2012

Ray Chandler found 18 prime numbers of the form k·10n-1 (including 45 known prime numbers at least). 50th of n=5849194205932532, 50th of n=10471993823152799, 49th-50th of n=11885302750562514, 50th-52nd of n=13523719823507418, 45th-46th of n=24395082050363864, 47th of n=37731518958711032, 51st of n=2265457412699262446, 45th of n=2960341158972475544, 46th-47th of n=5586437116317036434, 50th-51st of n=6758517141263266764, 45th of n=7270120168119633986 and 49th of n=8953919255802171035.

Prime numbers of the form k·10n-1 (including 45 known prime numbers at least)
 digitsflabelwlabelexpressionwhenwho
3549619 72701201681196339859w7270120168119633986·1049600-1February 21, 2012Ray Chandler
4148828 58491942059325319w5849194205932532·1048812-1February 21, 2012Ray Chandler
4747963 104719938231527989w10471993823152799·1047946-1February 21, 2012Ray Chandler
5047669 118853027505625139w11885302750562514·1047652-1February 21, 2012Ray Chandler
5946852 377315189587110319w37731518958711032·1046835-1February 21, 2012Ray Chandler
7545185 243950820503638639w24395082050363864·1045168-1February 21, 2012Ray Chandler
8044310 118853027505625139w11885302750562514·1044293-1February 21, 2012Ray Chandler
8943300 29603411589724755439w2960341158972475544·1043281-1February 21, 2012Ray Chandler
9442534 135237198235074179w13523719823507418·1042517-1February 21, 2012Ray Chandler
9642496 89539192558021710349w8953919255802171035·1042477-1February 21, 2012Ray Chandler
9742480 243950820503638639w24395082050363864·1042463-1February 21, 2012Ray Chandler
10042390 135237198235074179w13523719823507418·1042373-1February 21, 2012Ray Chandler
11440967 55864371163170364339w5586437116317036434·1040948-1February 21, 2012Ray Chandler
11740748 135237198235074179w13523719823507418·1040731-1February 21, 2012Ray Chandler
12040105 55864371163170364339w5586437116317036434·1040086-1February 21, 2012Ray Chandler
12539600 67585171412632667639w6758517141263266764·1039581-1February 21, 2012Ray Chandler
12839434 22654574126992624459w2265457412699262446·1039415-1February 21, 2012Ray Chandler
13039317 67585171412632667639w6758517141263266764·1039298-1February 21, 2012Ray Chandler

Factorizations of 911...117 have been extended up to n=250. 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, 2012

Ray Chandler found 16 prime numbers of the form k·10n-1 (including 45 known prime numbers at least). 45th-47th of n=1085096464828759446, 47th-48th of n=12627335841170253, 47th of n=1473996556504596663, 45th-46th of n=1770173404019815998, 46th-47th of n=18337020241048446, 44th-45th of n=3074342565732763052, 45th of n=3673162065033455603, 46th of n=3956926644759313113, 49th of n=8849719619597556 and 47th of n=9866995547651697.

Prime numbers of the form k·10n-1 (including 45 known prime numbers at least)
 digitsflabelwlabelexpressionwhenwho
3649357 126273358411702529w12627335841170253·1049340-1February 19, 2012Ray Chandler
3849098 126273358411702529w12627335841170253·1049081-1February 19, 2012Ray Chandler
3948846 14739965565045966629w1473996556504596663·1048827-1February 19, 2012Ray Chandler
4547908 10850964648287594459w1085096464828759446·1047889-1February 19, 2012Ray Chandler
4747621 17701734040198159979w1770173404019815998·1047602-1February 19, 2012Ray Chandler
5346956 36731620650334556029w3673162065033455603·1046937-1February 19, 2012Ray Chandler
5846502 10850964648287594459w1085096464828759446·1046483-1February 19, 2012Ray Chandler
5946328 30743425657327630519w3074342565732763052·1046309-1February 19, 2012Ray Chandler
7045039 30743425657327630519w3074342565732763052·1045020-1February 19, 2012Ray Chandler
7643717 88497196195975559w8849719619597556·1043701-1February 19, 2012Ray Chandler
8442798 98669955476516969w9866995547651697·1042782-1February 19, 2012Ray Chandler
8642526 183370202410484459w18337020241048446·1042509-1February 19, 2012Ray Chandler
8942248 10850964648287594459w1085096464828759446·1042229-1February 19, 2012Ray Chandler
9641543 17701734040198159979w1770173404019815998·1041524-1February 19, 2012Ray Chandler
10141014 39569266447593131129w3956926644759313113·1040995-1February 19, 2012Ray Chandler
10240928 183370202410484459w18337020241048446·1040911-1February 19, 2012Ray Chandler

February 18, 2012

Factorizations of 866...669 have been extended up to n=250. Added composite numbers had passed ECM iterations 118 times at the level 35. Most unknown factors are supposed to be greater than 1030.

February 15, 2012

Factorizations of 766...663 have been extended up to n=250. Added composite numbers had passed ECM iterations 118 times at the level 35. Most unknown factors are supposed to be greater than 1030.

February 13, 2012

Factorizations of 822...223 have been extended up to n=250. Added composite numbers had passed ECM iterations 118 times at the level 35. Most unknown factors are supposed to be greater than 1030.

February 11, 2012

Ray Chandler found 4 unprovable near-repdigit PRPs.

Unprovable near-repdigit PRPs
 digitsflabelwlabelexpressionwhenwho
12902126111161w(55·1090211-1)/9February 11, 2012Ray Chandler
27610986111161w(55·1061097-1)/9February 11, 2012Ray Chandler
43491706111161w(55·1049169-1)/9February 11, 2012Ray Chandler
66326336111161w(55·1032632-1)/9February 11, 2012Ray Chandler

February 10, 2012

Factorizations of 800...009 have been extended up to n=250. Added composite numbers had passed ECM iterations 118 times at the level 35. Most unknown factors are supposed to be greater than 1030.

February 9, 2012

Ray Chandler found 16 prime numbers of the form k·10n-1 (including 45 known prime numbers at least). 51st of n=11749536972569333, 50th of n=13651074048698702, 52nd of n=191368947589402968, 53rd-54th of n=2998375267299290424, 50th-51st of n=3752621885794525128, 48th of n=401115243497052, 50th of n=4512565955069796981, 51st of n=4964807464647923921, 46th-47th of n=5294970814496095005, 49th of n=81610032903525693, 46th of n=8681897852553216354 and 48th-49th of n=920700247429683.

Prime numbers of the form k·10n-1 (including 45 known prime numbers at least)
 digitsflabelwlabelexpressionwhenwho
3649306 52949708144960950049w5294970814496095005·1049287-1February 9, 2012Ray Chandler
3948453 37526218857945251279w3752621885794525128·1048434-1February 9, 2012Ray Chandler
4148137 29983752672992904239w2998375267299290424·1048118-1February 9, 2012Ray Chandler
4547534 52949708144960950049w5294970814496095005·1047515-1February 9, 2012Ray Chandler
4647259 37526218857945251279w3752621885794525128·1047240-1February 9, 2012Ray Chandler
4846926 9207002474296829w920700247429683·1046911-1February 9, 2012Ray Chandler
4946681 816100329035256929w81610032903525693·1046664-1February 9, 2012Ray Chandler
5046648 9207002474296829w920700247429683·1046633-1February 9, 2012Ray Chandler
5945588 29983752672992904239w2998375267299290424·1045569-1February 9, 2012Ray Chandler
6344794 117495369725693329w11749536972569333·1044777-1February 9, 2012Ray Chandler
7242902 45125659550697969809w4512565955069796981·1042883-1February 9, 2012Ray Chandler
7642405 4011152434970519w401115243497052·1042390-1February 9, 2012Ray Chandler
7742153 136510740486987019w13651074048698702·1042136-1February 9, 2012Ray Chandler
7842074 49648074646479239209w4964807464647923921·1042055-1February 9, 2012Ray Chandler
8441419 86818978525532163539w8681897852553216354·1041400-1February 9, 2012Ray Chandler
8541418 1913689475894029679w191368947589402968·1041400-1February 9, 2012Ray Chandler

February 8, 2012

Edward Trice found the largest known quasi-repdigit prime number of the form k·10n+1. Congratulations!

Proven quasi-repdigit primes (except pd)
 digitsflabelwlabelexpressionwhenwho
12316186000160w16·10231617+1February 8, 2012Edward Trice

Ray Chandler found 1 unprovable near-repdigit PRP.

Unprovable near-repdigit PRPs
 digitsflabelwlabelexpressionwhenwho
23665766777767w(61·1066575-7)/9February 8, 2012Ray Chandler

February 7, 2012

Factorizations of 799...991 have been extended up to n=250. Added composite numbers had passed ECM iterations 118 times at the level 35. Most unknown factors are supposed to be greater than 1030.

February 5, 2012

Factorizations of 755...557 have been extended up to n=250. Added composite numbers had passed ECM iterations 118 times at the level 35. Most unknown factors are supposed to be greater than 1030.

February 4, 2012

Ray Chandler found an 74254-digit unprovable near-repdigit PRP of the form 21w.

Unprovable near-repdigit PRPs
 digitsflabelwlabelexpressionwhenwho
19742542111121w(19·1074253-1)/9February 4, 2012Ray Chandler

February 2, 2012

Factorizations of 33...33733...33 have been extended up to n=150. Added composite numbers had passed ECM iterations 118 times at the level 35. Most unknown factors are supposed to be greater than 1030.

Markus Tervooren proved the primality of a 10297-digit near-repdigit number (19·1010296-1)/9 by Primo.

Proven near-repdigit primes
 digitsflabelwlabelexpressionwhenwho
303102972111121w(19·1010296-1)/9February 2, 2012Markus Tervooren

Factorizations of 55...553 have been extended up to n=250 by Serge Batalov. Added composite numbers had passed ECM iterations 530 times at the level 30. Most unknown factors are supposed to be greater than 1030.

January 2012

January 30, 2012

Factorizations of 844...443 have been extended up to n=250. Added composite numbers had passed ECM iterations 118 times at the level 35. Most unknown factors are supposed to be greater than 1030.

January 27, 2012

Factorizations of 499...993 have been extended up to n=250. Added composite numbers had passed ECM iterations 118 times at the level 35. Most unknown factors are supposed to be greater than 1030.

January 24, 2012

Factorizations of 299...993 have been extended up to n=250. Added composite numbers had passed ECM iterations 118 times at the level 35. Most unknown factors are supposed to be greater than 1030.

January 22, 2012

Factorizations of 166...669 have been extended up to n=250. Added composite numbers had passed ECM iterations 118 times at the level 35. Most unknown factors are supposed to be greater than 1030.

January 20, 2012

Factorizations of 99...99299...99 have been extended up to n=150. Added composite numbers had passed ECM iterations 118 times at the level 35. Most unknown factors are supposed to be greater than 1030.

January 17, 2012

Factorizations of 99...99199...99 have been extended up to n=150. Added composite numbers had passed ECM iterations 118 times at the level 35. Most unknown factors are supposed to be greater than 1030.

January 14, 2012

Factorizations of 77...77677...77 have been extended up to n=150. Added composite numbers had passed ECM iterations 118 times at the level 35. Most unknown factors are supposed to be greater than 1030.

January 11, 2012

Factorizations of 33...33533...33 have been extended up to n=150. Added composite numbers had passed ECM iterations 118 times at the level 35. Most unknown factors are supposed to be greater than 1030.

January 10, 2012

Leonid Durman found the second largest known unprovable near-repdigit PRP so far. Congratulations!

Unprovable near-repdigit PRPs
 digitsflabelwlabelexpressionwhenwho
2380976333313w1(10380976-7)/3January 10, 2012Leonid Durman

January 9, 2012

Leonid Durman found the largest known unprovable near-repdigit PRP so far. Congratulations!

Unprovable near-repdigit PRPs
 digitsflabelwlabelexpressionwhenwho
1424861333313w1(10424861-7)/3January 9, 2012Leonid Durman

January 8, 2012

Factorizations of 77...77377...77 have been extended up to n=150. Added composite numbers had passed ECM iterations 118 times at the level 35. Most unknown factors are supposed to be greater than 1030.

January 5, 2012

Factorizations of 33...33833...33 have been extended up to n=150. Added composite numbers had passed ECM iterations 118 times at the level 35. Most unknown factors are supposed to be greater than 1030.

January 2, 2012

Factorizations of 33...33133...33 have been extended up to n=150. Added composite numbers had passed ECM iterations 118 times at the level 35. Most unknown factors are supposed to be greater than 1030.