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News of 2011

Table of contents

  1. December 2011
  2. November 2011
  3. October 2011
  4. September 2011
  5. August 2011
  6. July 2011
  7. June 2011
  8. May 2011
  9. April 2011
  10. March 2011
  11. February 2011
  12. January 2011

December 2011

December 31, 2011

Factorizations of 955...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.

December 29, 2011

Factorizations of 877...771 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, 2011

Factorizations of 688...887 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 24, 2011

Factorizations of 99...99599...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.

December 23, 2011

Ray Chandler found 23 prime numbers of the form k·10n-1, 46th-48th of k=8849719619597556, 44th-46th of k=9866995547651697, 47th of k=12385008795614294, 46th of k=12627335841170253, 43rd-45th of k=18337020241048446, 42nd-45th of k=20342090729098691, 46th-47th of k=26075627483886897, 46th of k=1473996556504596663, 45th of k=2266438199628379476 and 42nd-45th of k=3956926644759313113.

Ray Chandler found 91 prime numbers of the form k·10n-1, 47th-52nd of k=8861036989751958627, 45th of k=8124529194875611707, 45th-47th of k=8058799722014140442, 47th of k=6136678104778761932, 46th-47th of k=5906181743052623648, 45th of k=5410621003833542777, 47th-48th of k=5324532551360646435, 46th-47th of k=5189395769656459445, 45th of k=4155941632109082935, 46th-47th of k=3745413626697133958, 49th-51st of k=3688107672047143961, 47th of k=2086228385017249928, 46th of k=1513868073147018162, 45th-46th of k=529220357182862954, 48th-49th of k=330640210602617363, 47th of k=248108640286930808, 46th-47th of k=30895035496936877, 45th-46th of k=29472578289080199, 45th-46th of k=26821618164263951, 43rd-45th of k=24255533047620308, 46th-47th of k=16337430201479681, 47th of k=15775373068537271, 48th of k=11314478175891338, 43rd-46th of k=10690189813288797, 46th-47th of k=9334983988275764, 46th-48th of k=7440784135439319, 46th-48th of k=1677510348112053, 47th-48th of k=8953919255802171035, 44th-47th of k=6896180437289770655, 47th-49th of k=6758517141263266764, 45th of k=5586437116317036434, 48th-50th of k=2265457412699262446, 46th-50th of k=273612655080436938, 46th of k=37731518958711032, 48th of k=20049572996361209, 49th of k=13680125387256776, 49th of k=13523719823507418, 45th-48th of k=11885302750562514, 46th-49th of k=10471993823152799, 50th of k=9977839106671499 and 45th-47th of k=9697992253044102.

Prime numbers of the form k·10n-1 (including 45 known prime numbers at least)
 digitsflabelwlabelexpressionwhenwho
8139003 98669955476516969w9866995547651697·1038987-1December 23, 2011Ray Chandler
8638582 377315189587110319w37731518958711032·1038565-1December 23, 2011Ray Chandler
9937456 14739965565045966629w1473996556504596663·1037437-1December 23, 2011Ray Chandler
10037382 67585171412632667639w6758517141263266764·1037363-1December 23, 2011Ray Chandler
10536908 136801253872567759w13680125387256776·1036891-1December 23, 2011Ray Chandler
10636878 96979922530441019w9697992253044102·1036862-1December 23, 2011Ray Chandler
10836764 98669955476516969w9866995547651697·1036748-1December 23, 2011Ray Chandler
11036550 200495729963612089w20049572996361209·1036533-1December 23, 2011Ray Chandler
11336394 98669955476516969w9866995547651697·1036378-1December 23, 2011Ray Chandler
12335377 123850087956142939w12385008795614294·1035360-1December 23, 2011Ray Chandler
12535146 89539192558021710349w8953919255802171035·1035127-1December 23, 2011Ray Chandler
12635087 203420907290986909w20342090729098691·1035070-1December 23, 2011Ray Chandler
13234602 260756274838868969w26075627483886897·1034585-1December 23, 2011Ray Chandler
13434450 183370202410484459w18337020241048446·1034433-1December 23, 2011Ray Chandler
13534353 68961804372897706549w6896180437289770655·1034334-1December 23, 2011Ray Chandler
13634294 88497196195975559w8849719619597556·1034278-1December 23, 2011Ray Chandler
13834215 104719938231527989w10471993823152799·1034198-1December 23, 2011Ray Chandler
14034065 39569266447593131129w3956926644759313113·1034046-1December 23, 2011Ray Chandler
14134021 96979922530441019w9697992253044102·1034005-1December 23, 2011Ray Chandler
14233964 22664381996283794759w2266438199628379476·1033945-1December 23, 2011Ray Chandler
14533856 126273358411702529w12627335841170253·1033839-1December 23, 2011Ray Chandler
14833805 67585171412632667639w6758517141263266764·1033786-1December 23, 2011Ray Chandler
15233223 99778391066714989w9977839106671499·1033207-1December 23, 2011Ray Chandler
15432979 68961804372897706549w6896180437289770655·1032960-1December 23, 2011Ray Chandler
15532959 3306402106026173629w330640210602617363·1032941-1December 23, 2011Ray Chandler
15632944 93349839882757639w9334983988275764·1032928-1December 23, 2011Ray Chandler
15732930 242555330476203079w24255533047620308·1032913-1December 23, 2011Ray Chandler
16032831 39569266447593131129w3956926644759313113·1032812-1December 23, 2011Ray Chandler
16132797 51893957696564594449w5189395769656459445·1032778-1December 23, 2011Ray Chandler
16432701 22654574126992624459w2265457412699262446·1032682-1December 23, 2011Ray Chandler
16632593 88497196195975559w8849719619597556·1032577-1December 23, 2011Ray Chandler
17032248 22654574126992624459w2265457412699262446·1032229-1December 23, 2011Ray Chandler
17132220 203420907290986909w20342090729098691·1032203-1December 23, 2011Ray Chandler
17232109 80587997220141404419w8058799722014140442·1032090-1December 23, 2011Ray Chandler
17531916 5292203571828629539w529220357182862954·1031898-1December 23, 2011Ray Chandler
17731801 88497196195975559w8849719619597556·1031785-1December 23, 2011Ray Chandler
17931463 2736126550804369379w273612655080436938·1031445-1December 23, 2011Ray Chandler
18131387 88610369897519586269w8861036989751958627·1031368-1December 23, 2011Ray Chandler
18231361 68961804372897706549w6896180437289770655·1031342-1December 23, 2011Ray Chandler
18431101 36881076720471439609w3688107672047143961·1031082-1December 23, 2011Ray Chandler
18530951 5292203571828629539w529220357182862954·1030933-1December 23, 2011Ray Chandler
18730935 53245325513606464349w5324532551360646435·1030916-1December 23, 2011Ray Chandler
19230574 106901898132887969w10690189813288797·1030557-1December 23, 2011Ray Chandler
19330456 16775103481120529w1677510348112053·1030440-1December 23, 2011Ray Chandler
19430341 74407841354393189w7440784135439319·1030325-1December 23, 2011Ray Chandler
19530330 118853027505625139w11885302750562514·1030313-1December 23, 2011Ray Chandler
20329870 260756274838868969w26075627483886897·1029853-1December 23, 2011Ray Chandler
21029496 51893957696564594449w5189395769656459445·1029477-1December 23, 2011Ray Chandler
21129493 242555330476203079w24255533047620308·1029476-1December 23, 2011Ray Chandler
21329409 118853027505625139w11885302750562514·1029392-1December 23, 2011Ray Chandler
21629265 163374302014796809w16337430201479681·1029248-1December 23, 2011Ray Chandler
21829202 106901898132887969w10690189813288797·1029185-1December 23, 2011Ray Chandler
21929189 37454136266971339579w3745413626697133958·1029170-1December 23, 2011Ray Chandler
22029102 41559416321090829349w4155941632109082935·1029083-1December 23, 2011Ray Chandler
22328984 59061817430526236479w5906181743052623648·1028965-1December 23, 2011Ray Chandler
22428973 59061817430526236479w5906181743052623648·1028954-1December 23, 2011Ray Chandler
22628738 2736126550804369379w273612655080436938·1028720-1December 23, 2011Ray Chandler
22728502 2736126550804369379w273612655080436938·1028484-1December 23, 2011Ray Chandler
22828457 55864371163170364339w5586437116317036434·1028438-1December 23, 2011Ray Chandler
22928439 106901898132887969w10690189813288797·1028422-1December 23, 2011Ray Chandler
23028430 61366781047787619319w6136678104778761932·1028411-1December 23, 2011Ray Chandler
23228389 104719938231527989w10471993823152799·1028372-1December 23, 2011Ray Chandler
23328221 203420907290986909w20342090729098691·1028204-1December 23, 2011Ray Chandler
23628137 183370202410484459w18337020241048446·1028120-1December 23, 2011Ray Chandler
23728060 96979922530441019w9697992253044102·1028044-1December 23, 2011Ray Chandler
23827891 22654574126992624459w2265457412699262446·1027872-1December 23, 2011Ray Chandler
23927887 118853027505625139w11885302750562514·1027870-1December 23, 2011Ray Chandler
24427678 88610369897519586269w8861036989751958627·1027659-1December 23, 2011Ray Chandler
24827346 113144781758913379w11314478175891338·1027329-1December 23, 2011Ray Chandler
24927308 89539192558021710349w8953919255802171035·1027289-1December 23, 2011Ray Chandler
25427043 88610369897519586269w8861036989751958627·1027024-1December 23, 2011Ray Chandler
25627010 93349839882757639w9334983988275764·1026994-1December 23, 2011Ray Chandler
25826878 2736126550804369379w273612655080436938·1026860-1December 23, 2011Ray Chandler
25926714 36881076720471439609w3688107672047143961·1026695-1December 23, 2011Ray Chandler
26026658 16775103481120529w1677510348112053·1026642-1December 23, 2011Ray Chandler
26126643 67585171412632667639w6758517141263266764·1026624-1December 23, 2011Ray Chandler
26526481 80587997220141404419w8058799722014140442·1026462-1December 23, 2011Ray Chandler
26626476 39569266447593131129w3956926644759313113·1026457-1December 23, 2011Ray Chandler
27226179 308950354969368769w30895035496936877·1026162-1December 23, 2011Ray Chandler
27526103 104719938231527989w10471993823152799·1026086-1December 23, 2011Ray Chandler
27626057 268216181642639509w26821618164263951·1026040-1December 23, 2011Ray Chandler
27725969 104719938231527989w10471993823152799·1025952-1December 23, 2011Ray Chandler
27825909 135237198235074179w13523719823507418·1025892-1December 23, 2011Ray Chandler
27925899 2736126550804369379w273612655080436938·1025881-1December 23, 2011Ray Chandler
28125731 118853027505625139w11885302750562514·1025714-1December 23, 2011Ray Chandler
28725538 80587997220141404419w8058799722014140442·1025519-1December 23, 2011Ray Chandler
29025286 39569266447593131129w3956926644759313113·1025267-1December 23, 2011Ray Chandler
29125234 81245291948756117069w8124529194875611707·1025215-1December 23, 2011Ray Chandler
29325153 106901898132887969w10690189813288797·1025136-1December 23, 2011Ray Chandler
29425152 68961804372897706549w6896180437289770655·1025133-1December 23, 2011Ray Chandler
29525150 183370202410484459w18337020241048446·1025133-1December 23, 2011Ray Chandler
29825014 53245325513606464349w5324532551360646435·1024995-1December 23, 2011Ray Chandler
29925000 74407841354393189w7440784135439319·1024984-1December 23, 2011Ray Chandler
30124797 20862283850172499279w2086228385017249928·1024778-1December 23, 2011Ray Chandler
30224760 242555330476203079w24255533047620308·1024743-1December 23, 2011Ray Chandler
31424069 268216181642639509w26821618164263951·1024052-1December 23, 2011Ray Chandler
31923913 88610369897519586269w8861036989751958627·1023894-1December 23, 2011Ray Chandler
32023906 88610369897519586269w8861036989751958627·1023887-1December 23, 2011Ray Chandler
32223777 203420907290986909w20342090729098691·1023760-1December 23, 2011Ray Chandler
33023378 88610369897519586269w8861036989751958627·1023359-1December 23, 2011Ray Chandler
33723168 157753730685372709w15775373068537271·1023151-1December 23, 2011Ray Chandler
34023146 308950354969368769w30895035496936877·1023129-1December 23, 2011Ray Chandler
34123117 36881076720471439609w3688107672047143961·1023098-1December 23, 2011Ray Chandler
34522994 294725782890801989w29472578289080199·1022977-1December 23, 2011Ray Chandler
34622970 294725782890801989w29472578289080199·1022953-1December 23, 2011Ray Chandler
34722841 74407841354393189w7440784135439319·1022825-1December 23, 2011Ray Chandler
35922420 54106210038335427769w5410621003833542777·1022401-1December 23, 2011Ray Chandler
36322144 2481086402869308079w248108640286930808·1022126-1December 23, 2011Ray Chandler
36821991 37454136266971339579w3745413626697133958·1021972-1December 23, 2011Ray Chandler
37021789 16775103481120529w1677510348112053·1021773-1December 23, 2011Ray Chandler
37521560 163374302014796809w16337430201479681·1021543-1December 23, 2011Ray Chandler
37721341 15138680731470181619w1513868073147018162·1021322-1December 23, 2011Ray Chandler
37821235 3306402106026173629w330640210602617363·1021217-1December 23, 2011Ray Chandler

December 22, 2011

Ray Chandler found 35 prime numbers of the form k·10n-1, 46th-47th of k=401115243497052, 44th-47th of k=920700247429683, 46th of k=1581943787314688, 49th-51st of k=2470787120503499, 48th of k=9673647494155806, 50th of k=11749536972569333, 45th-49th of k=13651074048698702, 48th of k=81610032903525693, 50th-51st of k=191368947589402968, 50th-52nd of k=2998375267299290424, 49th of k=4173754157978594343, 47th-49th of k=4512565955069796981, 48th-50th of k=4964807464647923921, 46th-47th of k=5830309478870479995, 45th of k=8681897852553216354 and 45th-46th of k=8886864074998805511.

Prime numbers of the form k·10n-1 (including 45 known prime numbers at least)
 digitsflabelwlabelexpressionwhenwho
7639628 1913689475894029679w191368947589402968·1039610-1December 22, 2011Ray Chandler
8238749 136510740486987019w13651074048698702·1038732-1December 22, 2011Ray Chandler
8338667 49648074646479239209w4964807464647923921·1038648-1December 22, 2011Ray Chandler
8438655 816100329035256929w81610032903525693·1038638-1December 22, 2011Ray Chandler
9837208 9207002474296829w920700247429683·1037193-1December 22, 2011Ray Chandler
10037069 136510740486987019w13651074048698702·1037052-1December 22, 2011Ray Chandler
10536364 96736474941558059w9673647494155806·1036348-1December 22, 2011Ray Chandler
11035949 45125659550697969809w4512565955069796981·1035930-1December 22, 2011Ray Chandler
11335413 29983752672992904239w2998375267299290424·1035394-1December 22, 2011Ray Chandler
11535015 41737541579785943429w4173754157978594343·1034996-1December 22, 2011Ray Chandler
12134289 24707871205034989w2470787120503499·1034273-1December 22, 2011Ray Chandler
12333912 136510740486987019w13651074048698702·1033895-1December 22, 2011Ray Chandler
13332761 136510740486987019w13651074048698702·1032744-1December 22, 2011Ray Chandler
13432728 24707871205034989w2470787120503499·1032712-1December 22, 2011Ray Chandler
13532620 4011152434970519w401115243497052·1032605-1December 22, 2011Ray Chandler
13732281 45125659550697969809w4512565955069796981·1032262-1December 22, 2011Ray Chandler
13932070 29983752672992904239w2998375267299290424·1032051-1December 22, 2011Ray Chandler
14032051 29983752672992904239w2998375267299290424·1032032-1December 22, 2011Ray Chandler
14231663 58303094788704799949w5830309478870479995·1031644-1December 22, 2011Ray Chandler
14530940 88868640749988055109w8886864074998805511·1030921-1December 22, 2011Ray Chandler
14630896 24707871205034989w2470787120503499·1030880-1December 22, 2011Ray Chandler
14730819 49648074646479239209w4964807464647923921·1030800-1December 22, 2011Ray Chandler
15030309 86818978525532163539w8681897852553216354·1030290-1December 22, 2011Ray Chandler
15829706 58303094788704799949w5830309478870479995·1029687-1December 22, 2011Ray Chandler
15929630 9207002474296829w920700247429683·1029615-1December 22, 2011Ray Chandler
16429288 9207002474296829w920700247429683·1029273-1December 22, 2011Ray Chandler
16729040 4011152434970519w401115243497052·1029025-1December 22, 2011Ray Chandler
16928828 15819437873146879w1581943787314688·1028812-1December 22, 2011Ray Chandler
17028407 1913689475894029679w191368947589402968·1028389-1December 22, 2011Ray Chandler
18027205 49648074646479239209w4964807464647923921·1027186-1December 22, 2011Ray Chandler
18327053 88868640749988055109w8886864074998805511·1027034-1December 22, 2011Ray Chandler
19026437 136510740486987019w13651074048698702·1026420-1December 22, 2011Ray Chandler
19126424 45125659550697969809w4512565955069796981·1026405-1December 22, 2011Ray Chandler
19226389 9207002474296829w920700247429683·1026374-1December 22, 2011Ray Chandler
19526143 117495369725693329w11749536972569333·1026126-1December 22, 2011Ray Chandler

December 21, 2011

Factorizations of 77...77977...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.

December 20, 2011

Ray Chandler found 24 prime numbers of the form k·10n-1, 49th-52nd of k=41945128176534744, 49th-50th of k=42347460076759481, 46th-49th of k=50857767980257511, 46th-49th of k=51215596469881907, 48th-49th of k=50637515049938733, 45th-47th of k=52797555212895374, 44th-46th of k=46473172030295717 and 45th-46th of k=46219659610534935.

Prime numbers of the form k·10n-1 (including 45 known prime numbers at least)
 digitsflabelwlabelexpressionwhenwho
3249835 508577679802575109w50857767980257511·1049818-1December 20, 2011Ray Chandler
3349789 527975552128953739w52797555212895374·1049772-1December 20, 2011Ray Chandler
3748551 423474600767594809w42347460076759481·1048534-1December 20, 2011Ray Chandler
3947778 527975552128953739w52797555212895374·1047761-1December 20, 2011Ray Chandler
4047615 508577679802575109w50857767980257511·1047598-1December 20, 2011Ray Chandler
4247172 419451281765347439w41945128176534744·1047155-1December 20, 2011Ray Chandler
5643928 506375150499387329w50637515049938733·1043911-1December 20, 2011Ray Chandler
5743590 506375150499387329w50637515049938733·1043573-1December 20, 2011Ray Chandler
5843496 419451281765347439w41945128176534744·1043479-1December 20, 2011Ray Chandler
6841652 464731720302957169w46473172030295717·1041635-1December 20, 2011Ray Chandler
7041048 527975552128953739w52797555212895374·1041031-1December 20, 2011Ray Chandler
7340106 512155964698819069w51215596469881907·1040089-1December 20, 2011Ray Chandler
8038844 419451281765347439w41945128176534744·1038827-1December 20, 2011Ray Chandler
8138549 462196596105349349w46219659610534935·1038532-1December 20, 2011Ray Chandler
8238527 512155964698819069w51215596469881907·1038510-1December 20, 2011Ray Chandler
8438122 423474600767594809w42347460076759481·1038105-1December 20, 2011Ray Chandler
9337282 508577679802575109w50857767980257511·1037265-1December 20, 2011Ray Chandler
9636705 512155964698819069w51215596469881907·1036688-1December 20, 2011Ray Chandler
9936336 464731720302957169w46473172030295717·1036319-1December 20, 2011Ray Chandler
10934818 462196596105349349w46219659610534935·1034801-1December 20, 2011Ray Chandler
11833111 512155964698819069w51215596469881907·1033094-1December 20, 2011Ray Chandler
12431391 508577679802575109w50857767980257511·1031374-1December 20, 2011Ray Chandler
12531361 464731720302957169w46473172030295717·1031344-1December 20, 2011Ray Chandler
12830302 419451281765347439w41945128176534744·1030285-1December 20, 2011Ray Chandler

December 18, 2011

Factorizations of 77...77577...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.

December 15, 2011

Factorizations of 766...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.

December 13, 2011

Factorizations of 344...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.

December 7, 2011

Factorizations of 11...11911...11 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.

December 4, 2011

Factorizations of 99...99499...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.

December 1, 2011

Factorizations of 77...77277...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.

November 2011

November 28, 2011

Factorizations of 77...77177...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.

November 26, 2011

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

Unprovable near-repdigit PRPs
 digitsflabelwlabelexpressionwhenwho
1260198777717w1(7·10260198-61)/9November 26, 2011Erik Branger

November 24, 2011

Factorizations of 11...11811...11 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.

November 21, 2011

Factorizations of 11...11611...11 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.

November 18, 2011

Factorizations of 11...11511...11 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.

November 15, 2011

Factorizations of 33...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.

November 13, 2011

Ray Chander found 60 prime numbers of the form k·10n-1. 57 prime numbers were put on the list.

Prime numbers of the form k·10n-1 (including 45 known prime numbers at least)
 digitsflabelwlabelexpressionwhenwho
14225479 29983752672992904239w2998375267299290424·1025460-1November 13, 2011Ray Chandler
14724856 1913689475894029679w191368947589402968·1024838-1November 13, 2011Ray Chandler
15424375 24707871205034989w2470787120503499·1024359-1November 13, 2011Ray Chandler
15624145 117495369725693329w11749536972569333·1024128-1November 13, 2011Ray Chandler
15724112 117495369725693329w11749536972569333·1024095-1November 13, 2011Ray Chandler
16223832 24707871205034989w2470787120503499·1023816-1November 13, 2011Ray Chandler
16323704 1913689475894029679w191368947589402968·1023686-1November 13, 2011Ray Chandler
16523672 49648074646479239209w4964807464647923921·1023653-1November 13, 2011Ray Chandler
17223310 41737541579785943429w4173754157978594343·1023291-1November 13, 2011Ray Chandler
19622047 117495369725693329w11749536972569333·1022030-1November 13, 2011Ray Chandler
20920890 45125659550697969809w4512565955069796981·1020871-1November 13, 2011Ray Chandler
21420724 37526218857945251279w3752621885794525128·1020705-1November 13, 2011Ray Chandler
23319826 52949708144960950049w5294970814496095005·1019807-1November 13, 2011Ray Chandler
25118925 4011152434970519w401115243497052·1018910-1November 13, 2011Ray Chandler
25618680 816100329035256929w81610032903525693·1018663-1November 13, 2011Ray Chandler
26218558 1913689475894029679w191368947589402968·1018540-1November 13, 2011Ray Chandler
26618414 41737541579785943429w4173754157978594343·1018395-1November 13, 2011Ray Chandler
27818009 117495369725693329w11749536972569333·1017992-1November 13, 2011Ray Chandler
27917960 29983752672992904239w2998375267299290424·1017941-1November 13, 2011Ray Chandler
28017933 96736474941558059w9673647494155806·1017917-1November 13, 2011Ray Chandler
28417705 816100329035256929w81610032903525693·1017688-1November 13, 2011Ray Chandler
28517680 29983752672992904239w2998375267299290424·1017661-1November 13, 2011Ray Chandler
28617664 37526218857945251279w3752621885794525128·1017645-1November 13, 2011Ray Chandler
29117387 41737541579785943429w4173754157978594343·1017368-1November 13, 2011Ray Chandler
33016160 96736474941558059w9673647494155806·1016144-1November 13, 2011Ray Chandler
33216156 29983752672992904239w2998375267299290424·1016137-1November 13, 2011Ray Chandler
33915999 96736474941558059w9673647494155806·1015983-1November 13, 2011Ray Chandler
34215946 52949708144960950049w5294970814496095005·1015927-1November 13, 2011Ray Chandler
34615753 49648074646479239209w4964807464647923921·1015734-1November 13, 2011Ray Chandler
35715443 15819437873146879w1581943787314688·1015427-1November 13, 2011Ray Chandler
36315278 816100329035256929w81610032903525693·1015261-1November 13, 2011Ray Chandler
37614784 1913689475894029679w191368947589402968·1014766-1November 13, 2011Ray Chandler
39414148 24707871205034989w2470787120503499·1014132-1November 13, 2011Ray Chandler
40613943 29983752672992904239w2998375267299290424·1013924-1November 13, 2011Ray Chandler
40713941 15819437873146879w1581943787314688·1013925-1November 13, 2011Ray Chandler
40913901 24707871205034989w2470787120503499·1013885-1November 13, 2011Ray Chandler
41413773 37526218857945251279w3752621885794525128·1013754-1November 13, 2011Ray Chandler
41513752 816100329035256929w81610032903525693·1013735-1November 13, 2011Ray Chandler
42313613 24707871205034989w2470787120503499·1013597-1November 13, 2011Ray Chandler
42913459 58303094788704799949w5830309478870479995·1013440-1November 13, 2011Ray Chandler
43313311 41737541579785943429w4173754157978594343·1013292-1November 13, 2011Ray Chandler
44113218 41737541579785943429w4173754157978594343·1013199-1November 13, 2011Ray Chandler
45112959 45125659550697969809w4512565955069796981·1012940-1November 13, 2011Ray Chandler
46112556 4011152434970519w401115243497052·1012541-1November 13, 2011Ray Chandler
46212505 1913689475894029679w191368947589402968·1012487-1November 13, 2011Ray Chandler
46912413 96736474941558059w9673647494155806·1012397-1November 13, 2011Ray Chandler
47312300 1913689475894029679w191368947589402968·1012282-1November 13, 2011Ray Chandler
48212011 37526218857945251279w3752621885794525128·1011992-1November 13, 2011Ray Chandler
48511919 37526218857945251279w3752621885794525128·1011900-1November 13, 2011Ray Chandler
50111636 29983752672992904239w2998375267299290424·1011617-1November 13, 2011Ray Chandler
50811443 117495369725693329w11749536972569333·1011426-1November 13, 2011Ray Chandler
52211144 117495369725693329w11749536972569333·1011127-1November 13, 2011Ray Chandler
55110621 49648074646479239209w4964807464647923921·1010602-1November 13, 2011Ray Chandler
55410586 49648074646479239209w4964807464647923921·1010567-1November 13, 2011Ray Chandler
55910427 45125659550697969809w4512565955069796981·1010408-1November 13, 2011Ray Chandler
57110129 58303094788704799949w5830309478870479995·1010110-1November 13, 2011Ray Chandler
57710037 37526218857945251279w3752621885794525128·1010018-1November 13, 2011Ray Chandler

November 12, 2011

Ray Chander found 249 prime numbers of the form k·10n-1. 171 prime numbers were put on the list.

Prime numbers of the form k·10n-1 (including 45 known prime numbers at least)
 digitsflabelwlabelexpressionwhenwho
15524050 67585171412632667639w6758517141263266764·1024031-1November 12, 2011Ray Chandler
16023581 99778391066714989w9977839106671499·1023565-1November 12, 2011Ray Chandler
16123479 200495729963612089w20049572996361209·1023462-1November 12, 2011Ray Chandler
16723164 67585171412632667639w6758517141263266764·1023145-1November 12, 2011Ray Chandler
16923096 67585171412632667639w6758517141263266764·1023077-1November 12, 2011Ray Chandler
17522728 89539192558021710349w8953919255802171035·1022709-1November 12, 2011Ray Chandler
17622659 200495729963612089w20049572996361209·1022642-1November 12, 2011Ray Chandler
17722635 99778391066714989w9977839106671499·1022619-1November 12, 2011Ray Chandler
18222452 123850087956142939w12385008795614294·1022435-1November 12, 2011Ray Chandler
18722029 260756274838868969w26075627483886897·1022012-1November 12, 2011Ray Chandler
18921899 89539192558021710349w8953919255802171035·1021880-1November 12, 2011Ray Chandler
19321151 88497196195975559w8849719619597556·1021135-1November 12, 2011Ray Chandler
19520994 3306402106026173629w330640210602617363·1020976-1November 12, 2011Ray Chandler
19620970 14739965565045966629w1473996556504596663·1020951-1November 12, 2011Ray Chandler
19720955 163374302014796809w16337430201479681·1020938-1November 12, 2011Ray Chandler
20020800 16775103481120529w1677510348112053·1020784-1November 12, 2011Ray Chandler
20320688 123850087956142939w12385008795614294·1020671-1November 12, 2011Ray Chandler
20620596 59061817430526236479w5906181743052623648·1020577-1November 12, 2011Ray Chandler
20820587 200495729963612089w20049572996361209·1020570-1November 12, 2011Ray Chandler
21020524 377315189587110319w37731518958711032·1020507-1November 12, 2011Ray Chandler
21220378 136801253872567759w13680125387256776·1020361-1November 12, 2011Ray Chandler
21320365 157753730685372709w15775373068537271·1020348-1November 12, 2011Ray Chandler
21420218 89539192558021710349w8953919255802171035·1020199-1November 12, 2011Ray Chandler
21520177 123850087956142939w12385008795614294·1020160-1November 12, 2011Ray Chandler
21620087 3306402106026173629w330640210602617363·1020069-1November 12, 2011Ray Chandler
21820060 14739965565045966629w1473996556504596663·1020041-1November 12, 2011Ray Chandler
21919928 113144781758913379w11314478175891338·1019911-1November 12, 2011Ray Chandler
22119806 123850087956142939w12385008795614294·1019789-1November 12, 2011Ray Chandler
22419672 61366781047787619319w6136678104778761932·1019653-1November 12, 2011Ray Chandler
22619470 88610369897519586269w8861036989751958627·1019451-1November 12, 2011Ray Chandler
22819343 136801253872567759w13680125387256776·1019326-1November 12, 2011Ray Chandler
23019238 89539192558021710349w8953919255802171035·1019219-1November 12, 2011Ray Chandler
23319137 53245325513606464349w5324532551360646435·1019118-1November 12, 2011Ray Chandler
23519007 74407841354393189w7440784135439319·1018991-1November 12, 2011Ray Chandler
23618993 20862283850172499279w2086228385017249928·1018974-1November 12, 2011Ray Chandler
23718962 36881076720471439609w3688107672047143961·1018943-1November 12, 2011Ray Chandler
24418625 88610369897519586269w8861036989751958627·1018606-1November 12, 2011Ray Chandler
24618576 163374302014796809w16337430201479681·1018559-1November 12, 2011Ray Chandler
24718480 123850087956142939w12385008795614294·1018463-1November 12, 2011Ray Chandler
25118287 157753730685372709w15775373068537271·1018270-1November 12, 2011Ray Chandler
25218258 207104321535235669w20710432153523567·1018241-1November 12, 2011Ray Chandler
25518158 74407841354393189w7440784135439319·1018142-1November 12, 2011Ray Chandler
25718105 308950354969368769w30895035496936877·1018088-1November 12, 2011Ray Chandler
26018058 2481086402869308079w248108640286930808·1018040-1November 12, 2011Ray Chandler
26217842 59061817430526236479w5906181743052623648·1017823-1November 12, 2011Ray Chandler
26317826 22654574126992624459w2265457412699262446·1017807-1November 12, 2011Ray Chandler
26617484 135237198235074179w13523719823507418·1017467-1November 12, 2011Ray Chandler
27217260 93349839882757639w9334983988275764·1017244-1November 12, 2011Ray Chandler
27417190 99778391066714989w9977839106671499·1017174-1November 12, 2011Ray Chandler
27517166 22654574126992624459w2265457412699262446·1017147-1November 12, 2011Ray Chandler
27617142 2481086402869308079w248108640286930808·1017124-1November 12, 2011Ray Chandler
27717140 51893957696564594449w5189395769656459445·1017121-1November 12, 2011Ray Chandler
27917108 93349839882757639w9334983988275764·1017092-1November 12, 2011Ray Chandler
28117028 59061817430526236479w5906181743052623648·1017009-1November 12, 2011Ray Chandler
28217018 163374302014796809w16337430201479681·1017001-1November 12, 2011Ray Chandler
28716699 36881076720471439609w3688107672047143961·1016680-1November 12, 2011Ray Chandler
28916655 126273358411702529w12627335841170253·1016638-1November 12, 2011Ray Chandler
29516442 58491942059325319w5849194205932532·1016426-1November 12, 2011Ray Chandler
29816351 58491942059325319w5849194205932532·1016335-1November 12, 2011Ray Chandler
30016337 11996201564155695949w1199620156415569595·1016318-1November 12, 2011Ray Chandler
30116336 36881076720471439609w3688107672047143961·1016317-1November 12, 2011Ray Chandler
30416215 37454136266971339579w3745413626697133958·1016196-1November 12, 2011Ray Chandler
30816125 20862283850172499279w2086228385017249928·1016106-1November 12, 2011Ray Chandler
30916123 51893957696564594449w5189395769656459445·1016104-1November 12, 2011Ray Chandler
31116111 58491942059325319w5849194205932532·1016095-1November 12, 2011Ray Chandler
31216088 15138680731470181619w1513868073147018162·1016069-1November 12, 2011Ray Chandler
31315994 157753730685372709w15775373068537271·1015977-1November 12, 2011Ray Chandler
31515851 113144781758913379w11314478175891338·1015834-1November 12, 2011Ray Chandler
31615791 11996201564155695949w1199620156415569595·1015772-1November 12, 2011Ray Chandler
31715772 61366781047787619319w6136678104778761932·1015753-1November 12, 2011Ray Chandler
31815726 37454136266971339579w3745413626697133958·1015707-1November 12, 2011Ray Chandler
32215533 22654574126992624459w2265457412699262446·1015514-1November 12, 2011Ray Chandler
32315530 123850087956142939w12385008795614294·1015513-1November 12, 2011Ray Chandler
32415512 308950354969368769w30895035496936877·1015495-1November 12, 2011Ray Chandler
32715445 126273358411702529w12627335841170253·1015428-1November 12, 2011Ray Chandler
32815414 15138680731470181619w1513868073147018162·1015395-1November 12, 2011Ray Chandler
33115290 20862283850172499279w2086228385017249928·1015271-1November 12, 2011Ray Chandler
33215279 53245325513606464349w5324532551360646435·1015260-1November 12, 2011Ray Chandler
33515219 36881076720471439609w3688107672047143961·1015200-1November 12, 2011Ray Chandler
33615113 74407841354393189w7440784135439319·1015097-1November 12, 2011Ray Chandler
33715080 200495729963612089w20049572996361209·1015063-1November 12, 2011Ray Chandler
33815076 260756274838868969w26075627483886897·1015059-1November 12, 2011Ray Chandler
33915057 16775103481120529w1677510348112053·1015041-1November 12, 2011Ray Chandler
34314807 88610369897519586269w8861036989751958627·1014788-1November 12, 2011Ray Chandler
34514749 15138680731470181619w1513868073147018162·1014730-1November 12, 2011Ray Chandler
34614716 51893957696564594449w5189395769656459445·1014697-1November 12, 2011Ray Chandler
34814608 126273358411702529w12627335841170253·1014591-1November 12, 2011Ray Chandler
34914588 113144781758913379w11314478175891338·1014571-1November 12, 2011Ray Chandler
35014575 16775103481120529w1677510348112053·1014559-1November 12, 2011Ray Chandler
35114551 126273358411702529w12627335841170253·1014534-1November 12, 2011Ray Chandler
35314523 99778391066714989w9977839106671499·1014507-1November 12, 2011Ray Chandler
35414418 61366781047787619319w6136678104778761932·1014399-1November 12, 2011Ray Chandler
35614391 93349839882757639w9334983988275764·1014375-1November 12, 2011Ray Chandler
35714342 88497196195975559w8849719619597556·1014326-1November 12, 2011Ray Chandler
36214125 113144781758913379w11314478175891338·1014108-1November 12, 2011Ray Chandler
36314120 11996201564155695949w1199620156415569595·1014101-1November 12, 2011Ray Chandler
36514072 3306402106026173629w330640210602617363·1014054-1November 12, 2011Ray Chandler
36914007 104719938231527989w10471993823152799·1013990-1November 12, 2011Ray Chandler
37013999 59061817430526236479w5906181743052623648·1013980-1November 12, 2011Ray Chandler
37113966 99778391066714989w9977839106671499·1013950-1November 12, 2011Ray Chandler
37513848 2736126550804369379w273612655080436938·1013830-1November 12, 2011Ray Chandler
37713813 53245325513606464349w5324532551360646435·1013794-1November 12, 2011Ray Chandler
37913747 36881076720471439609w3688107672047143961·1013728-1November 12, 2011Ray Chandler
38113655 14739965565045966629w1473996556504596663·1013636-1November 12, 2011Ray Chandler
38713498 2481086402869308079w248108640286930808·1013480-1November 12, 2011Ray Chandler
39213332 93349839882757639w9334983988275764·1013316-1November 12, 2011Ray Chandler
39513276 2736126550804369379w273612655080436938·1013258-1November 12, 2011Ray Chandler
39713255 22654574126992624459w2265457412699262446·1013236-1November 12, 2011Ray Chandler
39813228 308950354969368769w30895035496936877·1013211-1November 12, 2011Ray Chandler
40013198 377315189587110319w37731518958711032·1013181-1November 12, 2011Ray Chandler
40513066 61366781047787619319w6136678104778761932·1013047-1November 12, 2011Ray Chandler
40712997 308950354969368769w30895035496936877·1012980-1November 12, 2011Ray Chandler
40812992 88497196195975559w8849719619597556·1012976-1November 12, 2011Ray Chandler
41112826 104719938231527989w10471993823152799·1012809-1November 12, 2011Ray Chandler
41412685 53245325513606464349w5324532551360646435·1012666-1November 12, 2011Ray Chandler
41512660 20862283850172499279w2086228385017249928·1012641-1November 12, 2011Ray Chandler
41612617 135237198235074179w13523719823507418·1012600-1November 12, 2011Ray Chandler
42412402 157753730685372709w15775373068537271·1012385-1November 12, 2011Ray Chandler
42712257 58491942059325319w5849194205932532·1012241-1November 12, 2011Ray Chandler
43012142 135237198235074179w13523719823507418·1012125-1November 12, 2011Ray Chandler
43112129 136801253872567759w13680125387256776·1012112-1November 12, 2011Ray Chandler
43312078 136801253872567759w13680125387256776·1012061-1November 12, 2011Ray Chandler
43412019 157753730685372709w15775373068537271·1012002-1November 12, 2011Ray Chandler
43511948 113144781758913379w11314478175891338·1011931-1November 12, 2011Ray Chandler
43711905 22654574126992624459w2265457412699262446·1011886-1November 12, 2011Ray Chandler
44111836 3306402106026173629w330640210602617363·1011818-1November 12, 2011Ray Chandler
44211827 20862283850172499279w2086228385017249928·1011808-1November 12, 2011Ray Chandler
44511762 126273358411702529w12627335841170253·1011745-1November 12, 2011Ray Chandler
44711715 88610369897519586269w8861036989751958627·1011696-1November 12, 2011Ray Chandler
44911687 2481086402869308079w248108640286930808·1011669-1November 12, 2011Ray Chandler
45011675 88497196195975559w8849719619597556·1011659-1November 12, 2011Ray Chandler
45111667 163374302014796809w16337430201479681·1011650-1November 12, 2011Ray Chandler
45211625 136801253872567759w13680125387256776·1011608-1November 12, 2011Ray Chandler
45311510 135237198235074179w13523719823507418·1011493-1November 12, 2011Ray Chandler
45411504 207104321535235669w20710432153523567·1011487-1November 12, 2011Ray Chandler
45511492 104719938231527989w10471993823152799·1011475-1November 12, 2011Ray Chandler
45611475 14739965565045966629w1473996556504596663·1011456-1November 12, 2011Ray Chandler
45711449 135237198235074179w13523719823507418·1011432-1November 12, 2011Ray Chandler
45911387 99778391066714989w9977839106671499·1011371-1November 12, 2011Ray Chandler
46011374 51893957696564594449w5189395769656459445·1011355-1November 12, 2011Ray Chandler
46111350 2481086402869308079w248108640286930808·1011332-1November 12, 2011Ray Chandler
46511269 15138680731470181619w1513868073147018162·1011250-1November 12, 2011Ray Chandler
46711195 67585171412632667639w6758517141263266764·1011176-1November 12, 2011Ray Chandler
46911175 260756274838868969w26075627483886897·1011158-1November 12, 2011Ray Chandler
47011165 58491942059325319w5849194205932532·1011149-1November 12, 2011Ray Chandler
47211103 16775103481120529w1677510348112053·1011087-1November 12, 2011Ray Chandler
47411084 37454136266971339579w3745413626697133958·1011065-1November 12, 2011Ray Chandler
47511067 2736126550804369379w273612655080436938·1011049-1November 12, 2011Ray Chandler
47611056 88610369897519586269w8861036989751958627·1011037-1November 12, 2011Ray Chandler
47711044 37454136266971339579w3745413626697133958·1011025-1November 12, 2011Ray Chandler
47811035 99778391066714989w9977839106671499·1011019-1November 12, 2011Ray Chandler
47911017 207104321535235669w20710432153523567·1011000-1November 12, 2011Ray Chandler
48110967 260756274838868969w26075627483886897·1010950-1November 12, 2011Ray Chandler
48210966 113144781758913379w11314478175891338·1010949-1November 12, 2011Ray Chandler
48510960 88497196195975559w8849719619597556·1010944-1November 12, 2011Ray Chandler
48710939 58491942059325319w5849194205932532·1010923-1November 12, 2011Ray Chandler
48810931 3306402106026173629w330640210602617363·1010913-1November 12, 2011Ray Chandler
48910878 36881076720471439609w3688107672047143961·1010859-1November 12, 2011Ray Chandler
49110863 3306402106026173629w330640210602617363·1010845-1November 12, 2011Ray Chandler
49410705 260756274838868969w26075627483886897·1010688-1November 12, 2011Ray Chandler
49810646 58491942059325319w5849194205932532·1010630-1November 12, 2011Ray Chandler
49910601 200495729963612089w20049572996361209·1010584-1November 12, 2011Ray Chandler
50010601 11996201564155695949w1199620156415569595·1010582-1November 12, 2011Ray Chandler
50110571 377315189587110319w37731518958711032·1010554-1November 12, 2011Ray Chandler
50310524 36881076720471439609w3688107672047143961·1010505-1November 12, 2011Ray Chandler
50710231 61366781047787619319w6136678104778761932·1010212-1November 12, 2011Ray Chandler
51010179 53245325513606464349w5324532551360646435·1010160-1November 12, 2011Ray Chandler
51110175 136801253872567759w13680125387256776·1010158-1November 12, 2011Ray Chandler
51210154 14739965565045966629w1473996556504596663·1010135-1November 12, 2011Ray Chandler
51410133 74407841354393189w7440784135439319·1010117-1November 12, 2011Ray Chandler
51710084 135237198235074179w13523719823507418·1010067-1November 12, 2011Ray Chandler

November 11, 2011

Serge Batalov found a quasi-repdigit PRP.

Unprovable quasi-repdigit PRPs (except pd)
 digitsflabelwlabelexpressionwhenwho
854028620111201w(181·1040284-1)/9November 11, 2011Serge Batalov

Ray Chandler found 30 prime numbers of the form k·10n-1, 42nd-48th of k=41945128176534744, 45th-48th of k=42347460076759481, 44th of k=46219659610534935, 42nd-43rd of k=46473172030295717, 42nd-45th of k=49744364829902015, 45th-47th of k=50637515049938733, 43rd-45th of k=50857767980257511, 44th-45th of k=51215596469881907 and 41st-44th of k=52797555212895374.

Prime numbers of the form k·10n-1 (including 45 known prime numbers at least)
 digitsflabelwlabelexpressionwhenwho
11828211 419451281765347439w41945128176534744·1028194-1November 11, 2011Ray Chandler
12227696 508577679802575109w50857767980257511·1027679-1November 11, 2011Ray Chandler
12327668 419451281765347439w41945128176534744·1027651-1November 11, 2011Ray Chandler
12727066 506375150499387329w50637515049938733·1027049-1November 11, 2011Ray Chandler
12926993 497443648299020149w49744364829902015·1026976-1November 11, 2011Ray Chandler
18221123 512155964698819069w51215596469881907·1021106-1November 11, 2011Ray Chandler
18720687 497443648299020149w49744364829902015·1020670-1November 11, 2011Ray Chandler
19120447 497443648299020149w49744364829902015·1020430-1November 11, 2011Ray Chandler
19419758 423474600767594809w42347460076759481·1019741-1November 11, 2011Ray Chandler
20418793 506375150499387329w50637515049938733·1018776-1November 11, 2011Ray Chandler
20518753 512155964698819069w51215596469881907·1018736-1November 11, 2011Ray Chandler
21318206 508577679802575109w50857767980257511·1018189-1November 11, 2011Ray Chandler
21418129 419451281765347439w41945128176534744·1018112-1November 11, 2011Ray Chandler
22717071 506375150499387329w50637515049938733·1017054-1November 11, 2011Ray Chandler
23016946 423474600767594809w42347460076759481·1016929-1November 11, 2011Ray Chandler
24416159 508577679802575109w50857767980257511·1016142-1November 11, 2011Ray Chandler
25814990 419451281765347439w41945128176534744·1014973-1November 11, 2011Ray Chandler
26414318 423474600767594809w42347460076759481·1014301-1November 11, 2011Ray Chandler
26514288 423474600767594809w42347460076759481·1014271-1November 11, 2011Ray Chandler
28013638 497443648299020149w49744364829902015·1013621-1November 11, 2011Ray Chandler
28513352 419451281765347439w41945128176534744·1013335-1November 11, 2011Ray Chandler
29413110 419451281765347439w41945128176534744·1013093-1November 11, 2011Ray Chandler
34210227 419451281765347439w41945128176534744·1010210-1November 11, 2011Ray Chandler

Factorizations of 11...11711...11 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.

November 9, 2011

Factorizations of 11...11311...11 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.

November 6, 2011

Factorizations of 11...11411...11 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.

November 3, 2011

Factorizations of 11...19 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 2, 2011

Serge Batalov proved the primality of a 5384-digit near-repdigit-related number (11·105383-119)/9 = 110·R5382-1 by CHG.

Proven near-repdigit-related primes (except ru/nr/pd/qr)
 digitsflabelwlabelexpressionwhenwho
70853841220912w09(11·105383-119)/9November 2, 2011Serge Batalov

November 1, 2011

RSALS and Serge Batalov factored a 169-digit composite factor of 6·10273-1 into 82-digit and 87-digit prime factors. It's the largest number factored by GNFS in our tables so far. Congratulations!

October 2011

October 27, 2011

Markus Tervooren factored a 166-digit composite factor of 2·10241-1 into 49-digit, 55-digit and 63-digit prime factors. It's the largest number factored by GNFS in our tables so far. Congratulations!

October 18, 2011

matsui factored an 198-digit composite number (16·10217-1)/3/41/468117319/18369134449 into two 99-digit prime numbers. It's the largest known nontrivial nice-split in our tables. Congratulations!

October 5, 2011

Ray Chandler found 8 prime numbers of the form k·10n-1. 51st of 204621546536159689w, 52nd of 276531952053868139w, 50th of 297349836083272769w, 48th-49th of 310267170933217889w and 53rd-55th of 378706641575875549w.

Prime numbers of the form k·10n-1 (including 45 known prime numbers at least)
 digitsflabelwlabelexpressionwhenwho
3746591 297349836083272769w29734983608327277·1046574-1October 5, 2011Ray Chandler
4445441 204621546536159689w20462154653615969·1045424-1October 5, 2011Ray Chandler
4545201 310267170933217889w31026717093321789·1045184-1October 5, 2011Ray Chandler
5542028 378706641575875549w37870664157587555·1042011-1October 5, 2011Ray Chandler
7537479 310267170933217889w31026717093321789·1037462-1October 5, 2011Ray Chandler
8236033 378706641575875549w37870664157587555·1036016-1October 5, 2011Ray Chandler
9034089 276531952053868139w27653195205386814·1034072-1October 5, 2011Ray Chandler
9633424 378706641575875549w37870664157587555·1033407-1October 5, 2011Ray Chandler

September 2011

September 30, 2011

Ray Chandler found 30 prime numbers of the form k·10n-1.

Prime numbers of the form k·10n-1 (including 45 known prime numbers at least)
 digitsflabelwlabelexpressionwhenwho
11127754 378706641575875549w37870664157587555·1027737-1September 30, 2011Ray Chandler
11826596 378706641575875549w37870664157587555·1026579-1September 30, 2011Ray Chandler
12225816 310267170933217889w31026717093321789·1025799-1September 30, 2011Ray Chandler
13124704 250222986112031729w25022298611203173·1024687-1September 30, 2011Ray Chandler
13324582 378706641575875549w37870664157587555·1024565-1September 30, 2011Ray Chandler
15622572 378706641575875549w37870664157587555·1022555-1September 30, 2011Ray Chandler
15922343 204621546536159689w20462154653615969·1022326-1September 30, 2011Ray Chandler
16421779 204621546536159689w20462154653615969·1021762-1September 30, 2011Ray Chandler
16720897 250222986112031729w25022298611203173·1020880-1September 30, 2011Ray Chandler
17320583 250222986112031729w25022298611203173·1020566-1September 30, 2011Ray Chandler
18418845 378706641575875549w37870664157587555·1018828-1September 30, 2011Ray Chandler
19218083 204621546536159689w20462154653615969·1018066-1September 30, 2011Ray Chandler
19317865 250222986112031729w25022298611203173·1017848-1September 30, 2011Ray Chandler
20316977 276531952053868139w27653195205386814·1016960-1September 30, 2011Ray Chandler
20516904 250222986112031729w25022298611203173·1016887-1September 30, 2011Ray Chandler
20816517 204621546536159689w20462154653615969·1016500-1September 30, 2011Ray Chandler
20916515 319555114216347379w31955511421634738·1016498-1September 30, 2011Ray Chandler
21116473 319555114216347379w31955511421634738·1016456-1September 30, 2011Ray Chandler
22115583 276531952053868139w27653195205386814·1015566-1September 30, 2011Ray Chandler
22615320 297349836083272769w29734983608327277·1015303-1September 30, 2011Ray Chandler
23314537 204621546536159689w20462154653615969·1014520-1September 30, 2011Ray Chandler
24213857 276531952053868139w27653195205386814·1013840-1September 30, 2011Ray Chandler
25013462 297349836083272769w29734983608327277·1013445-1September 30, 2011Ray Chandler
25213293 276531952053868139w27653195205386814·1013276-1September 30, 2011Ray Chandler
27212344 310267170933217889w31026717093321789·1012327-1September 30, 2011Ray Chandler
27512093 276531952053868139w27653195205386814·1012076-1September 30, 2011Ray Chandler
27611932 250222986112031729w25022298611203173·1011915-1September 30, 2011Ray Chandler
29510706 319555114216347379w31955511421634738·1010689-1September 30, 2011Ray Chandler
30710081 276531952053868139w27653195205386814·1010064-1September 30, 2011Ray Chandler
30810075 297349836083272769w29734983608327277·1010058-1September 30, 2011Ray Chandler

September 22, 2011

Bruno DallOsto found the largest known near-repdigit prime number. Congratulations!

Proven near-repdigit primes
 digitsflabelwlabelexpressionwhenwho
184652195999959w96·10846519-1September 22, 2011Bruno DallOsto

September 20, 2011

David Broadhurst found the record-breaking 68th prime number of the form 5166409399321812845·10n-1. Congratulations!

Prime numbers of the form k·10n-1 (including 45 known prime numbers at least)
 digitsflabelwlabelexpressionwhenwho
2237743 51664093993218128449w5166409399321812845·10237724-1September 20, 2011David Broadhurst

September 14, 2011

Factorizations of 55...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.

September 11, 2011

David Broadhurst found the record-breaking 67th prime number of the form 5166409399321812845·10n-1. Congratulations!

Prime numbers of the form k·10n-1 (including 45 known prime numbers at least)
 digitsflabelwlabelexpressionwhenwho
5200252 51664093993218128449w5166409399321812845·10200233-1September 11, 2011David Broadhurst

September 8, 2011

David Broadhurst found the 65th prime number and the record-tying 66th prime number of the form 5166409399321812845·10n-1. See also primecount.txt.

Prime numbers of the form k·10n-1 (including 45 known prime numbers at least)
 digitsflabelwlabelexpressionwhenwho
7149359 51664093993218128449w5166409399321812845·10149340-1September 8, 2011David Broadhurst
8146822 51664093993218128449w5166409399321812845·10146803-1September 8, 2011David Broadhurst

September 4, 2011

David Broadhurst found the 64th prime number of the form 5166409399321812845·10n-1.

Prime numbers of the form k·10n-1 (including 45 known prime numbers at least)
 digitsflabelwlabelexpressionwhenwho
1491859 51664093993218128449w5166409399321812845·1091840-1September 4, 2011David Broadhurst

September 3, 2011

David Broadhurst found the 62nd-63rd prime numbers of the form 5166409399321812845·10n-1 and the 59th prime number of the form 7347764627675020164·10n-1.

Prime numbers of the form k·10n-1 (including 45 known prime numbers at least)
 digitsflabelwlabelexpressionwhenwho
1099203 73477646276750201639w7347764627675020164·1099184-1September 3, 2011David Broadhurst
1293724 51664093993218128449w5166409399321812845·1093705-1September 3, 2011David Broadhurst
1392195 51664093993218128449w5166409399321812845·1092176-1September 3, 2011David Broadhurst

September 2, 2011

David Broadhurst found the 61st prime number of the form 5166409399321812845·10n-1.

Prime numbers of the form k·10n-1 (including 45 known prime numbers at least)
 digitsflabelwlabelexpressionwhenwho
1374237 51664093993218128449w5166409399321812845·1074218-1September 2, 2011David Broadhurst

September 1, 2011

David Broadhurst found the 58th prime number of the form 7347764627675020164·10n-1.

Prime numbers of the form k·10n-1 (including 45 known prime numbers at least)
 digitsflabelwlabelexpressionwhenwho
1373485 73477646276750201639w7347764627675020164·1073466-1September 1, 2011David Broadhurst

David Broadhurst found the 59th-60th prime numbers of the form 5166409399321812845·10n-1.

Prime numbers of the form k·10n-1 (including 45 known prime numbers at least)
 digitsflabelwlabelexpressionwhenwho
1958526 51664093993218128449w5166409399321812845·1058507-1September 1, 2011David Broadhurst
2058004 51664093993218128449w5166409399321812845·1057985-1September 1, 2011David Broadhurst

August 2011

August 24, 2011

I found the 57th prime number of the form 7347764627675020164·10n-1.

Prime numbers of the form k·10n-1 (including 45 known prime numbers at least)
 digitsflabelwlabelexpressionwhenwho
7034859 73477646276750201639w7347764627675020164·1034840-1August 24, 2011Makoto Kamada

August 22, 2011

I found the 56th prime number of the form 7347764627675020164·10n-1.

Prime numbers of the form k·10n-1 (including 45 known prime numbers at least)
 digitsflabelwlabelexpressionwhenwho
7632907 73477646276750201639w7347764627675020164·1032888-1August 22, 2011Makoto Kamada

August 18, 2011

Markus Tervooren proved 9 quasi-repdigit prime numbers by Primo.

Proven quasi-repdigit primes (except pd)
 digitsflabelwlabelexpressionwhenwho
28829691444714w7(13·102968+23)/9August 18, 2011Markus Tervooren
29329191333713w7(4·102918+11)/3August 18, 2011Markus Tervooren
29928421000910w9102841+9August 18, 2011Markus Tervooren
31926321555915w9(14·102631+31)/9August 18, 2011Markus Tervooren
32226281666716w7(5·102627+1)/3August 18, 2011Markus Tervooren
32426231666916w9(5·102622+7)/3August 18, 2011Markus Tervooren
32726081000310w3102607+3August 18, 2011Markus Tervooren
33525341222712w7(11·102533+43)/9August 18, 2011Markus Tervooren
33725091555915w9(14·102508+31)/9August 18, 2011Markus Tervooren

August 16, 2011

Markus Tervooren proved a 9812-digit near-repdigit prime number by Primo. Congratulations!

Proven near-repdigit primes
 digitsflabelwlabelexpressionwhenwho
3069812888898w9(8·109812+1)/9August 16, 2011Markus Tervooren

August 5, 2011

Ray Chandler found the 4th largest known unprovable plateau and depression PRP.

Unprovable plateau and depression PRPs
 digitsflabelwlabelexpressionwhenwho
41158117888778w7(71·10115810-17)/9August 5, 2011Ray Chandler

July 2011

July 25, 2011

Ray Chandler found the 46th-51st prime number of the form 20889401543045007·10n-1.

Prime numbers of the form k·10n-1 (including 45 known prime numbers at least)
 digitsflabelwlabelexpressionwhenwho
7333827 208894015430450069w20889401543045007·1033810-1July 25, 2011Ray Chandler
7433491 208894015430450069w20889401543045007·1033474-1July 25, 2011Ray Chandler
10526171 208894015430450069w20889401543045007·1026154-1July 25, 2011Ray Chandler
13023033 208894015430450069w20889401543045007·1023016-1July 25, 2011Ray Chandler
14919835 208894015430450069w20889401543045007·1019818-1July 25, 2011Ray Chandler
20313917 208894015430450069w20889401543045007·1013900-1July 25, 2011Ray Chandler

July 18, 2011

Stefano D'Urso found a near-repdigit prime.

Proven near-repdigit primes
 digitsflabelwlabelexpressionwhenwho
13255045 99999989w9999999·10255038-1July 18, 2011Stefano D'Urso

July 11, 2011

Ray Chandler found 1 near-repdigit PRP, 24 quasi-repdigit PRPs and 71 near-repdigit-related PRPs in the range 29001≤n≤30000.

Unprovable near-repdigit PRPs
 digitsflabelwlabelexpressionwhenwho
632970571777717w(646·1029703-7)/9July 11, 2011Ray Chandler
Unprovable quasi-repdigit PRPs (except pd)
 digitsflabelwlabelexpressionwhenwho
1292998228229282w9(254·1029980+61)/9July 11, 2011Ray Chandler
13029955222832w83(2·1029955+547)/9July 11, 2011Ray Chandler
13229917222512w51(2·1029917+259)/9July 11, 2011Ray Chandler
13429899222672w67(2·1029899+403)/9July 11, 2011Ray Chandler
13529893777297w29(7·1029893-439)/9July 11, 2011Ray Chandler
13629770444234w23(4·1029770-193)/9July 11, 2011Ray Chandler
138296704776747w67(43·1029669-97)/9July 11, 2011Ray Chandler
14029600222612w61(2·1029600+349)/9July 11, 2011Ray Chandler
14129585888198w19(8·1029585-629)/9July 11, 2011Ray Chandler
1422955525229252w9(227·1029553+61)/9July 11, 2011Ray Chandler
14329541888298w29(8·1029541-539)/9July 11, 2011Ray Chandler
1462946682889828w9(746·1029464+1)/9July 11, 2011Ray Chandler
1492942528221282w1(254·1029423-11)/9July 11, 2011Ray Chandler
1512938360111601w(541·1029381-1)/9July 11, 2011Ray Chandler
15229377888498w49(8·1029377-359)/9July 11, 2011Ray Chandler
1552934774111741w(667·1029345-1)/9July 11, 2011Ray Chandler
15829320777237w23(7·1029320-493)/9July 11, 2011Ray Chandler
161292906776767w67(61·1029289-97)/9July 11, 2011Ray Chandler
16229273111491w49(1029273+341)/9July 11, 2011Ray Chandler
1652919976779767w9(691·1029197+11)/9July 11, 2011Ray Chandler
17129062888218w21(8·1029062-611)/9July 11, 2011Ray Chandler
1732903880889808w9(728·1029036+1)/9July 11, 2011Ray Chandler
174290299112191w21(82·1029028+89)/9July 11, 2011Ray Chandler
1752900982889828w9(746·1029007+1)/9July 11, 2011Ray Chandler
Unprovable near-repdigit-related PRPs (except ru/nr/pd/qr)
 digitsflabelwlabelexpressionwhenwho
4929988 98w11(89·1029987-701)/9July 11, 2011Ray Chandler
50299764114341w43(37·1029975+287)/9July 11, 2011Ray Chandler
51299747884978w49(71·1029973-359)/9July 11, 2011Ray Chandler
53299442550325w03(23·1029943-473)/9July 11, 2011Ray Chandler
55299398447984w79(76·1029938+311)/9July 11, 2011Ray Chandler
56299383885938w59(35·1029937-269)/9July 11, 2011Ray Chandler
61298965228752w87(47·1029895+583)/9July 11, 2011Ray Chandler
63298828440384w03(76·1029881-373)/9July 11, 2011Ray Chandler
64298658445984w59(76·1029864+131)/9July 11, 2011Ray Chandler
65298533554735w47(32·1029852-77)/9July 11, 2011Ray Chandler
66298149229792w97(83·1029813+673)/9July 11, 2011Ray Chandler
67298024887948w79(44·1029801-89)/9July 11, 2011Ray Chandler
69297967224372w43(65·1029795+187)/9July 11, 2011Ray Chandler
70297967220172w01(65·1029795-191)/9July 11, 2011Ray Chandler
71297931559315w93(14·1029792+337)/9July 11, 2011Ray Chandler
72297715117951w79(46·1029770+611)/9July 11, 2011Ray Chandler
73297695446954w69(49·1029768+221)/9July 11, 2011Ray Chandler
74297542885128w51(26·1029753-341)/9July 11, 2011Ray Chandler
7529752 665w3(599·1029750-23)/9July 11, 2011Ray Chandler
7729728 997w9(898·1029726+11)/9July 11, 2011Ray Chandler
78297208559785w97(77·1029719+373)/9July 11, 2011Ray Chandler
7929720 78w11(71·1029719-701)/9July 11, 2011Ray Chandler
80297006224762w47(56·1029699+223)/9July 11, 2011Ray Chandler
8129697 118w3(107·1029695-53)/9July 11, 2011Ray Chandler
83296728446984w69(76·1029671+221)/9July 11, 2011Ray Chandler
85296352114921w49(19·1029634+341)/9July 11, 2011Ray Chandler
86296308551785w17(77·1029629-347)/9July 11, 2011Ray Chandler
87296166119761w97(55·1029615+773)/9July 11, 2011Ray Chandler
88296106770167w01(61·1029609-691)/9July 11, 2011Ray Chandler
89296087551775w17(68·1029607-347)/9July 11, 2011Ray Chandler
92295922550325w03(23·1029591-473)/9July 11, 2011Ray Chandler
9329591 27w33(25·1029590-403)/9July 11, 2011Ray Chandler
97295429228192w81(83·1029541+529)/9July 11, 2011Ray Chandler
98295289226792w67(83·1029527+403)/9July 11, 2011Ray Chandler
99295228441384w13(76·1029521-283)/9July 11, 2011Ray Chandler
100295228223782w37(74·1029521+133)/9July 11, 2011Ray Chandler
101295157447174w71(67·1029514+239)/9July 11, 2011Ray Chandler
102295121443914w39(13·1029511-49)/9July 11, 2011Ray Chandler
103295084110941w09(37·1029507-19)/9July 11, 2011Ray Chandler
105295041443114w31(13·1029503-121)/9July 11, 2011Ray Chandler
106295028115981w59(73·1029501+431)/9July 11, 2011Ray Chandler
10729494 117w1(106·1029492-61)/9July 11, 2011Ray Chandler
10829492 662w3(596·1029490+7)/9July 11, 2011Ray Chandler
109294906885968w59(62·1029489-269)/9July 11, 2011Ray Chandler
110294884772347w23(43·1029487-493)/9July 11, 2011Ray Chandler
112294726770167w01(61·1029471-691)/9July 11, 2011Ray Chandler
114294707881778w17(71·1029469-647)/9July 11, 2011Ray Chandler
115294702557925w79(23·1029469+211)/9July 11, 2011Ray Chandler
116294641448314w83(13·1029463+347)/9July 11, 2011Ray Chandler
118294401227112w71(11·1029439+439)/9July 11, 2011Ray Chandler
119294251884718w47(17·1029424-377)/9July 11, 2011Ray Chandler
12129402 94w99(85·1029401+491)/9July 11, 2011Ray Chandler
124293498112781w27(73·1029348+143)/9July 11, 2011Ray Chandler
125293482447324w73(22·1029347+257)/9July 11, 2011Ray Chandler
126293443221732w17(29·1029343-47)/9July 11, 2011Ray Chandler
128293221889318w93(17·1029321+37)/9July 11, 2011Ray Chandler
131292895114751w47(46·1029288+323)/9July 11, 2011Ray Chandler
133292377228772w87(65·1029236+583)/9July 11, 2011Ray Chandler
13629219 97w33(88·1029218-403)/9July 11, 2011Ray Chandler
137292134559345w93(41·1029212+337)/9July 11, 2011Ray Chandler
138292098448984w89(76·1029208+401)/9July 11, 2011Ray Chandler
143291648116781w67(73·1029163+503)/9July 11, 2011Ray Chandler
145291467227972w79(65·1029145+511)/9July 11, 2011Ray Chandler
146291446887368w73(62·1029143-143)/9July 11, 2011Ray Chandler
14929129 12w77(11·1029128+493)/9July 11, 2011Ray Chandler
154290812110721w07(19·1029080-37)/9July 11, 2011Ray Chandler
157290639442994w29(85·1029062-139)/9July 11, 2011Ray Chandler
161290555442354w23(49·1029054-193)/9July 11, 2011Ray Chandler
162290443446734w67(31·1029043+203)/9July 11, 2011Ray Chandler
16529017 441w7(397·1029015+53)/9July 11, 2011Ray Chandler
166290119552795w27(86·1029010-257)/9July 11, 2011Ray Chandler

July 7, 2011

Ray Chandler found the 53rd prime number of the form 16781897479411358·10n-1.

Prime numbers of the form k·10n-1 (including 45 known prime numbers at least)
 digitsflabelwlabelexpressionwhenwho
2149547 167818974794113579w16781897479411358·1049530-1July 7, 2011Ray Chandler

July 6, 2011

Markus Tervooren proved 2 near-repdigit primes by Primo. Certifications are available.

Proven near-repdigit primes
 digitsflabelwlabelexpressionwhenwho
3984472888898w9(8·104472+1)/9July 6, 2011Markus Tervooren
4114175888898w9(8·104175+1)/9July 6, 2011Markus Tervooren

July 4, 2011

Ray Chandler found 46th-52nd prime number of the form 13103465680138764·10n-1, 46th-48th of 14366136273120695·10n-1 and 46th-52nd of 16781897479411358·10n-1.

Prime numbers of the form k·10n-1 (including 45 known prime numbers at least)
 digitsflabelwlabelexpressionwhenwho
2845875 131034656801387639w13103465680138764·1045858-1July 4, 2011Ray Chandler
5238006 131034656801387639w13103465680138764·1037989-1July 4, 2011Ray Chandler
5637580 131034656801387639w13103465680138764·1037563-1July 4, 2011Ray Chandler
8729589 131034656801387639w13103465680138764·1029572-1July 4, 2011Ray Chandler
8829445 167818974794113579w16781897479411358·1029428-1July 4, 2011Ray Chandler
10026451 167818974794113579w16781897479411358·1026434-1July 4, 2011Ray Chandler
10425608 143661362731206949w14366136273120695·1025591-1July 4, 2011Ray Chandler
10825079 167818974794113579w16781897479411358·1025062-1July 4, 2011Ray Chandler
11823640 131034656801387639w13103465680138764·1023623-1July 4, 2011Ray Chandler
12722832 167818974794113579w16781897479411358·1022815-1July 4, 2011Ray Chandler
17416294 131034656801387639w13103465680138764·1016277-1July 4, 2011Ray Chandler
20213523 131034656801387639w13103465680138764·1013506-1July 4, 2011Ray Chandler
21013145 167818974794113579w16781897479411358·1013128-1July 4, 2011Ray Chandler
21812487 167818974794113579w16781897479411358·1012470-1July 4, 2011Ray Chandler
21912474 143661362731206949w14366136273120695·1012457-1July 4, 2011Ray Chandler
22412214 143661362731206949w14366136273120695·1012197-1July 4, 2011Ray Chandler
23011760 167818974794113579w16781897479411358·1011743-1July 4, 2011Ray Chandler

June 2011

June 30, 2011

Ray Chandler found 1 near-repdigit PRP, 16 quasi-repdigit PRPs and 49 near-repdigit-related PRPs in the range 28001≤n≤29000.

Unprovable near-repdigit PRPs
 digitsflabelwlabelexpressionwhenwho
7128320777377w37(7·1028320-367)/9June 30, 2011Ray Chandler
Unprovable quasi-repdigit PRPs (except pd)
 digitsflabelwlabelexpressionwhenwho
15428921222732w73(2·1028921+457)/9June 30, 2011Ray Chandler
1562882641449414w9(373·1028824+41)/9June 30, 2011Ray Chandler
158287333112131w21(28·1028732+89)/9June 30, 2011Ray Chandler
1592872923777237w(214·1028727-7)/9June 30, 2011Ray Chandler
1602871224227242w7(218·1028710+43)/9June 30, 2011Ray Chandler
1612871089883898w3(809·1028708-53)/9June 30, 2011Ray Chandler
165286373115131w51(28·1028636+359)/9June 30, 2011Ray Chandler
16728624111391w39(1028624+251)/9June 30, 2011Ray Chandler
169286075115151w51(46·1028606+359)/9June 30, 2011Ray Chandler
172285196110161w01(55·1028518-91)/9June 30, 2011Ray Chandler
1732846624221242w1(218·1028464-11)/9June 30, 2011Ray Chandler
1752836828223282w3(254·1028366+7)/9June 30, 2011Ray Chandler
18028294111591w59(1028294+431)/9June 30, 2011Ray Chandler
18328191 4w99(4·1028191+491)/9June 30, 2011Ray Chandler
18428105777037w03(7·1028105-673)/9June 30, 2011Ray Chandler
1882807154557545w7(491·1028069+13)/9June 30, 2011Ray Chandler
Unprovable near-repdigit-related PRPs (except ru/nr/pd/qr)
 digitsflabelwlabelexpressionwhenwho
100289659226192w61(83·1028964+349)/9June 30, 2011Ray Chandler
10128948 225w1(203·1028946-41)/9June 30, 2011Ray Chandler
104288999228392w83(83·1028898+547)/9June 30, 2011Ray Chandler
107288795440754w07(49·1028878-337)/9June 30, 2011Ray Chandler
108288776889768w97(62·1028876+73)/9June 30, 2011Ray Chandler
109288705114951w49(46·1028869+341)/9June 30, 2011Ray Chandler
111288512116321w63(19·1028850+467)/9June 30, 2011Ray Chandler
112288398772387w23(79·1028838-493)/9June 30, 2011Ray Chandler
114288111556315w63(14·1028810+67)/9June 30, 2011Ray Chandler
119287609881998w19(89·1028759-629)/9June 30, 2011Ray Chandler
120287323885138w51(35·1028731-341)/9June 30, 2011Ray Chandler
123286488553985w39(77·1028647-149)/9June 30, 2011Ray Chandler
126286035220952w09(47·1028602-119)/9June 30, 2011Ray Chandler
127286026884768w47(62·1028601-377)/9June 30, 2011Ray Chandler
131285418552985w29(77·1028540-239)/9June 30, 2011Ray Chandler
13228538 64w11(58·1028537-301)/9June 30, 2011Ray Chandler
13428485 228w7(206·1028483-17)/9June 30, 2011Ray Chandler
13828462 665w9(599·1028460+31)/9June 30, 2011Ray Chandler
140284536551765w17(59·1028452-347)/9June 30, 2011Ray Chandler
143284466885968w59(62·1028445-269)/9June 30, 2011Ray Chandler
14428435 667w9(601·1028433+11)/9June 30, 2011Ray Chandler
145284294884148w41(44·1028428-431)/9June 30, 2011Ray Chandler
14628417 27w11(25·1028416-601)/9June 30, 2011Ray Chandler
147284022889728w97(26·1028401+73)/9June 30, 2011Ray Chandler
148283833119731w97(28·1028382+773)/9June 30, 2011Ray Chandler
15228328 668w9(602·1028326+1)/9June 30, 2011Ray Chandler
153283242117921w79(19·1028323+611)/9June 30, 2011Ray Chandler
154283214559745w97(41·1028320+373)/9June 30, 2011Ray Chandler
158282757551375w13(68·1028274-383)/9June 30, 2011Ray Chandler
159282746556165w61(59·1028273+49)/9June 30, 2011Ray Chandler
160282738225782w57(74·1028272+313)/9June 30, 2011Ray Chandler
162282532882928w29(26·1028252-539)/9June 30, 2011Ray Chandler
163282521448914w89(13·1028251+401)/9June 30, 2011Ray Chandler
164282372558725w87(23·1028236+283)/9June 30, 2011Ray Chandler
167281972445724w57(22·1028196+113)/9June 30, 2011Ray Chandler
168281899552195w21(86·1028188-311)/9June 30, 2011Ray Chandler
169281815770957w09(52·1028180-619)/9June 30, 2011Ray Chandler
170281732445724w57(22·1028172+113)/9June 30, 2011Ray Chandler
171281676885368w53(62·1028166-323)/9June 30, 2011Ray Chandler
176281085116751w67(46·1028107+503)/9June 30, 2011Ray Chandler
177280954884348w43(44·1028094-413)/9June 30, 2011Ray Chandler
178280859775397w53(88·1028084-223)/9June 30, 2011Ray Chandler
179280855776357w63(52·1028084-133)/9June 30, 2011Ray Chandler
181280726774967w49(61·1028071-259)/9June 30, 2011Ray Chandler
182280708115781w57(73·1028069+413)/9June 30, 2011Ray Chandler
184280605227952w79(47·1028059+511)/9June 30, 2011Ray Chandler
18528055 24w99(22·1028054+491)/9June 30, 2011Ray Chandler
186280499775997w59(88·1028048-169)/9June 30, 2011Ray Chandler
187280344773147w31(43·1028033-421)/9June 30, 2011Ray Chandler

June 27, 2011

Ray Chandler found 52nd-53rd prime number of the form 11123337966287708·10n-1, 53rd-55st of 4781436698811612·10n-1 and 50th of 8165464858818701·10n-1.

Prime numbers of the form k·10n-1 (including 45 known prime numbers at least)
 digitsflabelwlabelexpressionwhenwho
2944877 111233379662877079w11123337966287708·1044860-1June 27, 2011Ray Chandler
4240674 47814366988116119w4781436698811612·1040658-1June 27, 2011Ray Chandler
4339825 81654648588187009w8165464858818701·1039809-1June 27, 2011Ray Chandler
5437516 111233379662877079w11123337966287708·1037499-1June 27, 2011Ray Chandler
5836458 47814366988116119w4781436698811612·1036442-1June 27, 2011Ray Chandler
7730277 47814366988116119w4781436698811612·1030261-1June 27, 2011Ray Chandler

June 22, 2011

Ray Chandler found 48th-52nd prime number of the form 4781436698811612·10n-1, 46th-51st of 11123337966287708·10n-1 and 46th-49th of 8165464858818701·10n-1.

Prime numbers of the form k·10n-1 (including 45 known prime numbers at least)
 digitsflabelwlabelexpressionwhenwho
9425296 81654648588187009w8165464858818701·1025280-1June 22, 2011Ray Chandler
9824447 111233379662877079w11123337966287708·1024430-1June 22, 2011Ray Chandler
13219143 47814366988116119w4781436698811612·1019127-1June 22, 2011Ray Chandler
13918436 111233379662877079w11123337966287708·1018419-1June 22, 2011Ray Chandler
14917289 81654648588187009w8165464858818701·1017273-1June 22, 2011Ray Chandler
15216975 47814366988116119w4781436698811612·1016959-1June 22, 2011Ray Chandler
16315597 111233379662877079w11123337966287708·1015580-1June 22, 2011Ray Chandler
17614117 81654648588187009w8165464858818701·1014101-1June 22, 2011Ray Chandler
18113750 111233379662877079w11123337966287708·1013733-1June 22, 2011Ray Chandler
18713292 111233379662877079w11123337966287708·1013275-1June 22, 2011Ray Chandler
19113160 81654648588187009w8165464858818701·1013144-1June 22, 2011Ray Chandler
19512819 111233379662877079w11123337966287708·1012802-1June 22, 2011Ray Chandler
20112419 47814366988116119w4781436698811612·1012403-1June 22, 2011Ray Chandler
20611798 47814366988116119w4781436698811612·1011782-1June 22, 2011Ray Chandler
21511090 47814366988116119w4781436698811612·1011074-1June 22, 2011Ray Chandler

June 20, 2011

Ray Chandler found 30 quasi-repdigit PRPs and 58 near-repdigit-related PRPs in the range 27001≤n≤28000.

Unprovable quasi-repdigit PRPs (except pd)
 digitsflabelwlabelexpressionwhenwho
17427969888278w27(8·1027969-557)/9June 20, 2011Ray Chandler
1752795746777467w(421·1027955-7)/9June 20, 2011Ray Chandler
17827885222572w57(2·1027885+313)/9June 20, 2011Ray Chandler
1812784976779767w9(691·1027847+11)/9June 20, 2011Ray Chandler
1842781136777367w(331·1027809-7)/9June 20, 2011Ray Chandler
18527805444174w17(4·1027805-247)/9June 20, 2011Ray Chandler
18827763111691w69(1027763+521)/9June 20, 2011Ray Chandler
1942773012777127w(115·1027728-7)/9June 20, 2011Ray Chandler
19527724555075w07(5·1027724-437)/9June 20, 2011Ray Chandler
19627721777537w53(7·1027721-223)/9June 20, 2011Ray Chandler
2012762926227262w7(236·1027627+43)/9June 20, 2011Ray Chandler
20427549 887w(799·1027547-7)/9June 20, 2011Ray Chandler
2052747719777197w(178·1027475-7)/9June 20, 2011Ray Chandler
207274362770727w07(25·1027435-637)/9June 20, 2011Ray Chandler
2082742478773787w3(709·1027422-43)/9June 20, 2011Ray Chandler
212273685778757w87(52·1027367+83)/9June 20, 2011Ray Chandler
21327367 7w99(7·1027367+191)/9June 20, 2011Ray Chandler
21427356222832w83(2·1027356+547)/9June 20, 2011Ray Chandler
2152733483887838w7(755·1027332-17)/9June 20, 2011Ray Chandler
21827255444674w67(4·1027255+203)/9June 20, 2011Ray Chandler
21927232444634w63(4·1027232+167)/9June 20, 2011Ray Chandler
224271903772737w27(34·1027189-457)/9June 20, 2011Ray Chandler
225271651775717w57(16·1027164-187)/9June 20, 2011Ray Chandler
2262712356559565w9(509·1027121+31)/9June 20, 2011Ray Chandler
2292709857557575w7(518·1027096+13)/9June 20, 2011Ray Chandler
230270877115171w51(64·1027086+359)/9June 20, 2011Ray Chandler
2312708278771787w1(709·1027080-61)/9June 20, 2011Ray Chandler
23227069111671w67(1027069+503)/9June 20, 2011Ray Chandler
23427055222912w91(2·1027055+619)/9June 20, 2011Ray Chandler
2352703517117171w7(154·1027033+53)/9June 20, 2011Ray Chandler
Unprovable near-repdigit-related PRPs (except ru/nr/pd/qr)
 digitsflabelwlabelexpressionwhenwho
141279876884768w47(62·1027986-377)/9June 20, 2011Ray Chandler
142279854885348w53(44·1027984-323)/9June 20, 2011Ray Chandler
143279852116721w67(19·1027984+503)/9June 20, 2011Ray Chandler
145279677447174w71(67·1027966+239)/9June 20, 2011Ray Chandler
14627941 772w1(695·1027939-11)/9June 20, 2011Ray Chandler
149278707886978w69(71·1027869-179)/9June 20, 2011Ray Chandler
151278476558965w89(59·1027846+301)/9June 20, 2011Ray Chandler
152278351550715w07(14·1027834-437)/9June 20, 2011Ray Chandler
153278189881398w13(89·1027817-683)/9June 20, 2011Ray Chandler
154278181774117w41(16·1027817-331)/9June 20, 2011Ray Chandler
156278145884958w49(53·1027813-359)/9June 20, 2011Ray Chandler
157278115442354w23(49·1027810-193)/9June 20, 2011Ray Chandler
158278083225332w53(29·1027807+277)/9June 20, 2011Ray Chandler
159277613445734w57(31·1027760+113)/9June 20, 2011Ray Chandler
161277379223792w37(83·1027736+133)/9June 20, 2011Ray Chandler
165276739221792w17(83·1027672-47)/9June 20, 2011Ray Chandler
168276363220732w07(29·1027635-137)/9June 20, 2011Ray Chandler
173276045886758w67(53·1027603-197)/9June 20, 2011Ray Chandler
174275906221962w19(56·1027589-29)/9June 20, 2011Ray Chandler
175275749773997w39(88·1027573-349)/9June 20, 2011Ray Chandler
176275719886398w63(89·1027570-233)/9June 20, 2011Ray Chandler
177275656225962w59(56·1027564+331)/9June 20, 2011Ray Chandler
178275653110331w03(28·1027564-73)/9June 20, 2011Ray Chandler
181275286882368w23(62·1027527-593)/9June 20, 2011Ray Chandler
183275117552975w29(68·1027510-239)/9June 20, 2011Ray Chandler
185274933440334w03(31·1027492-373)/9June 20, 2011Ray Chandler
186274811553115w31(14·1027480-221)/9June 20, 2011Ray Chandler
18727468 67w11(61·1027467-601)/9June 20, 2011Ray Chandler
18927442 884w9(796·1027440+41)/9June 20, 2011Ray Chandler
19227435 92w11(83·1027434-101)/9June 20, 2011Ray Chandler
194274124224342w43(38·1027411+187)/9June 20, 2011Ray Chandler
196274019887398w73(89·1027400-143)/9June 20, 2011Ray Chandler
197274011558115w81(14·1027400+229)/9June 20, 2011Ray Chandler
198273931223712w37(11·1027392+133)/9June 20, 2011Ray Chandler
200273741556915w69(14·1027373+121)/9June 20, 2011Ray Chandler
201273674559745w97(41·1027366+373)/9June 20, 2011Ray Chandler
203273447886978w69(71·1027343-179)/9June 20, 2011Ray Chandler
204273318443184w31(76·1027330-121)/9June 20, 2011Ray Chandler
205273268558385w83(77·1027325+247)/9June 20, 2011Ray Chandler
209272212441924w19(22·1027220-229)/9June 20, 2011Ray Chandler
21127200 87w33(79·1027199-403)/9June 20, 2011Ray Chandler
212271956881368w13(62·1027194-683)/9June 20, 2011Ray Chandler
213271947115371w53(64·1027193+377)/9June 20, 2011Ray Chandler
214271903886938w69(35·1027189-179)/9June 20, 2011Ray Chandler
215271834553945w39(41·1027182-149)/9June 20, 2011Ray Chandler
216271806884768w47(62·1027179-377)/9June 20, 2011Ray Chandler
217271698445984w59(76·1027168+131)/9June 20, 2011Ray Chandler
219271223773937w39(34·1027121-349)/9June 20, 2011Ray Chandler
22027111 558w7(503·1027109-17)/9June 20, 2011Ray Chandler
221271044558145w81(41·1027103+229)/9June 20, 2011Ray Chandler
22227080 71w77(64·1027079+593)/9June 20, 2011Ray Chandler
223270735228152w81(47·1027072+529)/9June 20, 2011Ray Chandler
225270558112381w23(73·1027054+107)/9June 20, 2011Ray Chandler
226270524551345w13(41·1027051-383)/9June 20, 2011Ray Chandler
228270375115351w53(46·1027036+377)/9June 20, 2011Ray Chandler
229270159449194w91(85·1027014+419)/9June 20, 2011Ray Chandler
230270156110761w07(55·1027014-37)/9June 20, 2011Ray Chandler
23327003 992w7(893·1027001+43)/9June 20, 2011Ray Chandler

June 11, 2011

Serge Batalov found 1 quasi-repdigit PRP.

Unprovable quasi-repdigit PRPs (except pd)
 digitsflabelwlabelexpressionwhenwho
49637191222312w3(11·1063718+7)/9June 11, 2011Serge Batalov

June 10, 2011

Ray Chandler found 2 near-repdigit PRPs, 29 quasi-repdigit PRPs and 65 near-repdigit-related PRPs in the range 26001≤n≤27000.

Unprovable near-repdigit PRPs
 digitsflabelwlabelexpressionwhenwho
8126693111611w61(1026693+449)/9June 10, 2011Ray Chandler
8626445777877w87(7·1026445+83)/9June 10, 2011Ray Chandler
Unprovable quasi-repdigit PRPs (except pd)
 digitsflabelwlabelexpressionwhenwho
2052699242441424w1(382·1026990-31)/9June 10, 2011Ray Chandler
2062698773111731w(658·1026985-1)/9June 10, 2011Ray Chandler
212268695774757w47(52·1026868-277)/9June 10, 2011Ray Chandler
2132685018777187w(169·1026848-7)/9June 10, 2011Ray Chandler
21426848888518w51(8·1026848-341)/9June 10, 2011Ray Chandler
2162680984889848w9(764·1026807+1)/9June 10, 2011Ray Chandler
218267909116191w61(82·1026789+449)/9June 10, 2011Ray Chandler
2202675982883828w3(746·1026757-53)/9June 10, 2011Ray Chandler
22126749777037w03(7·1026749-673)/9June 10, 2011Ray Chandler
226266689118191w81(82·1026667+629)/9June 10, 2011Ray Chandler
22726662111931w93(1026662+737)/9June 10, 2011Ray Chandler
228266524772747w27(43·1026651-457)/9June 10, 2011Ray Chandler
230265742778727w87(25·1026573+83)/9June 10, 2011Ray Chandler
2322654029227292w7(263·1026538+43)/9June 10, 2011Ray Chandler
23326538111571w57(1026538+413)/9June 10, 2011Ray Chandler
2352649514117141w7(127·1026493+53)/9June 10, 2011Ray Chandler
2392639982777827w(745·1026397-7)/9June 10, 2011Ray Chandler
240263878110181w01(73·1026386-91)/9June 10, 2011Ray Chandler
2432633689881898w1(809·1026334-71)/9June 10, 2011Ray Chandler
244263117112171w21(64·1026310+89)/9June 10, 2011Ray Chandler
247262326773767w37(61·1026231-367)/9June 10, 2011Ray Chandler
248262174119141w91(37·1026216+719)/9June 10, 2011Ray Chandler
24926206888218w21(8·1026206-611)/9June 10, 2011Ray Chandler
252261476115161w51(55·1026146+359)/9June 10, 2011Ray Chandler
2532612449447494w7(445·1026122+23)/9June 10, 2011Ray Chandler
2552610928111281w(253·1026107-1)/9June 10, 2011Ray Chandler
25726098444694w69(4·1026098+221)/9June 10, 2011Ray Chandler
2582603745777457w(412·1026035-7)/9June 10, 2011Ray Chandler
2592602359553595w3(536·1026021-23)/9June 10, 2011Ray Chandler
Unprovable near-repdigit-related PRPs (except ru/nr/pd/qr)
 digitsflabelwlabelexpressionwhenwho
178269769554795w47(86·1026975-77)/9June 10, 2011Ray Chandler
179269748773187w31(79·1026973-421)/9June 10, 2011Ray Chandler
180269723445734w57(31·1026971+113)/9June 10, 2011Ray Chandler
181269723223732w37(29·1026971+133)/9June 10, 2011Ray Chandler
182269702448724w87(22·1026969+383)/9June 10, 2011Ray Chandler
184269421881718w17(17·1026941-647)/9June 10, 2011Ray Chandler
185269373776137w61(34·1026936-151)/9June 10, 2011Ray Chandler
187269208229782w97(74·1026919+673)/9June 10, 2011Ray Chandler
188269086554165w41(59·1026907-131)/9June 10, 2011Ray Chandler
189269068119781w97(73·1026905+773)/9June 10, 2011Ray Chandler
190269046883768w37(62·1026903-467)/9June 10, 2011Ray Chandler
191268883554935w49(32·1026887-59)/9June 10, 2011Ray Chandler
192268786116961w69(55·1026877+521)/9June 10, 2011Ray Chandler
19626839 772w9(695·1026837+61)/9June 10, 2011Ray Chandler
197268118448384w83(76·1026810+347)/9June 10, 2011Ray Chandler
198267929223992w39(83·1026791+151)/9June 10, 2011Ray Chandler
199267823448134w81(31·1026781+329)/9June 10, 2011Ray Chandler
200267804775347w53(43·1026779-223)/9June 10, 2011Ray Chandler
203267557442174w21(67·1026754-211)/9June 10, 2011Ray Chandler
20426746 997w3(898·1026744-43)/9June 10, 2011Ray Chandler
206267449221992w19(83·1026743-29)/9June 10, 2011Ray Chandler
20726743 332w3(299·1026741+7)/9June 10, 2011Ray Chandler
20826734 558w1(503·1026732-71)/9June 10, 2011Ray Chandler
209267296557365w73(59·1026728+157)/9June 10, 2011Ray Chandler
21026729 554w1(499·1026727-31)/9June 10, 2011Ray Chandler
212267249772997w29(88·1026723-439)/9June 10, 2011Ray Chandler
213267153116731w67(28·1026714+503)/9June 10, 2011Ray Chandler
214266969226192w61(83·1026695+349)/9June 10, 2011Ray Chandler
216266716776367w63(61·1026670-133)/9June 10, 2011Ray Chandler
219266508113781w37(73·1026649+233)/9June 10, 2011Ray Chandler
220266445886758w67(53·1026643-197)/9June 10, 2011Ray Chandler
222266261554115w41(14·1026625-131)/9June 10, 2011Ray Chandler
225266069886198w61(89·1026605-251)/9June 10, 2011Ray Chandler
226265977449774w97(67·1026596+473)/9June 10, 2011Ray Chandler
227265941228112w81(11·1026593+529)/9June 10, 2011Ray Chandler
230265447446774w67(67·1026543+203)/9June 10, 2011Ray Chandler
231265225441954w19(49·1026521-229)/9June 10, 2011Ray Chandler
234264425885158w51(53·1026441-341)/9June 10, 2011Ray Chandler
23726410 221w3(199·1026408+17)/9June 10, 2011Ray Chandler
24026387 92w33(83·1026386+97)/9June 10, 2011Ray Chandler
242263784880948w09(44·1026377-719)/9June 10, 2011Ray Chandler
245263607550375w03(68·1026359-473)/9June 10, 2011Ray Chandler
246263516552165w21(59·1026350-311)/9June 10, 2011Ray Chandler
247263363776937w69(34·1026335-79)/9June 10, 2011Ray Chandler
249263244889348w93(44·1026323+37)/9June 10, 2011Ray Chandler
250263074556145w61(41·1026306+49)/9June 10, 2011Ray Chandler
25226288 998w3(899·1026286-53)/9June 10, 2011Ray Chandler
253262827882778w27(71·1026281-557)/9June 10, 2011Ray Chandler
25826238 35w77(32·1026237+193)/9June 10, 2011Ray Chandler
259262316445964w59(58·1026230+131)/9June 10, 2011Ray Chandler
260262248551385w13(77·1026223-383)/9June 10, 2011Ray Chandler
26326191 774w7(697·1026189+23)/9June 10, 2011Ray Chandler
264261855880358w03(53·1026184-773)/9June 10, 2011Ray Chandler
265261785881758w17(53·1026177-647)/9June 10, 2011Ray Chandler
266261769885398w53(89·1026175-323)/9June 10, 2011Ray Chandler
267261749110391w03(82·1026173-73)/9June 10, 2011Ray Chandler
268261635226352w63(47·1026162+367)/9June 10, 2011Ray Chandler
26926135 992w1(893·1026133-11)/9June 10, 2011Ray Chandler
274261129554395w43(86·1026111-113)/9June 10, 2011Ray Chandler
275261043227132w71(29·1026103+439)/9June 10, 2011Ray Chandler
276261043116731w67(28·1026103+503)/9June 10, 2011Ray Chandler
277260947116971w69(64·1026093+521)/9June 10, 2011Ray Chandler
28026036 92w33(83·1026035+97)/9June 10, 2011Ray Chandler
281260269774397w43(88·1026025-313)/9June 10, 2011Ray Chandler
28226013 334w7(301·1026011+23)/9June 10, 2011Ray Chandler

June 5, 2011

Stefano D'Urso found a near-repdigit prime.

Proven near-repdigit primes
 digitsflabelwlabelexpressionwhenwho
15234013 99999929w9999993·10234006-1June 5, 2011Stefano D'Urso

June 3, 2011

Ray Chandler proved 8 near-repdigit primes, 40 quasi-repdigit primes and 131 near-repdigit-related primes in the range 1845,1900≤n≤1999. Certifications are available.

Proven near-repdigit primes
 digitsflabelwlabelexpressionwhenwho
536199978777787w(709·101997-7)/9June 3, 2011Ray Chandler
5411947 9w899101947-101June 3, 2011Ray Chandler
5431946333433w43(101946+29)/3June 3, 2011Ray Chandler
5441934111611w61(101934+449)/9June 3, 2011Ray Chandler
5451932999599w59101932-41June 3, 2011Ray Chandler
5491919111611w61(101919+449)/9June 3, 2011Ray Chandler
5541909777277w27(7·101909-457)/9June 3, 2011Ray Chandler
5551908333233w23(101908-31)/3June 3, 2011Ray Chandler
Proven quasi-repdigit primes (except pd)
 digitsflabelwlabelexpressionwhenwho
4231999888218w21(8·101999-611)/9June 3, 2011Ray Chandler
42419996332363w23(19·101998-31)/3June 3, 2011Ray Chandler
426199620227202w7(182·101994+43)/9June 3, 2011Ray Chandler
4271995 2w11(2·101995-101)/9June 3, 2011Ray Chandler
428199367667676w7(203·101991+1)/3June 3, 2011Ray Chandler
4291992111871w87(101992+683)/9June 3, 2011Ray Chandler
4301991 557w(502·101989-7)/9June 3, 2011Ray Chandler
4311989333173w17(101989-49)/3June 3, 2011Ray Chandler
43219865775757w57(52·101985-187)/9June 3, 2011Ray Chandler
4331985222592w59(2·101985+331)/9June 3, 2011Ray Chandler
43419816112161w21(55·101980+89)/9June 3, 2011Ray Chandler
437197640777407w(367·101974-7)/9June 3, 2011Ray Chandler
440197016777167w(151·101968-7)/9June 3, 2011Ray Chandler
441196641333413w(124·101964-1)/3June 3, 2011Ray Chandler
443196581881818w1(737·101963-71)/9June 3, 2011Ray Chandler
4441965666436w43(2·101965-71)/3June 3, 2011Ray Chandler
445196543111431w(388·101963-1)/9June 3, 2011Ray Chandler
446196210119101w9(91·101960+71)/9June 3, 2011Ray Chandler
449195057557575w7(518·101948+13)/9June 3, 2011Ray Chandler
450195043777437w(394·101948-7)/9June 3, 2011Ray Chandler
451194615119151w9(136·101944+71)/9June 3, 2011Ray Chandler
452194458553585w3(527·101942-23)/9June 3, 2011Ray Chandler
4541939777097w09(7·101939-619)/9June 3, 2011Ray Chandler
4581935999079w07101935-93June 3, 2011Ray Chandler
4591935555635w63(5·101935+67)/9June 3, 2011Ray Chandler
460193489777897w(808·101932-7)/9June 3, 2011Ray Chandler
462193180111801w(721·101929-1)/9June 3, 2011Ray Chandler
4631931555475w47(5·101931-77)/9June 3, 2011Ray Chandler
464193130337303w7(91·101929+11)/3June 3, 2011Ray Chandler
465192629333293w(88·101924-1)/3June 3, 2011Ray Chandler
46619246110161w01(55·101923-91)/9June 3, 2011Ray Chandler
46719239773797w37(88·101922-367)/9June 3, 2011Ray Chandler
4681921888518w51(8·101921-341)/9June 3, 2011Ray Chandler
470191873773737w3(664·101916-43)/9June 3, 2011Ray Chandler
47219166772767w27(61·101915-457)/9June 3, 2011Ray Chandler
477190510117101w7(91·101903+53)/9June 3, 2011Ray Chandler
47819043778737w87(34·101903+83)/9June 3, 2011Ray Chandler
4791903111631w63(101903+467)/9June 3, 2011Ray Chandler
482190117119171w9(154·101899+71)/9June 3, 2011Ray Chandler
5341845 223w(67·101843-1)/3June 3, 2011Ray Chandler
Proven near-repdigit-related primes (except ru/nr/pd/qr)
 digitsflabelwlabelexpressionwhenwho
84319994778947w89(43·101998+101)/9June 3, 2011Ray Chandler
84419992114321w43(19·101998+287)/9June 3, 2011Ray Chandler
84519977661976w19(23·101996-143)/3June 3, 2011Ray Chandler
8461997 18w77(17·101996-107)/9June 3, 2011Ray Chandler
84719969664196w41(29·101995-77)/3June 3, 2011Ray Chandler
84819963662336w23(11·101995-131)/3June 3, 2011Ray Chandler
84919962117321w73(19·101995+557)/9June 3, 2011Ray Chandler
85019957882778w27(71·101994-557)/9June 3, 2011Ray Chandler
85119956771367w13(61·101994-583)/9June 3, 2011Ray Chandler
8531993 96w11(29·101992-167)/3June 3, 2011Ray Chandler
85419935880158w01(53·101992-791)/9June 3, 2011Ray Chandler
85619916116961w69(55·101990+521)/9June 3, 2011Ray Chandler
85719909776197w61(88·101989-151)/9June 3, 2011Ray Chandler
85819903551735w17(32·101989-347)/9June 3, 2011Ray Chandler
85919889445794w57(85·101987+113)/9June 3, 2011Ray Chandler
86019884334943w49(13·101987+47)/3June 3, 2011Ray Chandler
8611987 885w1(797·101985-41)/9June 3, 2011Ray Chandler
8621987 882w7(794·101985+43)/9June 3, 2011Ray Chandler
86419865228352w83(47·101985+547)/9June 3, 2011Ray Chandler
86519861226312w63(11·101985+367)/9June 3, 2011Ray Chandler
8661985 991w9(892·101983+71)/9June 3, 2011Ray Chandler
86719853446934w69(31·101984+221)/9June 3, 2011Ray Chandler
8681985 114w9(103·101983+41)/9June 3, 2011Ray Chandler
8701983 93w77(28·101982+131)/3June 3, 2011Ray Chandler
87119829440394w03(85·101981-373)/9June 3, 2011Ray Chandler
87219825110351w03(46·101981-73)/9June 3, 2011Ray Chandler
87319793889338w93(35·101978+37)/9June 3, 2011Ray Chandler
87519791552715w27(14·101978-257)/9June 3, 2011Ray Chandler
87619778550985w09(77·101976-419)/9June 3, 2011Ray Chandler
8771977 72w99(65·101976+691)/9June 3, 2011Ray Chandler
8781977 47w99(43·101976+191)/9June 3, 2011Ray Chandler
87919773447334w73(31·101976+257)/9June 3, 2011Ray Chandler
88019767556975w69(68·101975+121)/9June 3, 2011Ray Chandler
88119765446954w69(49·101975+221)/9June 3, 2011Ray Chandler
88219764334943w49(13·101975+47)/3June 3, 2011Ray Chandler
88419747883978w39(71·101973-449)/9June 3, 2011Ray Chandler
88519725008750w875·101971+87June 3, 2011Ray Chandler
88619717338773w87(22·101970+161)/3June 3, 2011Ray Chandler
88719715118751w87(46·101970+683)/9June 3, 2011Ray Chandler
88819714224942w49(38·101970+241)/9June 3, 2011Ray Chandler
89019704117341w73(37·101969+557)/9June 3, 2011Ray Chandler
8911969 65w33(59·101968-203)/9June 3, 2011Ray Chandler
89219692771327w13(25·101968-583)/9June 3, 2011Ray Chandler
8931968 886w3(266·101966-11)/3June 3, 2011Ray Chandler
89419686778367w83(61·101967+47)/9June 3, 2011Ray Chandler
89519677449774w97(67·101966+473)/9June 3, 2011Ray Chandler
89719672332923w29(7·101966-13)/3June 3, 2011Ray Chandler
89819668441384w13(76·101965-283)/9June 3, 2011Ray Chandler
89919665882758w27(53·101965-557)/9June 3, 2011Ray Chandler
9011965 994w7(895·101963+23)/9June 3, 2011Ray Chandler
90219651223112w31(11·101964+79)/9June 3, 2011Ray Chandler
90319646118961w89(55·101963+701)/9June 3, 2011Ray Chandler
90419639664196w41(29·101962-77)/3June 3, 2011Ray Chandler
90519639449794w97(85·101962+473)/9June 3, 2011Ray Chandler
90619639441994w19(85·101962-229)/9June 3, 2011Ray Chandler
90719629330193w01(28·101961-97)/3June 3, 2011Ray Chandler
90819618446784w67(76·101960+203)/9June 3, 2011Ray Chandler
90919617225372w53(65·101960+277)/9June 3, 2011Ray Chandler
91019614229342w93(38·101960+637)/9June 3, 2011Ray Chandler
91119589889398w93(89·101957+37)/9June 3, 2011Ray Chandler
91219571229712w97(11·101956+673)/9June 3, 2011Ray Chandler
91319567445174w51(67·101955+59)/9June 3, 2011Ray Chandler
91419567116771w67(64·101955+503)/9June 3, 2011Ray Chandler
91619546224762w47(56·101953+223)/9June 3, 2011Ray Chandler
91719528115781w57(73·101951+413)/9June 3, 2011Ray Chandler
91919524115341w53(37·101951+377)/9June 3, 2011Ray Chandler
9211951 664w1(598·101949-31)/9June 3, 2011Ray Chandler
92219514330943w09(13·101950-73)/3June 3, 2011Ray Chandler
92319499115391w53(82·101948+377)/9June 3, 2011Ray Chandler
92419489551795w17(86·101947-347)/9June 3, 2011Ray Chandler
92519488114981w49(73·101947+341)/9June 3, 2011Ray Chandler
92719483554735w47(32·101947-77)/9June 3, 2011Ray Chandler
92919458225782w57(74·101944+313)/9June 3, 2011Ray Chandler
9301945 46w33(14·101944-101)/3June 3, 2011Ray Chandler
93119453770337w03(34·101944-673)/9June 3, 2011Ray Chandler
93219447447374w73(67·101943+257)/9June 3, 2011Ray Chandler
93319446223162w31(56·101943+79)/9June 3, 2011Ray Chandler
93419438553185w31(77·101942-221)/9June 3, 2011Ray Chandler
93619427558375w83(68·101941+247)/9June 3, 2011Ray Chandler
9371941 42w33(38·101940+97)/9June 3, 2011Ray Chandler
9381941 24w77(22·101940+293)/9June 3, 2011Ray Chandler
93919411226312w63(11·101940+367)/9June 3, 2011Ray Chandler
9401940 447w3(403·101938-43)/9June 3, 2011Ray Chandler
94119387995179w518·101937-49June 3, 2011Ray Chandler
94219387553975w39(68·101937-149)/9June 3, 2011Ray Chandler
9431938 51w77(46·101937+593)/9June 3, 2011Ray Chandler
94519382334723w47(7·101937+41)/3June 3, 2011Ray Chandler
94619365114951w49(46·101935+341)/9June 3, 2011Ray Chandler
94719361774117w41(16·101935-331)/9June 3, 2011Ray Chandler
9481935 442w9(398·101933+61)/9June 3, 2011Ray Chandler
94919327114971w49(64·101931+341)/9June 3, 2011Ray Chandler
95019325228752w87(47·101931+583)/9June 3, 2011Ray Chandler
95119317660376w03(23·101930-191)/3June 3, 2011Ray Chandler
9521931 663w7(199·101929+11)/3June 3, 2011Ray Chandler
95419305882758w27(53·101929-557)/9June 3, 2011Ray Chandler
95519299229192w91(83·101928+619)/9June 3, 2011Ray Chandler
9561929 882w7(794·101927+43)/9June 3, 2011Ray Chandler
95719297446974w69(67·101928+221)/9June 3, 2011Ray Chandler
95819296449764w97(58·101928+473)/9June 3, 2011Ray Chandler
95919282440324w03(22·101927-373)/9June 3, 2011Ray Chandler
96019248226382w63(74·101923+367)/9June 3, 2011Ray Chandler
96419229880998w09(89·101921-719)/9June 3, 2011Ray Chandler
96519211330713w07(4·101920-79)/3June 3, 2011Ray Chandler
96619209558395w83(86·101919+247)/9June 3, 2011Ray Chandler
9671918 48w11(44·101917-701)/9June 3, 2011Ray Chandler
96819179665396w53(29·101916-41)/3June 3, 2011Ray Chandler
96919178119381w93(73·101916+737)/9June 3, 2011Ray Chandler
97019156884168w41(62·101914-431)/9June 3, 2011Ray Chandler
97119153119731w97(28·101914+773)/9June 3, 2011Ray Chandler
97219138221782w17(74·101912-47)/9June 3, 2011Ray Chandler
9751912 775w9(698·101910+31)/9June 3, 2011Ray Chandler
9771911 85w77(77·101910+193)/9June 3, 2011Ray Chandler
97819116884368w43(62·101910-413)/9June 3, 2011Ray Chandler
9811910 83w99(25·101909+197)/3June 3, 2011Ray Chandler
98219105778157w81(52·101909+29)/9June 3, 2011Ray Chandler
98419086881368w13(62·101907-683)/9June 3, 2011Ray Chandler
9851908 447w3(403·101906-43)/9June 3, 2011Ray Chandler
98619083119731w97(28·101907+773)/9June 3, 2011Ray Chandler
98719071669316w93(5·101906+79)/3June 3, 2011Ray Chandler
9881906 62w99(56·101905+691)/9June 3, 2011Ray Chandler
98919065220952w09(47·101905-119)/9June 3, 2011Ray Chandler
99019054669346w93(14·101904+79)/3June 3, 2011Ray Chandler
9911904 38w33(35·101903-503)/9June 3, 2011Ray Chandler
99219034660946w09(14·101902-173)/3June 3, 2011Ray Chandler
99319029224992w49(83·101901+241)/9June 3, 2011Ray Chandler
9941902 68w11(62·101901-701)/9June 3, 2011Ray Chandler
9951902 57w11(52·101901-601)/9June 3, 2011Ray Chandler
99619025228352w83(47·101901+547)/9June 3, 2011Ray Chandler
99719024336143w61(13·101901+83)/3June 3, 2011Ray Chandler
99819013442134w21(31·101900-211)/9June 3, 2011Ray Chandler
99919002559325w93(23·101899+337)/9June 3, 2011Ray Chandler

Stefano D'Urso found a near-repdigit prime.

Proven near-repdigit primes
 digitsflabelwlabelexpressionwhenwho
13249876 99999979w9999998·10249869-1June 3, 2011Stefano D'Urso

May 2011

May 31, 2011

Ray Chandler found 2 near-repdigit PRPs, 19 quasi-repdigit PRPs and 86 near-repdigit-related PRPs in the range 25001≤n≤26000.

Unprovable near-repdigit PRPs
 digitsflabelwlabelexpressionwhenwho
942539672777727w(655·1025394-7)/9May 31, 2011Ray Chandler
952535615111151w(136·1025354-1)/9May 31, 2011Ray Chandler
Unprovable quasi-repdigit PRPs (except pd)
 digitsflabelwlabelexpressionwhenwho
23525933888218w21(8·1025933-611)/9May 31, 2011Ray Chandler
2382583520777207w(187·1025833-7)/9May 31, 2011Ray Chandler
23925827 991w(892·1025825-1)/9May 31, 2011Ray Chandler
2402581956557565w7(509·1025817+13)/9May 31, 2011Ray Chandler
2422577525111251w(226·1025773-1)/9May 31, 2011Ray Chandler
243257426772767w27(61·1025741-457)/9May 31, 2011Ray Chandler
24625658111791w79(1025658+611)/9May 31, 2011Ray Chandler
249256216778767w87(61·1025620+83)/9May 31, 2011Ray Chandler
2502561185777857w(772·1025609-7)/9May 31, 2011Ray Chandler
25325549222512w51(2·1025549+259)/9May 31, 2011Ray Chandler
25525526888298w29(8·1025526-539)/9May 31, 2011Ray Chandler
257254935778757w87(52·1025492+83)/9May 31, 2011Ray Chandler
2582546764777647w(583·1025465-7)/9May 31, 2011Ray Chandler
2592538348777487w(439·1025381-7)/9May 31, 2011Ray Chandler
2632526364777647w(583·1025261-7)/9May 31, 2011Ray Chandler
26425262222892w89(2·1025262+601)/9May 31, 2011Ray Chandler
267252427118171w81(64·1025241+629)/9May 31, 2011Ray Chandler
2702517981881818w1(737·1025177-71)/9May 31, 2011Ray Chandler
27325078555635w63(5·1025078+67)/9May 31, 2011Ray Chandler
Unprovable near-repdigit-related PRPs (except ru/nr/pd/qr)
 digitsflabelwlabelexpressionwhenwho
22025981 772w3(695·1025979+7)/9May 31, 2011Ray Chandler
223259742770327w03(25·1025973-673)/9May 31, 2011Ray Chandler
22525959 551w7(496·1025957+53)/9May 31, 2011Ray Chandler
226259537110971w09(64·1025952-19)/9May 31, 2011Ray Chandler
227259361887318w73(17·1025935-143)/9May 31, 2011Ray Chandler
228259276224762w47(56·1025926+223)/9May 31, 2011Ray Chandler
229259219779397w93(88·1025920+137)/9May 31, 2011Ray Chandler
230259176889768w97(62·1025916+73)/9May 31, 2011Ray Chandler
23225889 28w77(26·1025888-107)/9May 31, 2011Ray Chandler
23425871 551w7(496·1025869+53)/9May 31, 2011Ray Chandler
235258707112971w29(64·1025869+161)/9May 31, 2011Ray Chandler
236258602882928w29(26·1025859-539)/9May 31, 2011Ray Chandler
23725858 334w3(301·1025856-13)/9May 31, 2011Ray Chandler
238258514773947w39(43·1025850-349)/9May 31, 2011Ray Chandler
239258503445734w57(31·1025849+113)/9May 31, 2011Ray Chandler
241258343447334w73(31·1025833+257)/9May 31, 2011Ray Chandler
242258262449124w91(22·1025825+419)/9May 31, 2011Ray Chandler
244258203559135w91(32·1025819+319)/9May 31, 2011Ray Chandler
245258097559775w97(68·1025808+373)/9May 31, 2011Ray Chandler
246258077445774w57(67·1025806+113)/9May 31, 2011Ray Chandler
247258051449114w91(13·1025804+419)/9May 31, 2011Ray Chandler
248257776550365w03(59·1025776-473)/9May 31, 2011Ray Chandler
249257747559175w91(68·1025773+319)/9May 31, 2011Ray Chandler
251257625449754w97(49·1025761+473)/9May 31, 2011Ray Chandler
25325751 78w11(71·1025750-701)/9May 31, 2011Ray Chandler
254257515225352w53(47·1025750+277)/9May 31, 2011Ray Chandler
256257345110351w03(46·1025733-73)/9May 31, 2011Ray Chandler
25825731 82w11(74·1025730-101)/9May 31, 2011Ray Chandler
259257312778127w81(25·1025730+29)/9May 31, 2011Ray Chandler
263257038441984w19(76·1025702-229)/9May 31, 2011Ray Chandler
26825674 887w9(799·1025672+11)/9May 31, 2011Ray Chandler
27025669 32w11(29·1025668-101)/9May 31, 2011Ray Chandler
272256191886918w69(17·1025618-179)/9May 31, 2011Ray Chandler
274255852552125w21(23·1025584-311)/9May 31, 2011Ray Chandler
276255697221372w13(65·1025568-83)/9May 31, 2011Ray Chandler
277255674226142w61(38·1025566+349)/9May 31, 2011Ray Chandler
278255641887118w71(17·1025563-161)/9May 31, 2011Ray Chandler
279255618229782w97(74·1025560+673)/9May 31, 2011Ray Chandler
280255471884718w47(17·1025546-377)/9May 31, 2011Ray Chandler
281255376226362w63(56·1025536+367)/9May 31, 2011Ray Chandler
282255341447114w71(13·1025533+239)/9May 31, 2011Ray Chandler
285255014556145w61(41·1025500+49)/9May 31, 2011Ray Chandler
28825449 334w7(301·1025447+23)/9May 31, 2011Ray Chandler
289254464557345w73(41·1025445+157)/9May 31, 2011Ray Chandler
291254324778347w83(43·1025431+47)/9May 31, 2011Ray Chandler
292254288220382w03(74·1025427-173)/9May 31, 2011Ray Chandler
296254038447984w79(76·1025402+311)/9May 31, 2011Ray Chandler
29725402 38w33(35·1025401-503)/9May 31, 2011Ray Chandler
298254017226172w61(65·1025400+349)/9May 31, 2011Ray Chandler
29925400 54w33(49·1025399-103)/9May 31, 2011Ray Chandler
300253967445374w53(67·1025395+77)/9May 31, 2011Ray Chandler
301253947445374w53(67·1025393+77)/9May 31, 2011Ray Chandler
302253945114351w43(46·1025393+287)/9May 31, 2011Ray Chandler
304253801558715w87(14·1025379+283)/9May 31, 2011Ray Chandler
30525374 35w77(32·1025373+193)/9May 31, 2011Ray Chandler
306253709556395w63(86·1025369+67)/9May 31, 2011Ray Chandler
308253578551385w13(77·1025356-383)/9May 31, 2011Ray Chandler
309253547445174w51(67·1025353+59)/9May 31, 2011Ray Chandler
310253454221742w17(38·1025344-47)/9May 31, 2011Ray Chandler
312253102880728w07(26·1025309-737)/9May 31, 2011Ray Chandler
313253094558345w83(41·1025308+247)/9May 31, 2011Ray Chandler
31525295 998w9(899·1025293+1)/9May 31, 2011Ray Chandler
31625288 92w11(83·1025287-101)/9May 31, 2011Ray Chandler
318252785445754w57(49·1025277+113)/9May 31, 2011Ray Chandler
319252663559135w91(32·1025265+319)/9May 31, 2011Ray Chandler
321252529110391w03(82·1025251-73)/9May 31, 2011Ray Chandler
323252391440914w09(13·1025238-319)/9May 31, 2011Ray Chandler
32525223 115w1(104·1025221-41)/9May 31, 2011Ray Chandler
33425163 335w7(302·1025161+13)/9May 31, 2011Ray Chandler
335251514885948w59(44·1025150-269)/9May 31, 2011Ray Chandler
336251437117371w73(64·1025142+557)/9May 31, 2011Ray Chandler
337251405440354w03(49·1025139-373)/9May 31, 2011Ray Chandler
338251261447114w71(13·1025125+239)/9May 31, 2011Ray Chandler
340251155883758w37(53·1025114-467)/9May 31, 2011Ray Chandler
342251048557185w71(77·1025103+139)/9May 31, 2011Ray Chandler
343250994779347w93(43·1025098+137)/9May 31, 2011Ray Chandler
344250992118921w89(19·1025098+701)/9May 31, 2011Ray Chandler
345250983554335w43(32·1025097-113)/9May 31, 2011Ray Chandler
346250879224792w47(83·1025086+223)/9May 31, 2011Ray Chandler
347250821774117w41(16·1025081-331)/9May 31, 2011Ray Chandler
348250797447174w71(67·1025078+239)/9May 31, 2011Ray Chandler
349250784226742w67(38·1025077+403)/9May 31, 2011Ray Chandler
351250714229342w93(38·1025070+637)/9May 31, 2011Ray Chandler
352250619223192w31(83·1025060+79)/9May 31, 2011Ray Chandler
353250445440954w09(49·1025043-319)/9May 31, 2011Ray Chandler
357250136880768w07(62·1025012-737)/9May 31, 2011Ray Chandler

May 29, 2011

Bob Price found 3 near-repdigit PRPs and 13 quasi-repdigit PRPs of the form 10n+k (|k|<100).

Unprovable near-repdigit PRPs
 digitsflabelwlabelexpressionwhenwho
1867863999899w891067863-11May 29, 2011Bob Price
2158437999899w891058437-11May 29, 2011Bob Price
3350929999499w491050929-51May 29, 2011Bob Price
Unprovable quasi-repdigit PRPs (except pd)
 digitsflabelwlabelexpressionwhenwho
2386816999019w011086816-99May 29, 2011Bob Price
2486110999319w311086110-69May 29, 2011Bob Price
2684305999439w431084305-57May 29, 2011Bob Price
2981297999439w431081297-57May 29, 2011Bob Price
3176875999479w471076875-53May 29, 2011Bob Price
3274335999479w471074335-53May 29, 2011Bob Price
3372730999019w011072730-99May 29, 2011Bob Price
4068297999079w071068297-93May 29, 2011Bob Price
4366793999379w371066793-63May 29, 2011Bob Price
4764436999479w471064436-53May 29, 2011Bob Price
5858225999079w071058225-93May 29, 2011Bob Price
6652041999079w071052041-93May 29, 2011Bob Price
7645130999319w311045130-69May 29, 2011Bob Price

May 26, 2011

Ray Chandler proved 5 near-repdigit primes, 58 quasi-repdigit primes and 127 near-repdigit-related primes in the range 1799≤n≤1898. Certifications are available.

Proven near-repdigit primes
 digitsflabelwlabelexpressionwhenwho
553186871777717w(646·101866-7)/9May 26, 2011Ray Chandler
555186434333343w(103·101862-1)/3May 26, 2011Ray Chandler
556185437333373w(112·101852-1)/3May 26, 2011Ray Chandler
559183915111151w(136·101837-1)/9May 26, 2011Ray Chandler
567180137333373w(112·101799-1)/3May 26, 2011Ray Chandler
Proven quasi-repdigit primes (except pd)
 digitsflabelwlabelexpressionwhenwho
44518992336323w63(7·101898+89)/3May 26, 2011Ray Chandler
4461897888138w13(8·101897-683)/9May 26, 2011Ray Chandler
44718954113141w31(37·101894+179)/9May 26, 2011Ray Chandler
448189513777137w(124·101893-7)/9May 26, 2011Ray Chandler
4491894888378w37(8·101894-467)/9May 26, 2011Ray Chandler
450189486111861w(775·101892-1)/9May 26, 2011Ray Chandler
452189374333743w(223·101891-1)/3May 26, 2011Ray Chandler
454188850111501w(451·101886-1)/9May 26, 2011Ray Chandler
457188694777947w(853·101884-7)/9May 26, 2011Ray Chandler
459188473111731w(658·101882-1)/9May 26, 2011Ray Chandler
460188452557525w7(473·101882+13)/9May 26, 2011Ray Chandler
46118834771747w17(43·101882-547)/9May 26, 2011Ray Chandler
462188150333503w(151·101879-1)/3May 26, 2011Ray Chandler
4631878888578w57(8·101878-287)/9May 26, 2011Ray Chandler
464187783777837w(754·101875-7)/9May 26, 2011Ray Chandler
46818764339343w93(13·101875+179)/3May 26, 2011Ray Chandler
4711874444614w61(4·101874+149)/9May 26, 2011Ray Chandler
474187131337313w7(94·101869+11)/3May 26, 2011Ray Chandler
47518676337363w73(19·101866+119)/3May 26, 2011Ray Chandler
4771867222812w81(2·101867+529)/9May 26, 2011Ray Chandler
4781866333413w41(101866+23)/3May 26, 2011Ray Chandler
47918651770717w07(16·101864-637)/9May 26, 2011Ray Chandler
48018639779797w97(88·101862+173)/9May 26, 2011Ray Chandler
481186263661636w1(191·101860-17)/3May 26, 2011Ray Chandler
48218615774757w47(52·101860-277)/9May 26, 2011Ray Chandler
4841861333073w07(101861-79)/3May 26, 2011Ray Chandler
485185854559545w9(491·101856+31)/9May 26, 2011Ray Chandler
4871856999239w23101856-77May 26, 2011Ray Chandler
48818561330313w03(4·101855-91)/3May 26, 2011Ray Chandler
490185298333983w(295·101850-1)/3May 26, 2011Ray Chandler
49118529770797w07(88·101851-637)/9May 26, 2011Ray Chandler
493185146777467w(421·101849-7)/9May 26, 2011Ray Chandler
49418499118191w81(82·101848+629)/9May 26, 2011Ray Chandler
4961841888438w43(8·101841-413)/9May 26, 2011Ray Chandler
497184165333653w(196·101839-1)/3May 26, 2011Ray Chandler
4981841444614w61(4·101841+149)/9May 26, 2011Ray Chandler
4991840222872w87(2·101840+583)/9May 26, 2011Ray Chandler
50018398114181w41(73·101838+269)/9May 26, 2011Ray Chandler
501183820111201w(181·101836-1)/9May 26, 2011Ray Chandler
5021837333473w47(101837+41)/3May 26, 2011Ray Chandler
504183147111471w(424·101829-1)/9May 26, 2011Ray Chandler
5051828333713w71(101828+113)/3May 26, 2011Ray Chandler
5061827555695w69(5·101827+121)/9May 26, 2011Ray Chandler
5071827111631w63(101827+467)/9May 26, 2011Ray Chandler
508182614117141w7(127·101824+53)/9May 26, 2011Ray Chandler
50918232338323w83(7·101822+149)/3May 26, 2011Ray Chandler
510182258557585w7(527·101820+13)/9May 26, 2011Ray Chandler
5111820777837w83(7·101820+47)/9May 26, 2011Ray Chandler
51618172773727w37(25·101816-367)/9May 26, 2011Ray Chandler
517181431331313w1(94·101812-7)/3May 26, 2011Ray Chandler
521181125229252w9(227·101809+61)/9May 26, 2011Ray Chandler
522181096777967w(871·101808-7)/9May 26, 2011Ray Chandler
523181048111481w(433·101808-1)/9May 26, 2011Ray Chandler
524180890991909w191·101806-9May 26, 2011Ray Chandler
52618061778717w87(16·101805+83)/9May 26, 2011Ray Chandler
52718058113181w31(73·101804+179)/9May 26, 2011Ray Chandler
528180317113171w3(154·101801+17)/9May 26, 2011Ray Chandler
5301800999139w13101800-87May 26, 2011Ray Chandler
Proven near-repdigit-related primes (except ru/nr/pd/qr)
 digitsflabelwlabelexpressionwhenwho
86918979551795w17(86·101896-347)/9May 26, 2011Ray Chandler
8721894 445w1(401·101892-41)/9May 26, 2011Ray Chandler
87318927559375w93(68·101891+337)/9May 26, 2011Ray Chandler
87418918554385w43(77·101890-113)/9May 26, 2011Ray Chandler
87518896448764w87(58·101888+383)/9May 26, 2011Ray Chandler
87718879119791w97(82·101886+773)/9May 26, 2011Ray Chandler
87818879118991w89(82·101886+701)/9May 26, 2011Ray Chandler
87918873664736w47(11·101886-59)/3May 26, 2011Ray Chandler
88018872884128w41(26·101886-431)/9May 26, 2011Ray Chandler
8811887 224w3(202·101885-13)/9May 26, 2011Ray Chandler
88218869330193w01(28·101885-97)/3May 26, 2011Ray Chandler
88418854332743w27(13·101884-19)/3May 26, 2011Ray Chandler
8851885 16w99(5·101884+97)/3May 26, 2011Ray Chandler
88718842550925w09(23·101883-419)/9May 26, 2011Ray Chandler
88818841338113w81(4·101883+143)/3May 26, 2011Ray Chandler
8891883 557w1(502·101881-61)/9May 26, 2011Ray Chandler
89018824220142w01(38·101881-191)/9May 26, 2011Ray Chandler
89118823557135w71(32·101881+139)/9May 26, 2011Ray Chandler
89218822883728w37(26·101881-467)/9May 26, 2011Ray Chandler
8941881 778w9(701·101879+1)/9May 26, 2011Ray Chandler
89518817330973w09(22·101880-73)/3May 26, 2011Ray Chandler
89718813886738w67(35·101880-197)/9May 26, 2011Ray Chandler
8981881 225w3(203·101879-23)/9May 26, 2011Ray Chandler
89918811881318w13(17·101880-683)/9May 26, 2011Ray Chandler
90018809779397w93(88·101879+137)/9May 26, 2011Ray Chandler
90118797665176w51(23·101878-47)/3May 26, 2011Ray Chandler
9031878 25w11(23·101877-401)/9May 26, 2011Ray Chandler
90418781664316w43(5·101877-71)/3May 26, 2011Ray Chandler
90618773554335w43(32·101876-113)/9May 26, 2011Ray Chandler
9071877 23w99(7·101876+197)/3May 26, 2011Ray Chandler
90918769885398w53(89·101875-323)/9May 26, 2011Ray Chandler
91018769664396w43(29·101875-71)/3May 26, 2011Ray Chandler
91118768778387w83(79·101875+47)/9May 26, 2011Ray Chandler
91218765668956w89(17·101875+67)/3May 26, 2011Ray Chandler
91318765117951w79(46·101875+611)/9May 26, 2011Ray Chandler
91418764668746w87(14·101875+61)/3May 26, 2011Ray Chandler
91518762553725w37(23·101875-167)/9May 26, 2011Ray Chandler
91618742770927w09(25·101873-619)/9May 26, 2011Ray Chandler
91718738557985w79(77·101872+211)/9May 26, 2011Ray Chandler
91818721770117w01(16·101871-691)/9May 26, 2011Ray Chandler
91918711771317w13(16·101870-583)/9May 26, 2011Ray Chandler
92018704330943w09(13·101869-73)/3May 26, 2011Ray Chandler
92118703779337w93(34·101869+137)/9May 26, 2011Ray Chandler
92218702774127w41(25·101869-331)/9May 26, 2011Ray Chandler
92318691337913w79(4·101868+137)/3May 26, 2011Ray Chandler
9241868 36w11(11·101867-167)/3May 26, 2011Ray Chandler
92518681669116w91(5·101867+73)/3May 26, 2011Ray Chandler
9261867 998w3(899·101865-53)/9May 26, 2011Ray Chandler
9271866 886w3(266·101864-11)/3May 26, 2011Ray Chandler
92818667551975w19(68·101865-329)/9May 26, 2011Ray Chandler
92918663883138w31(35·101865-521)/9May 26, 2011Ray Chandler
93018655776357w63(52·101864-133)/9May 26, 2011Ray Chandler
9311864 5813w2751(1744·101861-1747)/3May 26, 2011Ray Chandler
93218644556745w67(41·101863+103)/9May 26, 2011Ray Chandler
93318627667976w79(23·101861+37)/3May 26, 2011Ray Chandler
9341861 885w1(797·101859-41)/9May 26, 2011Ray Chandler
9351861 16w33(5·101860-101)/3May 26, 2011Ray Chandler
93618598330983w09(25·101858-73)/3May 26, 2011Ray Chandler
9371857 25w33(23·101856-203)/9May 26, 2011Ray Chandler
9391854 778w9(701·101852+1)/9May 26, 2011Ray Chandler
94118546119761w97(55·101853+773)/9May 26, 2011Ray Chandler
94218545446354w63(49·101853+167)/9May 26, 2011Ray Chandler
94318545445954w59(49·101853+131)/9May 26, 2011Ray Chandler
9441854 338w1(305·101852-71)/9May 26, 2011Ray Chandler
9451852 112w9(101·101850+61)/9May 26, 2011Ray Chandler
94718503118331w83(28·101849+647)/9May 26, 2011Ray Chandler
94818487662176w21(23·101847-137)/3May 26, 2011Ray Chandler
94918474114741w47(37·101846+323)/9May 26, 2011Ray Chandler
95118458228182w81(74·101844+529)/9May 26, 2011Ray Chandler
95218457667976w79(23·101844+37)/3May 26, 2011Ray Chandler
95318457448774w87(67·101844+383)/9May 26, 2011Ray Chandler
95418443229332w93(29·101843+637)/9May 26, 2011Ray Chandler
9551843 885w7(797·101841+13)/9May 26, 2011Ray Chandler
9581843 35w77(32·101842+193)/9May 26, 2011Ray Chandler
9591842 778w9(701·101840+1)/9May 26, 2011Ray Chandler
96118404887148w71(44·101839-161)/9May 26, 2011Ray Chandler
96218401224112w41(11·101839+169)/9May 26, 2011Ray Chandler
96418399559795w97(86·101838+373)/9May 26, 2011Ray Chandler
96518393117931w79(28·101838+611)/9May 26, 2011Ray Chandler
96618374778147w81(43·101836+29)/9May 26, 2011Ray Chandler
96718372118921w89(19·101836+701)/9May 26, 2011Ray Chandler
96818371553115w31(14·101836-221)/9May 26, 2011Ray Chandler
9691836 68w11(62·101835-701)/9May 26, 2011Ray Chandler
97018365669356w93(17·101835+79)/3May 26, 2011Ray Chandler
9711835 886w7(266·101833+1)/3May 26, 2011Ray Chandler
9721835 56w77(17·101834+31)/3May 26, 2011Ray Chandler
97418349118791w87(82·101833+683)/9May 26, 2011Ray Chandler
9761831 336w1(101·101829-17)/3May 26, 2011Ray Chandler
97718307220772w07(65·101829-137)/9May 26, 2011Ray Chandler
9791828 53w99(16·101827+197)/3May 26, 2011Ray Chandler
98018284881948w19(44·101827-629)/9May 26, 2011Ray Chandler
98218278229382w93(74·101826+637)/9May 26, 2011Ray Chandler
9831826 995w1(896·101824-41)/9May 26, 2011Ray Chandler
98518262668326w83(8·101825+49)/3May 26, 2011Ray Chandler
98618247556175w61(68·101823+49)/9May 26, 2011Ray Chandler
98918227448974w89(67·101821+401)/9May 26, 2011Ray Chandler
99018226557165w71(59·101821+139)/9May 26, 2011Ray Chandler
99118187884978w49(71·101817-359)/9May 26, 2011Ray Chandler
99218179112991w29(82·101816+161)/9May 26, 2011Ray Chandler
99318174112341w23(37·101816+107)/9May 26, 2011Ray Chandler
99418168116781w67(73·101815+503)/9May 26, 2011Ray Chandler
9951815 996w1(299·101813-17)/3May 26, 2011Ray Chandler
9961815 76w99(23·101814+97)/3May 26, 2011Ray Chandler
99718157336973w69(22·101814+107)/3May 26, 2011Ray Chandler
99818155336953w69(16·101814+107)/3May 26, 2011Ray Chandler
100018125663956w39(17·101811-83)/3May 26, 2011Ray Chandler
10011812 26w77(8·101811+31)/3May 26, 2011Ray Chandler
100218122336923w69(7·101811+107)/3May 26, 2011Ray Chandler
100318104554945w49(41·101809-59)/9May 26, 2011Ray Chandler
100418104550745w07(41·101809-437)/9May 26, 2011Ray Chandler
10051810 446w3(134·101808-11)/3May 26, 2011Ray Chandler
100718102117921w79(19·101809+611)/9May 26, 2011Ray Chandler
100818101330713w07(4·101809-79)/3May 26, 2011Ray Chandler
10091809 96w77(29·101808+31)/3May 26, 2011Ray Chandler
101018098442184w21(76·101808-211)/9May 26, 2011Ray Chandler
101118096339763w97(19·101808+191)/3May 26, 2011Ray Chandler
101218092442324w23(22·101808-193)/9May 26, 2011Ray Chandler
101318084882148w21(44·101807-611)/9May 26, 2011Ray Chandler
101418084001940w194·101807+19May 26, 2011Ray Chandler
10151808 18w11(17·101807-701)/9May 26, 2011Ray Chandler
101618079886398w63(89·101806-233)/9May 26, 2011Ray Chandler
101918075887358w73(53·101806-143)/9May 26, 2011Ray Chandler
102018073559335w93(32·101806+337)/9May 26, 2011Ray Chandler
102118056335963w59(19·101804+77)/3May 26, 2011Ray Chandler
102318046550965w09(59·101803-419)/9May 26, 2011Ray Chandler
102518019774397w43(88·101800-313)/9May 26, 2011Ray Chandler
102618014554945w49(41·101800-59)/9May 26, 2011Ray Chandler

May 25, 2011

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

Proven near-repdigit primes
 digitsflabelwlabelexpressionwhenwho
16089907999979w8·10608989-1May 25, 2011David Broadhurst

May 24, 2011

Ray Chandler found 2 near-repdigit PRPs, 26 quasi-repdigit PRPs and 84 near-repdigit-related PRPs in the range 24001≤n≤25000.

Unprovable near-repdigit PRPs
 digitsflabelwlabelexpressionwhenwho
1032445615111151w(136·1024454-1)/9May 24, 2011Ray Chandler
1052415775777757w(682·1024155-7)/9May 24, 2011Ray Chandler
Unprovable quasi-repdigit PRPs (except pd)
 digitsflabelwlabelexpressionwhenwho
2502499187883878w3(791·1024989-53)/9May 24, 2011Ray Chandler
251249903113131w31(28·1024989+179)/9May 24, 2011Ray Chandler
2542494054777547w(493·1024938-7)/9May 24, 2011Ray Chandler
2632482453777537w(484·1024822-7)/9May 24, 2011Ray Chandler
26524788444594w59(4·1024788+131)/9May 24, 2011Ray Chandler
2662478615777157w(142·1024784-7)/9May 24, 2011Ray Chandler
267247735776757w67(52·1024772-97)/9May 24, 2011Ray Chandler
2682476543443434w3(391·1024763-13)/9May 24, 2011Ray Chandler
26924754777937w93(7·1024754+137)/9May 24, 2011Ray Chandler
2722473718119181w9(163·1024735+71)/9May 24, 2011Ray Chandler
2742471048443484w3(436·1024708-13)/9May 24, 2011Ray Chandler
2752470815117151w7(136·1024706+53)/9May 24, 2011Ray Chandler
2772468896777967w(871·1024686-7)/9May 24, 2011Ray Chandler
2802465010777107w(97·1024648-7)/9May 24, 2011Ray Chandler
28124637777237w23(7·1024637-493)/9May 24, 2011Ray Chandler
28524533 441w(397·1024531-1)/9May 24, 2011Ray Chandler
2862448630111301w(271·1024484-1)/9May 24, 2011Ray Chandler
28724467222832w83(2·1024467+547)/9May 24, 2011Ray Chandler
2882445286777867w(781·1024450-7)/9May 24, 2011Ray Chandler
2892443519113191w3(172·1024433+17)/9May 24, 2011Ray Chandler
2922438686111861w(775·1024384-1)/9May 24, 2011Ray Chandler
296243049116191w61(82·1024303+449)/9May 24, 2011Ray Chandler
3002420046111461w(415·1024198-1)/9May 24, 2011Ray Chandler
3042413812117121w7(109·1024136+53)/9May 24, 2011Ray Chandler
3062408746111461w(415·1024085-1)/9May 24, 2011Ray Chandler
30924011555415w41(5·1024011-131)/9May 24, 2011Ray Chandler
Unprovable near-repdigit-related PRPs (except ru/nr/pd/qr)
 digitsflabelwlabelexpressionwhenwho
273250018557185w71(77·1025000+139)/9May 24, 2011Ray Chandler
275249732559325w93(23·1024972+337)/9May 24, 2011Ray Chandler
276249643114931w49(28·1024963+341)/9May 24, 2011Ray Chandler
277249633447334w73(31·1024962+257)/9May 24, 2011Ray Chandler
280249542772127w21(25·1024953-511)/9May 24, 2011Ray Chandler
281249516880168w01(62·1024950-791)/9May 24, 2011Ray Chandler
28324941 65w99(59·1024940+391)/9May 24, 2011Ray Chandler
28424939 228w9(206·1024937+1)/9May 24, 2011Ray Chandler
287249285884358w43(53·1024927-413)/9May 24, 2011Ray Chandler
288249202448124w81(22·1024919+329)/9May 24, 2011Ray Chandler
29024917 992w3(893·1024915+7)/9May 24, 2011Ray Chandler
292249042115921w59(19·1024903+431)/9May 24, 2011Ray Chandler
293248975880958w09(53·1024896-719)/9May 24, 2011Ray Chandler
294248951440914w09(13·1024894-319)/9May 24, 2011Ray Chandler
295248752116321w63(19·1024874+467)/9May 24, 2011Ray Chandler
297248631556315w63(14·1024862+67)/9May 24, 2011Ray Chandler
29824854 771w9(694·1024852+71)/9May 24, 2011Ray Chandler
299248479117391w73(82·1024846+557)/9May 24, 2011Ray Chandler
30224822 87w11(79·1024821-601)/9May 24, 2011Ray Chandler
305248076224762w47(56·1024806+223)/9May 24, 2011Ray Chandler
307247968552185w21(77·1024795-311)/9May 24, 2011Ray Chandler
309247933889338w93(35·1024792+37)/9May 24, 2011Ray Chandler
311247748552385w23(77·1024773-293)/9May 24, 2011Ray Chandler
312247657227372w73(65·1024764+457)/9May 24, 2011Ray Chandler
31724710 67w33(61·1024709-403)/9May 24, 2011Ray Chandler
319246769770397w03(88·1024675-673)/9May 24, 2011Ray Chandler
321246732881928w19(26·1024672-629)/9May 24, 2011Ray Chandler
323246718118781w87(73·1024670+683)/9May 24, 2011Ray Chandler
32424656 72w99(65·1024655+691)/9May 24, 2011Ray Chandler
32624619 774w1(697·1024617-31)/9May 24, 2011Ray Chandler
327246011884718w47(17·1024600-377)/9May 24, 2011Ray Chandler
32824597 335w7(302·1024595+13)/9May 24, 2011Ray Chandler
329245903446934w69(31·1024589+221)/9May 24, 2011Ray Chandler
332245824119741w97(37·1024581+773)/9May 24, 2011Ray Chandler
33424555 48w33(44·1024554-503)/9May 24, 2011Ray Chandler
335245476223962w39(56·1024546+151)/9May 24, 2011Ray Chandler
336245402442924w29(22·1024539-139)/9May 24, 2011Ray Chandler
337245333445334w53(31·1024532+77)/9May 24, 2011Ray Chandler
338245273226132w61(29·1024526+349)/9May 24, 2011Ray Chandler
339245094223942w39(38·1024508+151)/9May 24, 2011Ray Chandler
341244845220952w09(47·1024483-119)/9May 24, 2011Ray Chandler
342244689228392w83(83·1024467+547)/9May 24, 2011Ray Chandler
343244675226752w67(47·1024466+403)/9May 24, 2011Ray Chandler
34424456 21w99(19·1024455+791)/9May 24, 2011Ray Chandler
345244461771317w13(16·1024445-583)/9May 24, 2011Ray Chandler
346244388112781w27(73·1024437+143)/9May 24, 2011Ray Chandler
34824436 14w99(13·1024435+491)/9May 24, 2011Ray Chandler
349244235776357w63(52·1024422-133)/9May 24, 2011Ray Chandler
350244216550965w09(59·1024420-419)/9May 24, 2011Ray Chandler
351244213552335w23(32·1024420-293)/9May 24, 2011Ray Chandler
355244096551765w17(59·1024408-347)/9May 24, 2011Ray Chandler
356244035771957w19(52·1024402-529)/9May 24, 2011Ray Chandler
35824372 552w9(497·1024370+61)/9May 24, 2011Ray Chandler
359243657881778w17(71·1024364-647)/9May 24, 2011Ray Chandler
360243633558935w89(32·1024362+301)/9May 24, 2011Ray Chandler
362243449889198w91(89·1024343+19)/9May 24, 2011Ray Chandler
363243444228142w81(38·1024343+529)/9May 24, 2011Ray Chandler
364243437441774w17(67·1024342-247)/9May 24, 2011Ray Chandler
366243326110361w03(55·1024331-73)/9May 24, 2011Ray Chandler
367243319559395w93(86·1024330+337)/9May 24, 2011Ray Chandler
37424286 28w33(26·1024285-503)/9May 24, 2011Ray Chandler
375242845881358w13(53·1024283-683)/9May 24, 2011Ray Chandler
376242829228392w83(83·1024281+547)/9May 24, 2011Ray Chandler
37724282 331w7(298·1024280+53)/9May 24, 2011Ray Chandler
378242811779117w91(16·1024280+119)/9May 24, 2011Ray Chandler
37924276 47w33(43·1024275-403)/9May 24, 2011Ray Chandler
380242698554385w43(77·1024268-113)/9May 24, 2011Ray Chandler
383242399551995w19(86·1024238-329)/9May 24, 2011Ray Chandler
384242234556145w61(41·1024222+49)/9May 24, 2011Ray Chandler
386242101887918w79(17·1024209-89)/9May 24, 2011Ray Chandler
387242053552135w21(32·1024204-311)/9May 24, 2011Ray Chandler
389242029226392w63(83·1024201+367)/9May 24, 2011Ray Chandler
390241959554395w43(86·1024194-113)/9May 24, 2011Ray Chandler
393241644220942w09(38·1024163-119)/9May 24, 2011Ray Chandler
394241248229382w93(74·1024123+637)/9May 24, 2011Ray Chandler
395241228112781w27(73·1024121+143)/9May 24, 2011Ray Chandler
396241213220932w09(29·1024120-119)/9May 24, 2011Ray Chandler
39724119 332w3(299·1024117+7)/9May 24, 2011Ray Chandler
400240823776137w61(34·1024081-151)/9May 24, 2011Ray Chandler
402240706117361w73(55·1024069+557)/9May 24, 2011Ray Chandler
405240542446324w63(22·1024053+167)/9May 24, 2011Ray Chandler
407240373880338w03(35·1024036-773)/9May 24, 2011Ray Chandler
41024030 225w1(203·1024028-41)/9May 24, 2011Ray Chandler
411240032556325w63(23·1024002+67)/9May 24, 2011Ray Chandler

Ray Chandler found the 51st-52nd prime number of the form 1905983262411226187·10n-1.

Prime numbers of the form k·10n-1 (including 45 known prime numbers at least)
 digitsflabelwlabelexpressionwhenwho
3243378 19059832624112261869w1905983262411226187·1043359-1May 24, 2011Ray Chandler
6632417 19059832624112261869w1905983262411226187·1032398-1May 24, 2011Ray Chandler

May 20, 2011

Ray Chandler found the 46th-50th prime number of the form 1905983262411226187·10n-1.

Prime numbers of the form k·10n-1 (including 45 known prime numbers at least)
 digitsflabelwlabelexpressionwhenwho
7529624 19059832624112261869w1905983262411226187·1029605-1May 20, 2011Ray Chandler
7928165 19059832624112261869w1905983262411226187·1028146-1May 20, 2011Ray Chandler
8925603 19059832624112261869w1905983262411226187·1025584-1May 20, 2011Ray Chandler
16613958 19059832624112261869w1905983262411226187·1013939-1May 20, 2011Ray Chandler
17712941 19059832624112261869w1905983262411226187·1012922-1May 20, 2011Ray Chandler

May 18, 2011

Ray Chandler found 3 near-repdigit PRPs, 36 quasi-repdigit PRPs and 85 near-repdigit-related PRPs in the range 23001≤n≤24000.

Unprovable near-repdigit PRPs
 digitsflabelwlabelexpressionwhenwho
1112390010111101w(91·1023898-1)/9May 18, 2011Ray Chandler
11623498777477w47(7·1023498-277)/9May 18, 2011Ray Chandler
1182331475777757w(682·1023312-7)/9May 18, 2011Ray Chandler
Unprovable quasi-repdigit PRPs (except pd)
 digitsflabelwlabelexpressionwhenwho
28423996222012w01(2·1023996-191)/9May 18, 2011Ray Chandler
2852398683777837w(754·1023984-7)/9May 18, 2011Ray Chandler
2862397512119121w9(109·1023973+71)/9May 18, 2011Ray Chandler
28823933555795w79(5·1023933+211)/9May 18, 2011Ray Chandler
2892392725111251w(226·1023925-1)/9May 18, 2011Ray Chandler
290238985115151w51(46·1023897+359)/9May 18, 2011Ray Chandler
2912389540441404w1(364·1023893-31)/9May 18, 2011Ray Chandler
29323892555395w39(5·1023892-149)/9May 18, 2011Ray Chandler
2952385615117151w7(136·1023854+53)/9May 18, 2011Ray Chandler
29823808444974w97(4·1023808+473)/9May 18, 2011Ray Chandler
299237905115151w51(46·1023789+359)/9May 18, 2011Ray Chandler
3052368086777867w(781·1023678-7)/9May 18, 2011Ray Chandler
30623680555315w31(5·1023680-221)/9May 18, 2011Ray Chandler
3082366947441474w1(427·1023667-31)/9May 18, 2011Ray Chandler
313235939119191w91(82·1023592+719)/9May 18, 2011Ray Chandler
31423593111271w27(1023593+143)/9May 18, 2011Ray Chandler
31523584222692w69(2·1023584+421)/9May 18, 2011Ray Chandler
31623552222792w79(2·1023552+511)/9May 18, 2011Ray Chandler
31923470555435w43(5·1023470-113)/9May 18, 2011Ray Chandler
32023470444814w81(4·1023470+329)/9May 18, 2011Ray Chandler
3232341063111631w(568·1023408-1)/9May 18, 2011Ray Chandler
324233755772757w27(52·1023374-457)/9May 18, 2011Ray Chandler
32523349 4w99(4·1023349+491)/9May 18, 2011Ray Chandler
328232778778787w87(79·1023276+83)/9May 18, 2011Ray Chandler
3302327023111231w(208·1023268-1)/9May 18, 2011Ray Chandler
332232408779787w97(79·1023239+173)/9May 18, 2011Ray Chandler
3332321326111261w(235·1023211-1)/9May 18, 2011Ray Chandler
33423209 667w(601·1023207-7)/9May 18, 2011Ray Chandler
335232051773717w37(16·1023204-367)/9May 18, 2011Ray Chandler
3362318047443474w3(427·1023178-13)/9May 18, 2011Ray Chandler
33723131555675w67(5·1023131+103)/9May 18, 2011Ray Chandler
341230641775717w57(16·1023063-187)/9May 18, 2011Ray Chandler
343230536776767w67(61·1023052-97)/9May 18, 2011Ray Chandler
3442304676773767w3(691·1023044-43)/9May 18, 2011Ray Chandler
3452303185889858w9(773·1023029+1)/9May 18, 2011Ray Chandler
3462302371771717w1(646·1023021-61)/9May 18, 2011Ray Chandler
Unprovable near-repdigit-related PRPs (except ru/nr/pd/qr)
 digitsflabelwlabelexpressionwhenwho
328239984221942w19(38·1023997-29)/9May 18, 2011Ray Chandler
329239976220762w07(56·1023996-137)/9May 18, 2011Ray Chandler
330239814886948w69(44·1023980-179)/9May 18, 2011Ray Chandler
33123977 557w3(502·1023975-43)/9May 18, 2011Ray Chandler
332239757554175w41(68·1023974-131)/9May 18, 2011Ray Chandler
334239552885128w51(26·1023954-341)/9May 18, 2011Ray Chandler
33523952 338w7(305·1023950-17)/9May 18, 2011Ray Chandler
33723943 51w99(46·1023942+791)/9May 18, 2011Ray Chandler
338239417557375w73(68·1023940+157)/9May 18, 2011Ray Chandler
34023935 71w33(64·1023934+197)/9May 18, 2011Ray Chandler
341239345225752w57(47·1023933+313)/9May 18, 2011Ray Chandler
342239324557945w79(41·1023931+211)/9May 18, 2011Ray Chandler
34423918 15w99(14·1023917+391)/9May 18, 2011Ray Chandler
345239121559315w93(14·1023911+337)/9May 18, 2011Ray Chandler
34623910 28w11(26·1023909-701)/9May 18, 2011Ray Chandler
348239024557345w73(41·1023901+157)/9May 18, 2011Ray Chandler
352238718558385w83(77·1023870+247)/9May 18, 2011Ray Chandler
354238563774937w49(34·1023855-259)/9May 18, 2011Ray Chandler
355238554226942w69(38·1023854+421)/9May 18, 2011Ray Chandler
364237452884128w41(26·1023744-431)/9May 18, 2011Ray Chandler
365237405443154w31(49·1023739-121)/9May 18, 2011Ray Chandler
370237112446124w61(22·1023710+149)/9May 18, 2011Ray Chandler
371236862112921w29(19·1023685+161)/9May 18, 2011Ray Chandler
373236801880118w01(17·1023679-791)/9May 18, 2011Ray Chandler
376236572886728w67(26·1023656-197)/9May 18, 2011Ray Chandler
377236477221372w13(65·1023646-83)/9May 18, 2011Ray Chandler
379236342550925w09(23·1023633-419)/9May 18, 2011Ray Chandler
383235967445974w59(67·1023595+131)/9May 18, 2011Ray Chandler
384235716775967w59(61·1023570-169)/9May 18, 2011Ray Chandler
386235639110391w03(82·1023562-73)/9May 18, 2011Ray Chandler
387235618774387w43(79·1023560-313)/9May 18, 2011Ray Chandler
38923535 227w9(205·1023533+11)/9May 18, 2011Ray Chandler
390235298445384w53(76·1023528+77)/9May 18, 2011Ray Chandler
391235179447194w71(85·1023516+239)/9May 18, 2011Ray Chandler
39223517 882w3(794·1023515+7)/9May 18, 2011Ray Chandler
39323511 34w11(31·1023510-301)/9May 18, 2011Ray Chandler
394235097224972w49(65·1023508+241)/9May 18, 2011Ray Chandler
396234971446314w63(13·1023496+167)/9May 18, 2011Ray Chandler
397234949881798w17(89·1023493-647)/9May 18, 2011Ray Chandler
398234948778387w83(79·1023493+47)/9May 18, 2011Ray Chandler
399234816440164w01(58·1023480-391)/9May 18, 2011Ray Chandler
400234762886128w61(26·1023475-251)/9May 18, 2011Ray Chandler
401234588114381w43(73·1023457+287)/9May 18, 2011Ray Chandler
402234567553975w39(68·1023455-149)/9May 18, 2011Ray Chandler
40323454 221w9(199·1023452+71)/9May 18, 2011Ray Chandler
404234421558715w87(14·1023441+283)/9May 18, 2011Ray Chandler
406234243114731w47(28·1023423+323)/9May 18, 2011Ray Chandler
407234215227152w71(47·1023420+439)/9May 18, 2011Ray Chandler
408234176115761w57(55·1023416+413)/9May 18, 2011Ray Chandler
409234161774117w41(16·1023415-331)/9May 18, 2011Ray Chandler
411233861220112w01(11·1023385-191)/9May 18, 2011Ray Chandler
412233847228172w81(65·1023383+529)/9May 18, 2011Ray Chandler
41323382 881w3(793·1023380+17)/9May 18, 2011Ray Chandler
41423382 71w33(64·1023381+197)/9May 18, 2011Ray Chandler
41523380 884w9(796·1023378+41)/9May 18, 2011Ray Chandler
41823359 994w7(895·1023357+23)/9May 18, 2011Ray Chandler
419233522445124w51(22·1023351+59)/9May 18, 2011Ray Chandler
421233448556385w63(77·1023343+67)/9May 18, 2011Ray Chandler
42323328 17w33(16·1023327-403)/9May 18, 2011Ray Chandler
425232932117321w73(19·1023292+557)/9May 18, 2011Ray Chandler
427232807442774w27(67·1023279-157)/9May 18, 2011Ray Chandler
428232617880378w03(71·1023260-773)/9May 18, 2011Ray Chandler
430232556118961w89(55·1023254+701)/9May 18, 2011Ray Chandler
431232496883768w37(62·1023248-467)/9May 18, 2011Ray Chandler
432232478778187w81(79·1023246+29)/9May 18, 2011Ray Chandler
43523230 65w33(59·1023229-203)/9May 18, 2011Ray Chandler
437232202886328w63(26·1023219-233)/9May 18, 2011Ray Chandler
43823219 225w3(203·1023217-23)/9May 18, 2011Ray Chandler
440232167886378w63(71·1023215-233)/9May 18, 2011Ray Chandler
441232019557395w73(86·1023200+157)/9May 18, 2011Ray Chandler
445231626551965w19(59·1023161-329)/9May 18, 2011Ray Chandler
446231569448194w81(85·1023155+329)/9May 18, 2011Ray Chandler
44723143 65w11(59·1023142-401)/9May 18, 2011Ray Chandler
448231428442184w21(76·1023141-211)/9May 18, 2011Ray Chandler
450231051774117w41(16·1023104-331)/9May 18, 2011Ray Chandler
45123090 441w7(397·1023088+53)/9May 18, 2011Ray Chandler
452230901558115w81(14·1023089+229)/9May 18, 2011Ray Chandler
453230791554915w49(14·1023078-59)/9May 18, 2011Ray Chandler
454230764552745w27(41·1023075-257)/9May 18, 2011Ray Chandler
455230738554185w41(77·1023072-131)/9May 18, 2011Ray Chandler
45623054 118w7(107·1023052-17)/9May 18, 2011Ray Chandler
458230291770317w03(16·1023028-673)/9May 18, 2011Ray Chandler
459230252889328w93(26·1023024+37)/9May 18, 2011Ray Chandler
460230046770167w01(61·1023003-691)/9May 18, 2011Ray Chandler
461230021445914w59(13·1023001+131)/9May 18, 2011Ray Chandler

May 11, 2011

Ray Chandler found 2 near-repdigit PRPs, 30 quasi-repdigit PRPs and 79 near-repdigit-related PRPs in the range 22001≤n≤23000.

Unprovable near-repdigit PRPs
 digitsflabelwlabelexpressionwhenwho
1202284272777727w(655·1022840-7)/9May 11, 2011Ray Chandler
1262246917111171w(154·1022467-1)/9May 11, 2011Ray Chandler
Unprovable quasi-repdigit PRPs (except pd)
 digitsflabelwlabelexpressionwhenwho
314229956119161w91(55·1022994+719)/9May 11, 2011Ray Chandler
31822953 2w77(2·1022953+493)/9May 11, 2011Ray Chandler
3202293079779797w9(718·1022928+11)/9May 11, 2011Ray Chandler
3222292246777467w(421·1022920-7)/9May 11, 2011Ray Chandler
3232286936111361w(325·1022867-1)/9May 11, 2011Ray Chandler
3242285450553505w3(455·1022852-23)/9May 11, 2011Ray Chandler
328227645114151w41(46·1022763+269)/9May 11, 2011Ray Chandler
3292275035111351w(316·1022748-1)/9May 11, 2011Ray Chandler
33122718444014w01(4·1022718-391)/9May 11, 2011Ray Chandler
3342267646777467w(421·1022674-7)/9May 11, 2011Ray Chandler
3372264723223232w3(209·1022645+7)/9May 11, 2011Ray Chandler
339225993116131w61(28·1022598+449)/9May 11, 2011Ray Chandler
34122542777617w61(7·1022542-151)/9May 11, 2011Ray Chandler
3442247483883838w3(755·1022472-53)/9May 11, 2011Ray Chandler
3472239765111651w(586·1022395-1)/9May 11, 2011Ray Chandler
35022324222692w69(2·1022324+421)/9May 11, 2011Ray Chandler
351223034775747w57(43·1022302-187)/9May 11, 2011Ray Chandler
35322299777317w31(7·1022299-421)/9May 11, 2011Ray Chandler
3552229350559505w9(455·1022291+31)/9May 11, 2011Ray Chandler
356222905115151w51(46·1022289+359)/9May 11, 2011Ray Chandler
35922245555715w71(5·1022245+139)/9May 11, 2011Ray Chandler
3622222173779737w9(664·1022219+11)/9May 11, 2011Ray Chandler
3642221019119191w9(172·1022208+71)/9May 11, 2011Ray Chandler
366222005114151w41(46·1022199+269)/9May 11, 2011Ray Chandler
3682214115777157w(142·1022139-7)/9May 11, 2011Ray Chandler
36922138111631w63(1022138+467)/9May 11, 2011Ray Chandler
372221127110171w01(64·1022111-91)/9May 11, 2011Ray Chandler
37422078111931w93(1022078+737)/9May 11, 2011Ray Chandler
37522051111691w69(1022051+521)/9May 11, 2011Ray Chandler
37722033888198w19(8·1022033-629)/9May 11, 2011Ray Chandler
Unprovable near-repdigit-related PRPs (except ru/nr/pd/qr)
 digitsflabelwlabelexpressionwhenwho
377230015116951w69(46·1023000+521)/9May 11, 2011Ray Chandler
37922997 87w99(79·1022996+191)/9May 11, 2011Ray Chandler
382229525224352w43(47·1022951+187)/9May 11, 2011Ray Chandler
383229289223992w39(83·1022927+151)/9May 11, 2011Ray Chandler
384229288117981w79(73·1022927+611)/9May 11, 2011Ray Chandler
385229281884718w47(17·1022927-377)/9May 11, 2011Ray Chandler
38622914 82w99(74·1022913+691)/9May 11, 2011Ray Chandler
387229147116371w63(64·1022913+467)/9May 11, 2011Ray Chandler
388229141880118w01(17·1022913-791)/9May 11, 2011Ray Chandler
389228968778387w83(79·1022895+47)/9May 11, 2011Ray Chandler
390228952558925w89(23·1022894+301)/9May 11, 2011Ray Chandler
39222885 775w1(698·1022883-41)/9May 11, 2011Ray Chandler
393228496223962w39(56·1022848+151)/9May 11, 2011Ray Chandler
394228476442364w23(58·1022846-193)/9May 11, 2011Ray Chandler
395228437442174w21(67·1022842-211)/9May 11, 2011Ray Chandler
396228436442164w21(58·1022842-211)/9May 11, 2011Ray Chandler
39722839 884w3(796·1022837-13)/9May 11, 2011Ray Chandler
39822821 42w33(38·1022820+97)/9May 11, 2011Ray Chandler
40222790 91w99(82·1022789+791)/9May 11, 2011Ray Chandler
404227768114781w47(73·1022775+323)/9May 11, 2011Ray Chandler
405227759772997w29(88·1022774-439)/9May 11, 2011Ray Chandler
408227188220182w01(74·1022717-191)/9May 11, 2011Ray Chandler
409227164226742w67(38·1022715+403)/9May 11, 2011Ray Chandler
410227107446174w61(67·1022709+149)/9May 11, 2011Ray Chandler
411226982442724w27(22·1022697-157)/9May 11, 2011Ray Chandler
412226924224942w49(38·1022691+241)/9May 11, 2011Ray Chandler
41322687 885w1(797·1022685-41)/9May 11, 2011Ray Chandler
416226751882918w29(17·1022674-539)/9May 11, 2011Ray Chandler
418226686228962w89(56·1022667+601)/9May 11, 2011Ray Chandler
420226618448184w81(76·1022660+329)/9May 11, 2011Ray Chandler
422226609116991w69(82·1022659+521)/9May 11, 2011Ray Chandler
423226279229392w93(83·1022626+637)/9May 11, 2011Ray Chandler
424226166223962w39(56·1022615+151)/9May 11, 2011Ray Chandler
428225773776937w69(34·1022576-79)/9May 11, 2011Ray Chandler
429225541550915w09(14·1022553-419)/9May 11, 2011Ray Chandler
430225398443984w39(76·1022538-49)/9May 11, 2011Ray Chandler
43122528 661w9(595·1022526+71)/9May 11, 2011Ray Chandler
432225197118771w87(64·1022518+683)/9May 11, 2011Ray Chandler
434225093771337w13(34·1022508-583)/9May 11, 2011Ray Chandler
436224841556315w63(14·1022483+67)/9May 11, 2011Ray Chandler
437224776226362w63(56·1022476+367)/9May 11, 2011Ray Chandler
438224455119751w97(46·1022444+773)/9May 11, 2011Ray Chandler
439224276557365w73(59·1022426+157)/9May 11, 2011Ray Chandler
442224071557915w79(14·1022406+211)/9May 11, 2011Ray Chandler
443224034113741w37(37·1022402+233)/9May 11, 2011Ray Chandler
444224014226342w63(38·1022400+367)/9May 11, 2011Ray Chandler
44622385 42w99(38·1022384+691)/9May 11, 2011Ray Chandler
447223833882338w23(35·1022382-593)/9May 11, 2011Ray Chandler
448223805882758w27(53·1022379-557)/9May 11, 2011Ray Chandler
449223799775197w51(88·1022378-241)/9May 11, 2011Ray Chandler
456223352448324w83(22·1022334+347)/9May 11, 2011Ray Chandler
457223351774917w49(16·1022334-259)/9May 11, 2011Ray Chandler
45922324 75w77(68·1022323+193)/9May 11, 2011Ray Chandler
46222286 28w77(26·1022285-107)/9May 11, 2011Ray Chandler
46522253 441w7(397·1022251+53)/9May 11, 2011Ray Chandler
467222263113931w39(28·1022225+251)/9May 11, 2011Ray Chandler
469222169551795w17(86·1022215-347)/9May 11, 2011Ray Chandler
472222014773947w39(43·1022200-349)/9May 11, 2011Ray Chandler
473221939779397w93(88·1022192+137)/9May 11, 2011Ray Chandler
476221821441314w13(13·1022181-283)/9May 11, 2011Ray Chandler
477221803770137w01(34·1022179-691)/9May 11, 2011Ray Chandler
479221633119331w93(28·1022162+737)/9May 11, 2011Ray Chandler
480221604115341w53(37·1022159+377)/9May 11, 2011Ray Chandler
481221579226992w69(83·1022156+421)/9May 11, 2011Ray Chandler
482221452446324w63(22·1022144+167)/9May 11, 2011Ray Chandler
483221389446394w63(85·1022137+167)/9May 11, 2011Ray Chandler
484221372448124w81(22·1022136+329)/9May 11, 2011Ray Chandler
485221333226732w67(29·1022132+403)/9May 11, 2011Ray Chandler
490220989116791w67(82·1022097+503)/9May 11, 2011Ray Chandler
49122094 662w7(596·1022092+43)/9May 11, 2011Ray Chandler
49222090 667w9(601·1022088+11)/9May 11, 2011Ray Chandler
493220891774917w49(16·1022088-259)/9May 11, 2011Ray Chandler
494220879556995w69(86·1022086+121)/9May 11, 2011Ray Chandler
496220839225392w53(83·1022082+277)/9May 11, 2011Ray Chandler
497220708449184w91(76·1022069+419)/9May 11, 2011Ray Chandler
498220656554765w47(59·1022064-77)/9May 11, 2011Ray Chandler
499220526889368w93(62·1022051+37)/9May 11, 2011Ray Chandler
500220499880398w03(89·1022048-773)/9May 11, 2011Ray Chandler
501220328116981w69(73·1022031+521)/9May 11, 2011Ray Chandler

Ray Chandler found the 50nd prime number of the form 7216038841665661826·10n-1 and 49th of 9185936700836005047·10n-1.

Prime numbers of the form k·10n-1 (including 45 known prime numbers at least)
 digitsflabelwlabelexpressionwhenwho
3641935 72160388416656618259w7216038841665661826·1041916-1May 11, 2011Ray Chandler
4239512 91859367008360050469w9185936700836005047·1039493-1May 11, 2011Ray Chandler

May 7, 2011

Ray Chandler found the 51st-52nd prime number of the form 9186781445554781796·10n-1 and 47th-49th of 7216038841665661826·10n-1.

Prime numbers of the form k·10n-1 (including 45 known prime numbers at least)
 digitsflabelwlabelexpressionwhenwho
2248433 91867814455547817959w9186781445554781796·1048414-1May 7, 2011Ray Chandler
2746043 91867814455547817959w9186781445554781796·1046024-1May 7, 2011Ray Chandler
6530778 72160388416656618259w7216038841665661826·1030759-1May 7, 2011Ray Chandler
9224052 72160388416656618259w7216038841665661826·1024033-1May 7, 2011Ray Chandler
9423367 72160388416656618259w7216038841665661826·1023348-1May 7, 2011Ray Chandler

May 5, 2011

Ray Chandler found the 46th prime number of the form 7216038841665661826·10n-1, 55th of 8741441965233691049·10n-1, 48th of 9185936700836005047·10n-1 and 50th of 9186781445554781796·10n-1.

Prime numbers of the form k·10n-1 (including 45 known prime numbers at least)
 digitsflabelwlabelexpressionwhenwho
2247611 87414419652336910489w8741441965233691049·1047592-1May 5, 2011Ray Chandler
3541480 91867814455547817959w9186781445554781796·1041461-1May 5, 2011Ray Chandler
15813650 72160388416656618259w7216038841665661826·1013631-1May 5, 2011Ray Chandler
18211184 91859367008360050469w9185936700836005047·1011165-1May 5, 2011Ray Chandler

Ray Chandler found 1 near-repdigit PRP, 30 quasi-repdigit PRPs and 90 near-repdigit-related PRPs in the range 21001≤n≤22000.

Unprovable near-repdigit PRPs
 digitsflabelwlabelexpressionwhenwho
13721151777877w87(7·1021151+83)/9May 5, 2011Ray Chandler
Unprovable quasi-repdigit PRPs (except pd)
 digitsflabelwlabelexpressionwhenwho
3522189493111931w(838·1021892-1)/9May 5, 2011Ray Chandler
3552185039111391w(352·1021848-1)/9May 5, 2011Ray Chandler
3562183848441484w1(436·1021836-31)/9May 5, 2011Ray Chandler
360217433112131w21(28·1021742+89)/9May 5, 2011Ray Chandler
3632171648449484w9(436·1021714+41)/9May 5, 2011Ray Chandler
3642171512777127w(115·1021713-7)/9May 5, 2011Ray Chandler
366216805119151w91(46·1021679+719)/9May 5, 2011Ray Chandler
3672167938777387w(349·1021677-7)/9May 5, 2011Ray Chandler
368216648774787w47(79·1021663-277)/9May 5, 2011Ray Chandler
3722160827229272w9(245·1021606+61)/9May 5, 2011Ray Chandler
375215712771727w17(25·1021570-547)/9May 5, 2011Ray Chandler
3772156032777327w(295·1021558-7)/9May 5, 2011Ray Chandler
3802151379779797w9(718·1021511+11)/9May 5, 2011Ray Chandler
38121508777417w41(7·1021508-331)/9May 5, 2011Ray Chandler
384214239117191w71(82·1021422+539)/9May 5, 2011Ray Chandler
3862141750553505w3(455·1021415-23)/9May 5, 2011Ray Chandler
3872141479773797w3(718·1021412-43)/9May 5, 2011Ray Chandler
38921351 4w99(4·1021351+491)/9May 5, 2011Ray Chandler
39021346444894w89(4·1021346+401)/9May 5, 2011Ray Chandler
3922131086883868w3(782·1021308-53)/9May 5, 2011Ray Chandler
393212926773767w37(61·1021291-367)/9May 5, 2011Ray Chandler
3942128753551535w1(482·1021285-41)/9May 5, 2011Ray Chandler
3952127828223282w3(254·1021276+7)/9May 5, 2011Ray Chandler
3962126940111401w(361·1021267-1)/9May 5, 2011Ray Chandler
3982124884889848w9(764·1021246+1)/9May 5, 2011Ray Chandler
39921236555435w43(5·1021236-113)/9May 5, 2011Ray Chandler
4002122525221252w1(227·1021223-11)/9May 5, 2011Ray Chandler
4012120715777157w(142·1021205-7)/9May 5, 2011Ray Chandler
404211548116181w61(73·1021153+449)/9May 5, 2011Ray Chandler
4102101917117171w7(154·1021017+53)/9May 5, 2011Ray Chandler
Unprovable near-repdigit-related PRPs (except ru/nr/pd/qr)
 digitsflabelwlabelexpressionwhenwho
423219931440714w07(13·1021992-337)/9May 5, 2011Ray Chandler
424219919228992w89(83·1021990+601)/9May 5, 2011Ray Chandler
425219846556165w61(59·1021983+49)/9May 5, 2011Ray Chandler
426219793110731w07(28·1021978-37)/9May 5, 2011Ray Chandler
427219721770117w01(16·1021971-691)/9May 5, 2011Ray Chandler
431219324225142w51(38·1021931+259)/9May 5, 2011Ray Chandler
432219218551785w17(77·1021920-347)/9May 5, 2011Ray Chandler
436218641558115w81(14·1021863+229)/9May 5, 2011Ray Chandler
43721860 92w33(83·1021859+97)/9May 5, 2011Ray Chandler
439218339445994w59(85·1021832+131)/9May 5, 2011Ray Chandler
441218288225382w53(74·1021827+277)/9May 5, 2011Ray Chandler
442218235226752w67(47·1021822+403)/9May 5, 2011Ray Chandler
443218188227982w79(74·1021817+511)/9May 5, 2011Ray Chandler
448217885774957w49(52·1021787-259)/9May 5, 2011Ray Chandler
450217687448174w81(67·1021767+329)/9May 5, 2011Ray Chandler
453217427220172w01(65·1021741-191)/9May 5, 2011Ray Chandler
454217334882348w23(44·1021732-593)/9May 5, 2011Ray Chandler
455217294119341w93(37·1021728+737)/9May 5, 2011Ray Chandler
456217289775997w59(88·1021727-169)/9May 5, 2011Ray Chandler
458217132446324w63(22·1021712+167)/9May 5, 2011Ray Chandler
45921707 338w1(305·1021705-71)/9May 5, 2011Ray Chandler
460216991443114w31(13·1021698-121)/9May 5, 2011Ray Chandler
462216879442994w29(85·1021686-139)/9May 5, 2011Ray Chandler
463216815226352w63(47·1021680+367)/9May 5, 2011Ray Chandler
465216739443194w31(85·1021672-121)/9May 5, 2011Ray Chandler
466216735880358w03(53·1021672-773)/9May 5, 2011Ray Chandler
467216722885128w51(26·1021671-341)/9May 5, 2011Ray Chandler
469216465779157w91(52·1021645+119)/9May 5, 2011Ray Chandler
472216291220912w09(11·1021628-119)/9May 5, 2011Ray Chandler
474215975446954w69(49·1021596+221)/9May 5, 2011Ray Chandler
475215844220942w09(38·1021583-119)/9May 5, 2011Ray Chandler
476215694552745w27(41·1021568-257)/9May 5, 2011Ray Chandler
477215584550945w09(41·1021557-419)/9May 5, 2011Ray Chandler
47821543 445w3(401·1021541-23)/9May 5, 2011Ray Chandler
481215269553995w39(86·1021525-149)/9May 5, 2011Ray Chandler
48721475 97w99(88·1021474+191)/9May 5, 2011Ray Chandler
489214545116751w67(46·1021453+503)/9May 5, 2011Ray Chandler
490214498227382w73(74·1021448+457)/9May 5, 2011Ray Chandler
492214389447994w79(85·1021437+311)/9May 5, 2011Ray Chandler
493214382550925w09(23·1021437-419)/9May 5, 2011Ray Chandler
495214246228762w87(56·1021423+583)/9May 5, 2011Ray Chandler
49821411 28w77(26·1021410-107)/9May 5, 2011Ray Chandler
499214062115921w59(19·1021405+431)/9May 5, 2011Ray Chandler
500214053448934w89(31·1021404+401)/9May 5, 2011Ray Chandler
50121399 447w9(403·1021397+11)/9May 5, 2011Ray Chandler
50221389 882w3(794·1021387+7)/9May 5, 2011Ray Chandler
504213867886378w63(71·1021385-233)/9May 5, 2011Ray Chandler
505213861881718w17(17·1021385-647)/9May 5, 2011Ray Chandler
506213756116761w67(55·1021374+503)/9May 5, 2011Ray Chandler
50721374 332w9(299·1021372+61)/9May 5, 2011Ray Chandler
508213676552965w29(59·1021366-239)/9May 5, 2011Ray Chandler
509213669778397w83(88·1021365+47)/9May 5, 2011Ray Chandler
510213659119391w93(82·1021364+737)/9May 5, 2011Ray Chandler
511213645441754w17(49·1021363-247)/9May 5, 2011Ray Chandler
512213625224952w49(47·1021361+241)/9May 5, 2011Ray Chandler
513213554770947w09(43·1021354-619)/9May 5, 2011Ray Chandler
515213411445314w53(13·1021340+77)/9May 5, 2011Ray Chandler
516213351225112w51(11·1021334+259)/9May 5, 2011Ray Chandler
517213337113971w39(64·1021332+251)/9May 5, 2011Ray Chandler
518213326116361w63(55·1021331+467)/9May 5, 2011Ray Chandler
521213197884778w47(71·1021318-377)/9May 5, 2011Ray Chandler
522213178556785w67(77·1021316+103)/9May 5, 2011Ray Chandler
52321311 771w3(694·1021309+17)/9May 5, 2011Ray Chandler
524212888773987w39(79·1021287-349)/9May 5, 2011Ray Chandler
526212828225782w57(74·1021281+313)/9May 5, 2011Ray Chandler
528212706551765w17(59·1021269-347)/9May 5, 2011Ray Chandler
529212664224142w41(38·1021265+169)/9May 5, 2011Ray Chandler
53221239 998w7(899·1021237-17)/9May 5, 2011Ray Chandler
533212291445114w51(13·1021228+59)/9May 5, 2011Ray Chandler
53521216 91w77(82·1021215+593)/9May 5, 2011Ray Chandler
536212102776327w63(25·1021209-133)/9May 5, 2011Ray Chandler
538212006226962w69(56·1021199+421)/9May 5, 2011Ray Chandler
539211918443784w37(76·1021190-67)/9May 5, 2011Ray Chandler
542211792446324w63(22·1021178+167)/9May 5, 2011Ray Chandler
544211682442324w23(22·1021167-193)/9May 5, 2011Ray Chandler
546211593884938w49(35·1021158-359)/9May 5, 2011Ray Chandler
54821157 37w33(34·1021156-403)/9May 5, 2011Ray Chandler
549211564559345w93(41·1021155+337)/9May 5, 2011Ray Chandler
550211424225342w53(38·1021141+277)/9May 5, 2011Ray Chandler
551211348449184w91(76·1021133+419)/9May 5, 2011Ray Chandler
553211059221992w19(83·1021104-29)/9May 5, 2011Ray Chandler
55421104 334w9(301·1021102+41)/9May 5, 2011Ray Chandler
555211015221952w19(47·1021100-29)/9May 5, 2011Ray Chandler
557211006882768w27(62·1021099-557)/9May 5, 2011Ray Chandler
558210832884328w43(26·1021082-413)/9May 5, 2011Ray Chandler
56021076 337w9(304·1021074+11)/9May 5, 2011Ray Chandler
561210671227112w71(11·1021066+439)/9May 5, 2011Ray Chandler
562210669229192w91(83·1021065+619)/9May 5, 2011Ray Chandler
563210595779357w93(52·1021058+137)/9May 5, 2011Ray Chandler
56521023 95w33(86·1021022-203)/9May 5, 2011Ray Chandler

May 4, 2011

Ray Chandler found the 48th-49th prime number of the form 9186781445554781796·10n-1.

Prime numbers of the form k·10n-1 (including 45 known prime numbers at least)
 digitsflabelwlabelexpressionwhenwho
15613542 91867814455547817959w9186781445554781796·1013523-1May 4, 2011Ray Chandler
19110141 91867814455547817959w9186781445554781796·1010122-1May 4, 2011Ray Chandler

May 2, 2011

Erik Branger found 6 near-repdigit PRPs.

Unprovable near-repdigit PRPs
 digitsflabelwlabelexpressionwhenwho
1477309444414w1(4·1077309-31)/9May 2, 2011Erik Branger
1671546444414w1(4·1071546-31)/9May 2, 2011Erik Branger
2056989444414w1(4·1056989-31)/9May 2, 2011Erik Branger
3149529444414w1(4·1049529-31)/9May 2, 2011Erik Branger
3444358888878w7(8·1044358-17)/9May 2, 2011Erik Branger
5532176888878w7(8·1032176-17)/9May 2, 2011Erik Branger

May 1, 2011

Ray Chandler found the 52nd prime number of the form 8003155564092691821·10n-1, 48th-54th of 8741441965233691049·10n-1 and 46th-48th of 8910490455537715653·10n-1.

Prime numbers of the form k·10n-1 (including 45 known prime numbers at least)
 digitsflabelwlabelexpressionwhenwho
3440777 80031555640926918209w8003155564092691821·1040758-1May 1, 2011Ray Chandler
5832855 87414419652336910489w8741441965233691049·1032836-1May 1, 2011Ray Chandler
8923279 87414419652336910489w8741441965233691049·1023260-1May 1, 2011Ray Chandler
9622558 89104904555377156529w8910490455537715653·1022539-1May 1, 2011Ray Chandler
9822227 89104904555377156529w8910490455537715653·1022208-1May 1, 2011Ray Chandler
10321493 87414419652336910489w8741441965233691049·1021474-1May 1, 2011Ray Chandler
11219429 87414419652336910489w8741441965233691049·1019410-1May 1, 2011Ray Chandler
12118230 87414419652336910489w8741441965233691049·1018211-1May 1, 2011Ray Chandler
14215361 87414419652336910489w8741441965233691049·1015342-1May 1, 2011Ray Chandler
15014180 89104904555377156529w8910490455537715653·1014161-1May 1, 2011Ray Chandler
16112997 87414419652336910489w8741441965233691049·1012978-1May 1, 2011Ray Chandler

April 2011

April 29, 2011

Ray Chandler found 37 near-repdigit PRPs, 35 quasi-repdigit PRPs and 90 near-repdigit-related PRPs.

Unprovable near-repdigit PRPs
 digitsflabelwlabelexpressionwhenwho
5429648 9w59991029648-4001April 29, 2011Ray Chandler
5828751 9w499999999991028751-50000000001April 29, 2011Ray Chandler
5928683 9w5999999991028683-400000001April 29, 2011Ray Chandler
6227991 9w299999991027991-70000001April 29, 2011Ray Chandler
6527679 9w799999999991027679-20000000001April 29, 2011Ray Chandler
6627383 9w19991027383-8001April 29, 2011Ray Chandler
6727378 9w499991027378-50001April 29, 2011Ray Chandler
6927118 9w1999991027118-800001April 29, 2011Ray Chandler
7226677 9w2999991026677-700001April 29, 2011Ray Chandler
7426601 9w2999991026601-700001April 29, 2011Ray Chandler
8025961 9w299999991025961-70000001April 29, 2011Ray Chandler
8125819 9w5991025819-401April 29, 2011Ray Chandler
8325490 9w4999991025490-500001April 29, 2011Ray Chandler
8425407 9w799991025407-20001April 29, 2011Ray Chandler
8825263 9w59999991025263-4000001April 29, 2011Ray Chandler
8925214 9w1991025214-801April 29, 2011Ray Chandler
9025202 9w59999991025202-4000001April 29, 2011Ray Chandler
9125119 9w49991025119-5001April 29, 2011Ray Chandler
9324727 9w4999999991024727-500000001April 29, 2011Ray Chandler
9524511 9w29999991024511-7000001April 29, 2011Ray Chandler
9824108 9w79999991024108-2000001April 29, 2011Ray Chandler
10623722 9w599999999991023722-40000000001April 29, 2011Ray Chandler
11023105 9w199999991023105-80000001April 29, 2011Ray Chandler
11422809 9w59999991022809-4000001April 29, 2011Ray Chandler
11522760 9w1999991022760-800001April 29, 2011Ray Chandler
11722656 9w499999999991022656-50000000001April 29, 2011Ray Chandler
11922374 9w7999999991022374-200000001April 29, 2011Ray Chandler
12022321 9w59999991022321-4000001April 29, 2011Ray Chandler
12522077 9w799999999991022077-20000000001April 29, 2011Ray Chandler
12921331 9w499999999991021331-50000000001April 29, 2011Ray Chandler
13221014 9w499991021014-50001April 29, 2011Ray Chandler
1332094313111131w(118·1020941-1)/9April 29, 2011Ray Chandler
13420777 9w299991020777-70001April 29, 2011Ray Chandler
13520753 9w199999991020753-80000001April 29, 2011Ray Chandler
13720453 9w49999999991020453-5000000001April 29, 2011Ray Chandler
1382027778777787w(709·1020275-7)/9April 29, 2011Ray Chandler
14320008 9w49999999991020008-5000000001April 29, 2011Ray Chandler
Unprovable quasi-repdigit PRPs (except pd)
 digitsflabelwlabelexpressionwhenwho
383209419116191w61(82·1020940+449)/9April 29, 2011Ray Chandler
3872092150111501w(451·1020919-1)/9April 29, 2011Ray Chandler
388209184774747w47(43·1020917-277)/9April 29, 2011Ray Chandler
389209143772737w27(34·1020913-457)/9April 29, 2011Ray Chandler
3912089816777167w(151·1020896-7)/9April 29, 2011Ray Chandler
398208399116191w61(82·1020838+449)/9April 29, 2011Ray Chandler
3992082786111861w(775·1020825-1)/9April 29, 2011Ray Chandler
40020827555095w09(5·1020827-419)/9April 29, 2011Ray Chandler
401208246112161w21(55·1020823+89)/9April 29, 2011Ray Chandler
40320799 8w11(8·1020799-701)/9April 29, 2011Ray Chandler
40620786555435w43(5·1020786-113)/9April 29, 2011Ray Chandler
408207391779717w97(16·1020738+173)/9April 29, 2011Ray Chandler
4092073486777867w(781·1020732-7)/9April 29, 2011Ray Chandler
41020721444794w79(4·1020721+311)/9April 29, 2011Ray Chandler
41320715444214w21(4·1020715-211)/9April 29, 2011Ray Chandler
4142069673771737w1(664·1020694-61)/9April 29, 2011Ray Chandler
4152069668111681w(613·1020694-1)/9April 29, 2011Ray Chandler
4172066047111471w(424·1020658-1)/9April 29, 2011Ray Chandler
4182065036111361w(325·1020648-1)/9April 29, 2011Ray Chandler
42220550222932w93(2·1020550+637)/9April 29, 2011Ray Chandler
4232052989889898w9(809·1020527+1)/9April 29, 2011Ray Chandler
4242051041441414w1(373·1020508-31)/9April 29, 2011Ray Chandler
425204968112181w21(73·1020495+89)/9April 29, 2011Ray Chandler
4262048341443414w3(373·1020481-13)/9April 29, 2011Ray Chandler
42820431888218w21(8·1020431-611)/9April 29, 2011Ray Chandler
429204257112171w21(64·1020424+89)/9April 29, 2011Ray Chandler
432203952114121w41(19·1020394+269)/9April 29, 2011Ray Chandler
43520307222572w57(2·1020307+313)/9April 29, 2011Ray Chandler
43620246444534w53(4·1020246+77)/9April 29, 2011Ray Chandler
44020156888678w67(8·1020156-197)/9April 29, 2011Ray Chandler
44120111 881w(793·1020109-1)/9April 29, 2011Ray Chandler
4432010229227292w7(263·1020100+43)/9April 29, 2011Ray Chandler
4472005953777537w(484·1020057-7)/9April 29, 2011Ray Chandler
4482005623777237w(214·1020054-7)/9April 29, 2011Ray Chandler
45120010888598w59(8·1020010-269)/9April 29, 2011Ray Chandler
Unprovable near-repdigit-related PRPs (except ru/nr/pd/qr)
 digitsflabelwlabelexpressionwhenwho
478209978775987w59(79·1020996-169)/9April 29, 2011Ray Chandler
479209793441334w13(31·1020978-283)/9April 29, 2011Ray Chandler
48020975 48w99(44·1020974+91)/9April 29, 2011Ray Chandler
48120965 884w9(796·1020963+41)/9April 29, 2011Ray Chandler
482209636559165w91(59·1020962+319)/9April 29, 2011Ray Chandler
483209361449714w97(13·1020935+473)/9April 29, 2011Ray Chandler
487208982110321w03(19·1020897-73)/9April 29, 2011Ray Chandler
488208928775387w53(79·1020891-223)/9April 29, 2011Ray Chandler
490208823443934w39(31·1020881-49)/9April 29, 2011Ray Chandler
491208787110971w09(64·1020877-19)/9April 29, 2011Ray Chandler
492208775770357w03(52·1020876-673)/9April 29, 2011Ray Chandler
493208657885778w57(71·1020864-287)/9April 29, 2011Ray Chandler
495208556226762w67(56·1020854+403)/9April 29, 2011Ray Chandler
498208392441724w17(22·1020838-247)/9April 29, 2011Ray Chandler
503208071447914w79(13·1020806+311)/9April 29, 2011Ray Chandler
504208057443174w31(67·1020804-121)/9April 29, 2011Ray Chandler
506207954228342w83(38·1020794+547)/9April 29, 2011Ray Chandler
507207942887928w79(26·1020793-89)/9April 29, 2011Ray Chandler
508207938554185w41(77·1020792-131)/9April 29, 2011Ray Chandler
509207931779317w93(16·1020792+137)/9April 29, 2011Ray Chandler
510207866226762w67(56·1020785+403)/9April 29, 2011Ray Chandler
511207764224142w41(38·1020775+169)/9April 29, 2011Ray Chandler
514207573774937w49(34·1020756-259)/9April 29, 2011Ray Chandler
516207542779327w93(25·1020753+137)/9April 29, 2011Ray Chandler
517207492556125w61(23·1020748+49)/9April 29, 2011Ray Chandler
520206998221782w17(74·1020698-47)/9April 29, 2011Ray Chandler
521206929771997w19(88·1020691-529)/9April 29, 2011Ray Chandler
525206663447134w71(31·1020665+239)/9April 29, 2011Ray Chandler
526206662119321w93(19·1020665+737)/9April 29, 2011Ray Chandler
528206558226382w63(74·1020654+367)/9April 29, 2011Ray Chandler
529206546442164w21(58·1020653-211)/9April 29, 2011Ray Chandler
531206298223782w37(74·1020628+133)/9April 29, 2011Ray Chandler
532206239449794w97(85·1020622+473)/9April 29, 2011Ray Chandler
533206193885938w59(35·1020618-269)/9April 29, 2011Ray Chandler
534206163558335w83(32·1020615+247)/9April 29, 2011Ray Chandler
537206025887958w79(53·1020601-89)/9April 29, 2011Ray Chandler
540205705110751w07(46·1020569-37)/9April 29, 2011Ray Chandler
542205659776197w61(88·1020564-151)/9April 29, 2011Ray Chandler
54320525 61w77(55·1020524+593)/9April 29, 2011Ray Chandler
54520497 28w33(26·1020496-503)/9April 29, 2011Ray Chandler
547204689225792w57(83·1020467+313)/9April 29, 2011Ray Chandler
550204536558765w87(59·1020452+283)/9April 29, 2011Ray Chandler
551204518112781w27(73·1020450+143)/9April 29, 2011Ray Chandler
552204469119791w97(82·1020445+773)/9April 29, 2011Ray Chandler
553204387552775w27(68·1020437-257)/9April 29, 2011Ray Chandler
555204209551395w13(86·1020419-383)/9April 29, 2011Ray Chandler
556204137884978w49(71·1020412-359)/9April 29, 2011Ray Chandler
558204067114371w43(64·1020405+287)/9April 29, 2011Ray Chandler
559204026557965w79(59·1020401+211)/9April 29, 2011Ray Chandler
56020396 441w7(397·1020394+53)/9April 29, 2011Ray Chandler
56220386 992w3(893·1020384+7)/9April 29, 2011Ray Chandler
564203678112781w27(73·1020366+143)/9April 29, 2011Ray Chandler
565203531445914w59(13·1020352+131)/9April 29, 2011Ray Chandler
566203528118981w89(73·1020351+701)/9April 29, 2011Ray Chandler
567203487553975w39(68·1020347-149)/9April 29, 2011Ray Chandler
56820347 228w7(206·1020345-17)/9April 29, 2011Ray Chandler
569203134770947w09(43·1020312-619)/9April 29, 2011Ray Chandler
57020300 52w11(47·1020299-101)/9April 29, 2011Ray Chandler
571202944556945w69(41·1020293+121)/9April 29, 2011Ray Chandler
572202918441984w19(76·1020290-229)/9April 29, 2011Ray Chandler
57520271 558w7(503·1020269-17)/9April 29, 2011Ray Chandler
576202714550145w01(41·1020270-491)/9April 29, 2011Ray Chandler
577202672119321w93(19·1020266+737)/9April 29, 2011Ray Chandler
578202666774967w49(61·1020265-259)/9April 29, 2011Ray Chandler
579202509110791w07(82·1020249-37)/9April 29, 2011Ray Chandler
581202367885378w53(71·1020235-323)/9April 29, 2011Ray Chandler
582202301880118w01(17·1020229-791)/9April 29, 2011Ray Chandler
583202109552195w21(86·1020209-311)/9April 29, 2011Ray Chandler
584202059886198w61(89·1020204-251)/9April 29, 2011Ray Chandler
58520205 71w99(64·1020204+791)/9April 29, 2011Ray Chandler
58620199 45w33(41·1020198-203)/9April 29, 2011Ray Chandler
587201945441954w19(49·1020193-229)/9April 29, 2011Ray Chandler
590201837449774w97(67·1020182+473)/9April 29, 2011Ray Chandler
591201827115771w57(64·1020181+413)/9April 29, 2011Ray Chandler
597201252779127w91(25·1020124+119)/9April 29, 2011Ray Chandler
598201189229192w91(83·1020117+619)/9April 29, 2011Ray Chandler
601200925887958w79(53·1020091-89)/9April 29, 2011Ray Chandler
603200874882148w21(44·1020086-611)/9April 29, 2011Ray Chandler
606200754552345w23(41·1020074-293)/9April 29, 2011Ray Chandler
608200738220982w09(74·1020072-119)/9April 29, 2011Ray Chandler
609200728119381w93(73·1020071+737)/9April 29, 2011Ray Chandler
610200701557915w79(14·1020069+211)/9April 29, 2011Ray Chandler
61120068 884w9(796·1020066+41)/9April 29, 2011Ray Chandler
612200679221992w19(83·1020066-29)/9April 29, 2011Ray Chandler
613200655113751w37(46·1020064+233)/9April 29, 2011Ray Chandler
615200497225172w51(65·1020048+259)/9April 29, 2011Ray Chandler
61720035 118w1(107·1020033-71)/9April 29, 2011Ray Chandler
620200307223972w39(65·1020029+151)/9April 29, 2011Ray Chandler
622200264224342w43(38·1020025+187)/9April 29, 2011Ray Chandler
623200213225132w51(29·1020020+259)/9April 29, 2011Ray Chandler

April 28, 2011

Ray Chandler found the 50th-52nd prime number of the form 5017522614669347895·10n-1.

Prime numbers of the form k·10n-1 (including 45 known prime numbers at least)
 digitsflabelwlabelexpressionwhenwho
3639499 50175226146693478949w5017522614669347895·1039480-1April 28, 2011Ray Chandler
4038000 50175226146693478949w5017522614669347895·1037981-1April 28, 2011Ray Chandler
4436773 50175226146693478949w5017522614669347895·1036754-1April 28, 2011Ray Chandler

April 26, 2011

Bob Price found 3 near-repdigit PRPs and 6 quasi-repdigit PRPs.

Unprovable near-repdigit PRPs
 digitsflabelwlabelexpressionwhenwho
2153804999299w291053804-71April 26, 2011Bob Price
2752317999299w291052317-71April 26, 2011Bob Price
3043873999599w591043873-41April 26, 2011Bob Price
Unprovable quasi-repdigit PRPs (except pd)
 digitsflabelwlabelexpressionwhenwho
1791920999619w611091920-39April 26, 2011Bob Price
2482790999539w531082790-47April 26, 2011Bob Price
2677418999679w671077418-33April 26, 2011Bob Price
3764862999539w531064862-47April 26, 2011Bob Price
4161868999619w611061868-39April 26, 2011Bob Price
6941384999539w531041384-47April 26, 2011Bob Price

April 25, 2011

Ray Chandler found the 50th-51st prime number of the form 8003155564092691821·10n-1.

Prime numbers of the form k·10n-1 (including 45 known prime numbers at least)
 digitsflabelwlabelexpressionwhenwho
5034562 80031555640926918209w8003155564092691821·1034543-1April 25, 2011Ray Chandler
5333432 80031555640926918209w8003155564092691821·1033413-1April 25, 2011Ray Chandler

April 23, 2011

Ray Chandler found the 46th-47th prime number of the form 4660472483897651778·10n-1, 46th-49th of 5017522614669347895·10n-1 and 47th-49th of 8003155564092691821·10n-1.

Prime numbers of the form k·10n-1 (including 45 known prime numbers at least)
 digitsflabelwlabelexpressionwhenwho
6826634 50175226146693478949w5017522614669347895·1026615-1April 23, 2011Ray Chandler
7026296 46604724838976517779w4660472483897651778·1026277-1April 23, 2011Ray Chandler
8822475 50175226146693478949w5017522614669347895·1022456-1April 23, 2011Ray Chandler
8922148 50175226146693478949w5017522614669347895·1022129-1April 23, 2011Ray Chandler
9022069 80031555640926918209w8003155564092691821·1022050-1April 23, 2011Ray Chandler
9420760 50175226146693478949w5017522614669347895·1020741-1April 23, 2011Ray Chandler
9919682 46604724838976517779w4660472483897651778·1019663-1April 23, 2011Ray Chandler
11617114 80031555640926918209w8003155564092691821·1017095-1April 23, 2011Ray Chandler
15012426 80031555640926918209w8003155564092691821·1012407-1April 23, 2011Ray Chandler

April 21, 2011

Markus Tervooren found the 60-digit prime factor of 8·10173+3 by GMP-ECM. It's the second largest factor found by ECM in our list. Congratulations!

April 19, 2011

Ray Chandler found 6 quasi-repdigit PRPs and 19 near-repdigit-related PRPs.

Unprovable quasi-repdigit PRPs (except pd)
 digitsflabelwlabelexpressionwhenwho
11129674333973w97(1029674+191)/3April 19, 2011Ray Chandler
11929369333073w07(1029369-79)/3April 19, 2011Ray Chandler
12129327333593w59(1029327+77)/3April 19, 2011Ray Chandler
125292309331393w13(28·1029229-61)/3April 19, 2011Ray Chandler
1262916636331363w1(109·1029164-7)/3April 19, 2011Ray Chandler
127291657336373w63(22·1029164+89)/3April 19, 2011Ray Chandler
Unprovable near-repdigit-related PRPs (except ru/nr/pd/qr)
 digitsflabelwlabelexpressionwhenwho
4729998 76w33(23·1029997-101)/3April 19, 2011Ray Chandler
52299127330773w07(22·1029911-79)/3April 19, 2011Ray Chandler
53299053664336w43(11·1029904-71)/3April 19, 2011Ray Chandler
54299041661916w19(5·1029903-143)/3April 19, 2011Ray Chandler
56297985332153w21(16·1029797-37)/3April 19, 2011Ray Chandler
57297495335153w51(16·1029748+53)/3April 19, 2011Ray Chandler
58296969339193w91(28·1029695+173)/3April 19, 2011Ray Chandler
59296436339163w91(19·1029642+173)/3April 19, 2011Ray Chandler
62295907338773w87(22·1029589+161)/3April 19, 2011Ray Chandler
66294875668756w87(17·1029486+61)/3April 19, 2011Ray Chandler
68294442668126w81(8·1029443+43)/3April 19, 2011Ray Chandler
69294124335143w51(13·1029411+53)/3April 19, 2011Ray Chandler
71293666339763w97(19·1029365+191)/3April 19, 2011Ray Chandler
77292207336773w67(22·1029219+101)/3April 19, 2011Ray Chandler
78292082662126w21(8·1029207-137)/3April 19, 2011Ray Chandler
85291039339793w97(28·1029102+191)/3April 19, 2011Ray Chandler
86291018337183w71(25·1029100+113)/3April 19, 2011Ray Chandler
89290744665746w57(14·1029073-29)/3April 19, 2011Ray Chandler
94290384335743w57(13·1029037+71)/3April 19, 2011Ray Chandler

Bob Price found 3 PRPs of the form 10n+<2-digit>.

Unprovable near-repdigit-related PRPs (except ru/nr/pd/qr)
 digitsflabelwlabelexpressionwhenwho
3940171009110w911094016+91April 19, 2011Bob Price
4933571009110w911093356+91April 19, 2011Bob Price
5921791006110w611092178+61April 19, 2011Bob Price

April 16, 2011

Ray Chandler proved 96 near-repdigit primes by Primo 3.0.9. Certifications are available.

Proven near-repdigit primes
 digitsflabelwlabelexpressionwhenwho
5341991 9w499101991-501April 16, 2011Ray Chandler
5381946 9w19999999999101946-80000000001April 16, 2011Ray Chandler
5391931 9w79999101931-20001April 16, 2011Ray Chandler
5441914 9w7999101914-2001April 16, 2011Ray Chandler
5531851 9w29999101851-70001April 16, 2011Ray Chandler
5541844 9w1999999999101844-8000000001April 16, 2011Ray Chandler
5591810 9w49999999101810-50000001April 16, 2011Ray Chandler
5611805 9w4999999999101805-5000000001April 16, 2011Ray Chandler
5771729 9w79999999999101729-20000000001April 16, 2011Ray Chandler
5791726 9w2999999101726-7000001April 16, 2011Ray Chandler
5931676 9w799101676-201April 16, 2011Ray Chandler
5941676 9w59999101676-40001April 16, 2011Ray Chandler
5951674 9w1999101674-8001April 16, 2011Ray Chandler
6011629 9w499999999101629-500000001April 16, 2011Ray Chandler
6051621 9w199999101621-800001April 16, 2011Ray Chandler
6061617 9w79999999999101617-20000000001April 16, 2011Ray Chandler
6101585 9w499999101585-500001April 16, 2011Ray Chandler
6111562 9w19999101562-80001April 16, 2011Ray Chandler
6171532 9w5999101532-4001April 16, 2011Ray Chandler
6191513 9w799999999101513-200000001April 16, 2011Ray Chandler
6261485 9w599999999101485-400000001April 16, 2011Ray Chandler
6281483 9w49999999101483-50000001April 16, 2011Ray Chandler
6361441 9w499101441-501April 16, 2011Ray Chandler
6391420 9w799999999101420-200000001April 16, 2011Ray Chandler
6411415 9w2999999101415-7000001April 16, 2011Ray Chandler
6451392 9w59999999999101392-40000000001April 16, 2011Ray Chandler
6601348 9w199101348-801April 16, 2011Ray Chandler
6661332 9w199999999101332-800000001April 16, 2011Ray Chandler
6701322 9w299999101322-700001April 16, 2011Ray Chandler
6791303 9w199999101303-800001April 16, 2011Ray Chandler
6851283 9w4999101283-5001April 16, 2011Ray Chandler
6871275 9w199999999101275-800000001April 16, 2011Ray Chandler
6891270 9w299101270-701April 16, 2011Ray Chandler
6921251 9w199999999101251-800000001April 16, 2011Ray Chandler
6931249 9w19999999101249-80000001April 16, 2011Ray Chandler
6991240 9w7999999999101240-2000000001April 16, 2011Ray Chandler
7071210 9w19999101210-80001April 16, 2011Ray Chandler
7111178 9w199999101178-800001April 16, 2011Ray Chandler
7181171 9w5999999101171-4000001April 16, 2011Ray Chandler
7221161 9w599101161-401April 16, 2011Ray Chandler
7261147 9w2999999101147-7000001April 16, 2011Ray Chandler
7271139 9w499999999101139-500000001April 16, 2011Ray Chandler
7281138 9w199999999101138-800000001April 16, 2011Ray Chandler
7361108 9w599999101108-400001April 16, 2011Ray Chandler
7391106 9w7999101106-2001April 16, 2011Ray Chandler
7401106 9w29999999101106-70000001April 16, 2011Ray Chandler
7411101 9w7999999101101-2000001April 16, 2011Ray Chandler
7451089 9w2999999999101089-7000000001April 16, 2011Ray Chandler
7461087 9w599999999101087-400000001April 16, 2011Ray Chandler
7511079 9w29999101079-70001April 16, 2011Ray Chandler
7551068 9w799999999101068-200000001April 16, 2011Ray Chandler
7611043 9w199101043-801April 16, 2011Ray Chandler
7631034 9w59999101034-40001April 16, 2011Ray Chandler
7661024 9w29999999101024-70000001April 16, 2011Ray Chandler
7721009 9w2999101009-7001April 16, 2011Ray Chandler
7731007 9w499101007-501April 16, 2011Ray Chandler
7761000 9w499999101000-500001April 16, 2011Ray Chandler
779992 9w19910992-801April 16, 2011Ray Chandler
781990 9w4999910990-50001April 16, 2011Ray Chandler
783987 9w29999910987-700001April 16, 2011Ray Chandler
785979 9w29910979-701April 16, 2011Ray Chandler
786979 9w49999999910979-500000001April 16, 2011Ray Chandler
793958 9w19910958-801April 16, 2011Ray Chandler
796946 9w29910946-701April 16, 2011Ray Chandler
807899 9w19910899-801April 16, 2011Ray Chandler
809896 9w199910896-8001April 16, 2011Ray Chandler
811888 9w199910888-8001April 16, 2011Ray Chandler
814883 9w19999910883-800001April 16, 2011Ray Chandler
822869 9w29999999910869-700000001April 16, 2011Ray Chandler
829845 9w29999910845-700001April 16, 2011Ray Chandler
831843 9w79999999910843-200000001April 16, 2011Ray Chandler
833828 9w1999999910828-80000001April 16, 2011Ray Chandler
835824 9w29999999910824-700000001April 16, 2011Ray Chandler
837820 9w599999910820-4000001April 16, 2011Ray Chandler
841805 9w1999999999910805-80000000001April 16, 2011Ray Chandler
845794 9w49910794-501April 16, 2011Ray Chandler
849787 9w4999999999910787-50000000001April 16, 2011Ray Chandler
859768 9w599910768-4001April 16, 2011Ray Chandler
869748 9w19910748-801April 16, 2011Ray Chandler
876738 9w599999999910738-4000000001April 16, 2011Ray Chandler
878737 9w599999999910737-4000000001April 16, 2011Ray Chandler
881733 9w2999999999910733-70000000001April 16, 2011Ray Chandler
882729 9w499910729-5001April 16, 2011Ray Chandler
891715 9w1999999910715-80000001April 16, 2011Ray Chandler
892713 9w19910713-801April 16, 2011Ray Chandler
894707 9w7999910707-20001April 16, 2011Ray Chandler
898695 9w5999999999910695-40000000001April 16, 2011Ray Chandler
900692 9w299999999910692-7000000001April 16, 2011Ray Chandler
915646 9w59910646-401April 16, 2011Ray Chandler
920642 9w5999999999910642-40000000001April 16, 2011Ray Chandler
925638 9w599999999910638-4000000001April 16, 2011Ray Chandler
929623 9w499999999910623-5000000001April 16, 2011Ray Chandler
931622 9w7999910622-20001April 16, 2011Ray Chandler
932617 9w2999999910617-70000001April 16, 2011Ray Chandler
936615 9w5999999999910615-40000000001April 16, 2011Ray Chandler
938613 9w29999910613-700001April 16, 2011Ray Chandler

Ray Chandler found 9 quasi-repdigit PRPs and 23 near-repdigit-related PRPs in the range 28001≤n≤29000.

Unprovable quasi-repdigit PRPs (except pd)
 digitsflabelwlabelexpressionwhenwho
126289796331363w13(19·1028978-61)/3April 16, 2011Ray Chandler
1272896030337303w7(91·1028958+11)/3April 16, 2011Ray Chandler
1282888964663646w3(194·1028887-11)/3April 16, 2011Ray Chandler
130286637339373w93(22·1028662+179)/3April 16, 2011Ray Chandler
1322864295333953w(286·1028640-1)/3April 16, 2011Ray Chandler
1392835050333503w(151·1028348-1)/3April 16, 2011Ray Chandler
1422828265669656w9(197·1028280+7)/3April 16, 2011Ray Chandler
1432823579333793w(238·1028233-1)/3April 16, 2011Ray Chandler
145280898339383w93(25·1028088+179)/3April 16, 2011Ray Chandler
Unprovable near-repdigit-related PRPs (except ru/nr/pd/qr)
 digitsflabelwlabelexpressionwhenwho
75289955668756w87(17·1028994+61)/3April 16, 2011Ray Chandler
76289949664996w49(29·1028993-53)/3April 16, 2011Ray Chandler
79289021662716w27(5·1028901-119)/3April 16, 2011Ray Chandler
84288088662786w27(26·1028807-119)/3April 16, 2011Ray Chandler
85287961661916w19(5·1028795-143)/3April 16, 2011Ray Chandler
86287934339743w97(13·1028792+191)/3April 16, 2011Ray Chandler
87287829332993w29(28·1028781-13)/3April 16, 2011Ray Chandler
90286344660346w03(14·1028633-191)/3April 16, 2011Ray Chandler
91286268663986w39(26·1028625-83)/3April 16, 2011Ray Chandler
9328576 886w7(266·1028574+1)/3April 16, 2011Ray Chandler
94285638338783w87(25·1028562+161)/3April 16, 2011Ray Chandler
95285021332113w21(4·1028501-37)/3April 16, 2011Ray Chandler
97284701669716w97(5·1028469+91)/3April 16, 2011Ray Chandler
9828467 36w11(11·1028466-167)/3April 16, 2011Ray Chandler
100284502337123w71(7·1028449+113)/3April 16, 2011Ray Chandler
10128449 53w99(16·1028448+197)/3April 16, 2011Ray Chandler
103283429667996w79(29·1028341+37)/3April 16, 2011Ray Chandler
104283401663116w31(5·1028339-107)/3April 16, 2011Ray Chandler
10628304 23w99(7·1028303+197)/3April 16, 2011Ray Chandler
112281605665156w51(17·1028159-47)/3April 16, 2011Ray Chandler
113281572668726w87(8·1028156+61)/3April 16, 2011Ray Chandler
11428128 886w3(266·1028126-11)/3April 16, 2011Ray Chandler
117280107335773w57(22·1028009+71)/3April 16, 2011Ray Chandler

April 15, 2011

Ray Chandler found a plateau-and-depression PRP.

Unprovable plateau and depression PRPs
 digitsflabelwlabelexpressionwhenwho
41110331333113w1(4·10111032-7)/3April 15, 2011Ray Chandler

April 14, 2011

Ray Chandler found 55 near-repdigit PRPs.

Unprovable near-repdigit PRPs
 digitsflabelwlabelexpressionwhenwho
10619919 9w799991019919-20001April 14, 2011Ray Chandler
10819895 9w29999999991019895-7000000001April 14, 2011Ray Chandler
11319591 9w299999999991019591-70000000001April 14, 2011Ray Chandler
11619494 9w5999999991019494-400000001April 14, 2011Ray Chandler
11719325 9w599991019325-40001April 14, 2011Ray Chandler
11819278 9w79991019278-2001April 14, 2011Ray Chandler
11919270 9w79999999991019270-2000000001April 14, 2011Ray Chandler
12019049 9w499991019049-50001April 14, 2011Ray Chandler
12318902 9w199991018902-80001April 14, 2011Ray Chandler
12518852 9w1991018852-801April 14, 2011Ray Chandler
12618804 9w1999991018804-800001April 14, 2011Ray Chandler
13218308 9w29999991018308-7000001April 14, 2011Ray Chandler
13718140 9w19991018140-8001April 14, 2011Ray Chandler
14217940 9w4999999991017940-500000001April 14, 2011Ray Chandler
14317894 9w79999999991017894-2000000001April 14, 2011Ray Chandler
14817774 9w7999999991017774-200000001April 14, 2011Ray Chandler
15017407 9w799991017407-20001April 14, 2011Ray Chandler
15117401 9w299991017401-70001April 14, 2011Ray Chandler
15217054 9w599999991017054-40000001April 14, 2011Ray Chandler
15816604 9w199999999991016604-80000000001April 14, 2011Ray Chandler
15916514 9w4991016514-501April 14, 2011Ray Chandler
16316359 9w29991016359-7001April 14, 2011Ray Chandler
16716007 9w5991016007-401April 14, 2011Ray Chandler
17315822 9w799991015822-20001April 14, 2011Ray Chandler
18015231 9w599999999991015231-40000000001April 14, 2011Ray Chandler
18315205 9w7999999991015205-200000001April 14, 2011Ray Chandler
18515173 9w4999999991015173-500000001April 14, 2011Ray Chandler
19214729 9w499999991014729-50000001April 14, 2011Ray Chandler
19914419 9w799999999991014419-20000000001April 14, 2011Ray Chandler
21113715 9w59991013715-4001April 14, 2011Ray Chandler
21413616 9w199999991013616-80000001April 14, 2011Ray Chandler
23213035 9w299991013035-70001April 14, 2011Ray Chandler
23313002 9w1999999991013002-800000001April 14, 2011Ray Chandler
23412995 9w49991012995-5001April 14, 2011Ray Chandler
23712894 9w5991012894-401April 14, 2011Ray Chandler
23912837 9w4999991012837-500001April 14, 2011Ray Chandler
24212712 9w499999991012712-50000001April 14, 2011Ray Chandler
24812578 9w29999991012578-7000001April 14, 2011Ray Chandler
24912532 9w5999991012532-400001April 14, 2011Ray Chandler
25712303 9w199999991012303-80000001April 14, 2011Ray Chandler
25912281 9w499999999991012281-50000000001April 14, 2011Ray Chandler
27411622 9w19999999991011622-8000000001April 14, 2011Ray Chandler
27611510 9w1999999991011510-800000001April 14, 2011Ray Chandler
27811408 9w29999991011408-7000001April 14, 2011Ray Chandler
28111248 9w29999999991011248-7000000001April 14, 2011Ray Chandler
29310880 9w499991010880-50001April 14, 2011Ray Chandler
29410826 9w1999991010826-800001April 14, 2011Ray Chandler
29610796 9w1999991010796-800001April 14, 2011Ray Chandler
30510459 9w299999991010459-70000001April 14, 2011Ray Chandler
30610440 9w4999999991010440-500000001April 14, 2011Ray Chandler
30810410 9w4999991010410-500001April 14, 2011Ray Chandler
31610212 9w599999999991010212-40000000001April 14, 2011Ray Chandler
31910113 9w79999991010113-2000001April 14, 2011Ray Chandler
32010096 9w7999999991010096-200000001April 14, 2011Ray Chandler
32110095 9w4999999991010095-500000001April 14, 2011Ray Chandler

April 13, 2011

Ray Chandler found the 53rd-54th prime number of the form 7268016015701892332·10n-1.

Prime numbers of the form k·10n-1 (including 45 known prime numbers at least)
 digitsflabelwlabelexpressionwhenwho
4137110 72680160157018923319w7268016015701892332·1037091-1April 13, 2011Ray Chandler
4236543 72680160157018923319w7268016015701892332·1036524-1April 13, 2011Ray Chandler

April 12, 2011

Ray Chandler found the 52nd prime number of the form 7268016015701892332·10n-1.

Prime numbers of the form k·10n-1 (including 45 known prime numbers at least)
 digitsflabelwlabelexpressionwhenwho
5032262 72680160157018923319w7268016015701892332·1032243-1April 12, 2011Ray Chandler

Ray Chandler found 17 quasi-repdigit PRPs and 21 near-repdigit-related PRPs in the range 27001≤n≤28000.

Unprovable quasi-repdigit PRPs (except pd)
 digitsflabelwlabelexpressionwhenwho
1382798931337313w7(94·1027987+11)/3April 12, 2011Ray Chandler
1392793917333173w(52·1027937-1)/3April 12, 2011Ray Chandler
1402793120333203w(61·1027929-1)/3April 12, 2011Ray Chandler
1412787939337393w7(118·1027877+11)/3April 12, 2011Ray Chandler
1442781328333283w(85·1027811-1)/3April 12, 2011Ray Chandler
1462776360667606w7(182·1027761+1)/3April 12, 2011Ray Chandler
15027743333293w29(1027743-13)/3April 12, 2011Ray Chandler
1532769229333293w(88·1027690-1)/3April 12, 2011Ray Chandler
155276555330353w03(16·1027654-91)/3April 12, 2011Ray Chandler
1562761935339353w9(106·1027617+17)/3April 12, 2011Ray Chandler
15727559333893w89(1027559+167)/3April 12, 2011Ray Chandler
1582745871333713w(214·1027456-1)/3April 12, 2011Ray Chandler
160273765332353w23(16·1027375-31)/3April 12, 2011Ray Chandler
16127368666596w59(2·1027368-23)/3April 12, 2011Ray Chandler
163272626335363w53(19·1027261+59)/3April 12, 2011Ray Chandler
167271904337343w73(13·1027189+119)/3April 12, 2011Ray Chandler
16927101666296w29(2·1027101-113)/3April 12, 2011Ray Chandler
Unprovable near-repdigit-related PRPs (except ru/nr/pd/qr)
 digitsflabelwlabelexpressionwhenwho
95279962330923w09(7·1027995-73)/3April 12, 2011Ray Chandler
96279682668326w83(8·1027967+49)/3April 12, 2011Ray Chandler
97279046335963w59(19·1027903+77)/3April 12, 2011Ray Chandler
98279029331993w19(28·1027901-43)/3April 12, 2011Ray Chandler
10027814 86w11(26·1027813-167)/3April 12, 2011Ray Chandler
101277462337123w71(7·1027745+113)/3April 12, 2011Ray Chandler
102277157667976w79(23·1027714+37)/3April 12, 2011Ray Chandler
104277144331943w19(13·1027713-43)/3April 12, 2011Ray Chandler
107276358662786w27(26·1027634-119)/3April 12, 2011Ray Chandler
110276071335113w51(4·1027606+53)/3April 12, 2011Ray Chandler
111275432663926w39(8·1027542-83)/3April 12, 2011Ray Chandler
113275184669346w93(14·1027517+79)/3April 12, 2011Ray Chandler
115274459334993w49(28·1027444+47)/3April 12, 2011Ray Chandler
117274361338113w81(4·1027435+143)/3April 12, 2011Ray Chandler
120273852335123w51(7·1027384+53)/3April 12, 2011Ray Chandler
12227320 43w99(13·1027319+197)/3April 12, 2011Ray Chandler
12427241 46w33(14·1027240-101)/3April 12, 2011Ray Chandler
126271411336713w67(4·1027140+101)/3April 12, 2011Ray Chandler
12727056 116w3(35·1027054-11)/3April 12, 2011Ray Chandler
129270055668756w87(17·1027004+61)/3April 12, 2011Ray Chandler
130270055336953w69(16·1027004+107)/3April 12, 2011Ray Chandler

April 11, 2011

Ray Chandler found the 49th-51st prime number of the form 7268016015701892332·10n-1.

Prime numbers of the form k·10n-1 (including 45 known prime numbers at least)
 digitsflabelwlabelexpressionwhenwho
5330234 72680160157018923319w7268016015701892332·1030215-1April 11, 2011Ray Chandler
6526625 72680160157018923319w7268016015701892332·1026606-1April 11, 2011Ray Chandler
7324282 72680160157018923319w7268016015701892332·1024263-1April 11, 2011Ray Chandler

April 9, 2011

Ray Chandler found the largest known plateau and depression PRP. Congratulations! See also Plateau and Depression Primes (Patrick De Geest).

Unprovable plateau and depression PRPs
 digitsflabelwlabelexpressionwhenwho
11488617999779w78·10148860-3April 9, 2011Ray Chandler

Ray Chandler found the 46th-48th prime number of the form 7268016015701892332·10n-1 and 52nd of 6355977888567929342·10n-1.

Prime numbers of the form k·10n-1 (including 45 known prime numbers at least)
 digitsflabelwlabelexpressionwhenwho
2148682 63559778885679293419w6355977888567929342·1048663-1April 9, 2011Ray Chandler
9518357 72680160157018923319w7268016015701892332·1018338-1April 9, 2011Ray Chandler
9917413 72680160157018923319w7268016015701892332·1017394-1April 9, 2011Ray Chandler
14910656 72680160157018923319w7268016015701892332·1010637-1April 9, 2011Ray Chandler

April 8, 2011

Ray Chandler found 1 near-repdigit PRP, 9 quasi-repdigit PRPs and 23 near-repdigit-related PRPs in the range 26001≤n≤27000.

Unprovable near-repdigit PRPs
 digitsflabelwlabelexpressionwhenwho
602677738333383w(115·1026775-1)/3April 8, 2011Ray Chandler
Unprovable quasi-repdigit PRPs (except pd)
 digitsflabelwlabelexpressionwhenwho
1572689965669656w9(197·1026897+7)/3April 8, 2011Ray Chandler
158268816332363w23(19·1026880-31)/3April 8, 2011Ray Chandler
16026798666796w79(2·1026798+37)/3April 8, 2011Ray Chandler
16126766333293w29(1026766-13)/3April 8, 2011Ray Chandler
16426685666536w53(2·1026685-41)/3April 8, 2011Ray Chandler
166266348335383w53(25·1026633+59)/3April 8, 2011Ray Chandler
16826507333673w67(1026507+101)/3April 8, 2011Ray Chandler
1722638679333793w(238·1026384-1)/3April 8, 2011Ray Chandler
1742628261669616w9(185·1026280+7)/3April 8, 2011Ray Chandler
Unprovable near-repdigit-related PRPs (except ru/nr/pd/qr)
 digitsflabelwlabelexpressionwhenwho
112269427330773w07(22·1026941-79)/3April 8, 2011Ray Chandler
113269232668926w89(8·1026922+67)/3April 8, 2011Ray Chandler
114268769339193w91(28·1026875+173)/3April 8, 2011Ray Chandler
115268759334793w47(28·1026874+41)/3April 8, 2011Ray Chandler
116268615668756w87(17·1026860+61)/3April 8, 2011Ray Chandler
118267685665156w51(17·1026767-47)/3April 8, 2011Ray Chandler
120267264669346w93(14·1026725+79)/3April 8, 2011Ray Chandler
12126673 76w99(23·1026672+97)/3April 8, 2011Ray Chandler
124266361665116w51(5·1026635-47)/3April 8, 2011Ray Chandler
125266141660916w09(5·1026613-173)/3April 8, 2011Ray Chandler
12826550 86w99(26·1026549+97)/3April 8, 2011Ray Chandler
130264803668936w89(11·1026479+67)/3April 8, 2011Ray Chandler
131264325668156w81(17·1026431+43)/3April 8, 2011Ray Chandler
133264074663946w39(14·1026406-83)/3April 8, 2011Ray Chandler
136263715660356w03(17·1026370-191)/3April 8, 2011Ray Chandler
138263284336943w69(13·1026327+107)/3April 8, 2011Ray Chandler
14026274 883w1(265·1026272-7)/3April 8, 2011Ray Chandler
14226253 76w33(23·1026252-101)/3April 8, 2011Ray Chandler
143262488331783w17(25·1026247-49)/3April 8, 2011Ray Chandler
146261292338923w89(7·1026128+167)/3April 8, 2011Ray Chandler
14926120 83w99(25·1026119+197)/3April 8, 2011Ray Chandler
151260782662326w23(8·1026077-131)/3April 8, 2011Ray Chandler
152260131663116w31(5·1026012-107)/3April 8, 2011Ray Chandler

Ray Chandler found 212 near-repdigit PRPs.

Unprovable near-repdigit PRPs
 digitsflabelwlabelexpressionwhenwho
2659835 9w299999109835-700001April 8, 2011Ray Chandler
2729677 9w79999999999109677-20000000001April 8, 2011Ray Chandler
2739650 9w499999109650-500001April 8, 2011Ray Chandler
2749589 9w299109589-701April 8, 2011Ray Chandler
2759576 9w49999999109576-50000001April 8, 2011Ray Chandler
2769564 9w79999999999109564-20000000001April 8, 2011Ray Chandler
2809483 9w599999999109483-400000001April 8, 2011Ray Chandler
2819407 9w59999999109407-40000001April 8, 2011Ray Chandler
2889125 9w299109125-701April 8, 2011Ray Chandler
2908943 9w599999999108943-400000001April 8, 2011Ray Chandler
2938847 9w199108847-801April 8, 2011Ray Chandler
3008681 9w1999108681-8001April 8, 2011Ray Chandler
3038644 9w1999108644-8001April 8, 2011Ray Chandler
3138291 9w4999108291-5001April 8, 2011Ray Chandler
3208080 9w4999999999108080-5000000001April 8, 2011Ray Chandler
3227966 9w199999999107966-800000001April 8, 2011Ray Chandler
3307602 9w5999999107602-4000001April 8, 2011Ray Chandler
3317598 9w49999107598-50001April 8, 2011Ray Chandler
3347546 9w199999999107546-800000001April 8, 2011Ray Chandler
3397399 9w29999999999107399-70000000001April 8, 2011Ray Chandler
3417264 9w1999999999107264-8000000001April 8, 2011Ray Chandler
3447191 9w599107191-401April 8, 2011Ray Chandler
3487044 9w79999999999107044-20000000001April 8, 2011Ray Chandler
3606641 9w5999999999106641-4000000001April 8, 2011Ray Chandler
3616591 9w7999999106591-2000001April 8, 2011Ray Chandler
3626537 9w29999999106537-70000001April 8, 2011Ray Chandler
3666498 9w5999999999106498-4000000001April 8, 2011Ray Chandler
3696435 9w5999999106435-4000001April 8, 2011Ray Chandler
3746325 9w59999999106325-40000001April 8, 2011Ray Chandler
3796107 9w79999999999106107-20000000001April 8, 2011Ray Chandler
3826049 9w499106049-501April 8, 2011Ray Chandler
3855907 9w1999105907-8001April 8, 2011Ray Chandler
3875849 9w59999999105849-40000001April 8, 2011Ray Chandler
3925806 9w199999105806-800001April 8, 2011Ray Chandler
3935789 9w599999999105789-400000001April 8, 2011Ray Chandler
4025629 9w19999999999105629-80000000001April 8, 2011Ray Chandler
4045564 9w49999105564-50001April 8, 2011Ray Chandler
4085523 9w49999105523-50001April 8, 2011Ray Chandler
4095493 9w499999999105493-500000001April 8, 2011Ray Chandler
4105452 9w299999999105452-700000001April 8, 2011Ray Chandler
4115435 9w299105435-701April 8, 2011Ray Chandler
4155298 9w4999105298-5001April 8, 2011Ray Chandler
4185216 9w7999999999105216-2000000001April 8, 2011Ray Chandler
4195202 9w79999105202-20001April 8, 2011Ray Chandler
4205192 9w1999105192-8001April 8, 2011Ray Chandler
4225158 9w199999999105158-800000001April 8, 2011Ray Chandler
4265063 9w1999999999105063-8000000001April 8, 2011Ray Chandler
4304933 9w4999999104933-5000001April 8, 2011Ray Chandler
4324922 9w1999999999104922-8000000001April 8, 2011Ray Chandler
4384762 9w29999999999104762-70000000001April 8, 2011Ray Chandler
4404693 9w79999999999104693-20000000001April 8, 2011Ray Chandler
4414688 9w29999999104688-70000001April 8, 2011Ray Chandler
4534329 9w599104329-401April 8, 2011Ray Chandler
4594242 9w1999999999104242-8000000001April 8, 2011Ray Chandler
4644144 9w499999104144-500001April 8, 2011Ray Chandler
4674117 9w5999999104117-4000001April 8, 2011Ray Chandler
4694102 9w199104102-801April 8, 2011Ray Chandler
4714086 9w599999999104086-400000001April 8, 2011Ray Chandler
4754003 9w299999104003-700001April 8, 2011Ray Chandler
4773961 9w29999999999103961-70000000001April 8, 2011Ray Chandler
4783944 9w299103944-701April 8, 2011Ray Chandler
4863857 9w299103857-701April 8, 2011Ray Chandler
4963645 9w5999999999103645-4000000001April 8, 2011Ray Chandler
5013598 9w59999999999103598-40000000001April 8, 2011Ray Chandler
5033591 9w49999103591-50001April 8, 2011Ray Chandler
5043548 9w599999103548-400001April 8, 2011Ray Chandler
5053543 9w19999999103543-80000001April 8, 2011Ray Chandler
5063536 9w199999999103536-800000001April 8, 2011Ray Chandler
5093377 9w2999999999103377-7000000001April 8, 2011Ray Chandler
5123349 9w299999999103349-700000001April 8, 2011Ray Chandler
5163248 9w499103248-501April 8, 2011Ray Chandler
5173239 9w1999999999103239-8000000001April 8, 2011Ray Chandler
5183235 9w5999999103235-4000001April 8, 2011Ray Chandler
5203182 9w199103182-801April 8, 2011Ray Chandler
5213180 9w4999103180-5001April 8, 2011Ray Chandler
5233156 9w7999103156-2001April 8, 2011Ray Chandler
5263085 9w4999999103085-5000001April 8, 2011Ray Chandler
5273049 9w599999103049-400001April 8, 2011Ray Chandler
5283037 9w1999999999103037-8000000001April 8, 2011Ray Chandler
5303009 9w59999103009-40001April 8, 2011Ray Chandler
5332954 9w299999999102954-700000001April 8, 2011Ray Chandler
5342950 9w29999102950-70001April 8, 2011Ray Chandler
5372912 9w1999102912-8001April 8, 2011Ray Chandler
5382900 9w29999999102900-70000001April 8, 2011Ray Chandler
5402871 9w599999102871-400001April 8, 2011Ray Chandler
5412836 9w1999102836-8001April 8, 2011Ray Chandler
5422820 9w49999999999102820-50000000001April 8, 2011Ray Chandler
5432799 9w1999102799-8001April 8, 2011Ray Chandler
5482715 9w5999102715-4001April 8, 2011Ray Chandler
5502705 9w29999999999102705-70000000001April 8, 2011Ray Chandler
5542640 9w7999102640-2001April 8, 2011Ray Chandler
5572557 9w49999102557-50001April 8, 2011Ray Chandler
5592546 9w299999999102546-700000001April 8, 2011Ray Chandler
5602526 9w79999102526-20001April 8, 2011Ray Chandler
5622495 9w59999999102495-40000001April 8, 2011Ray Chandler
5642475 9w599102475-401April 8, 2011Ray Chandler
5652444 9w59999102444-40001April 8, 2011Ray Chandler
5662438 9w7999102438-2001April 8, 2011Ray Chandler
5672420 9w79999999102420-20000001April 8, 2011Ray Chandler
5682400 9w5999999102400-4000001April 8, 2011Ray Chandler
5692388 9w199102388-801April 8, 2011Ray Chandler
5702388 9w19999102388-80001April 8, 2011Ray Chandler
5712350 9w799999999102350-200000001April 8, 2011Ray Chandler
5762311 9w1999102311-8001April 8, 2011Ray Chandler
5792269 9w5999999102269-4000001April 8, 2011Ray Chandler
5812238 9w79999102238-20001April 8, 2011Ray Chandler
5822221 9w19999999102221-80000001April 8, 2011Ray Chandler
5832204 9w799999999102204-200000001April 8, 2011Ray Chandler
5842192 9w1999999999102192-8000000001April 8, 2011Ray Chandler
5852189 9w79999102189-20001April 8, 2011Ray Chandler
5862175 9w79999102175-20001April 8, 2011Ray Chandler
5872169 9w5999999102169-4000001April 8, 2011Ray Chandler
5882168 9w4999999102168-5000001April 8, 2011Ray Chandler
5922130 9w499999102130-500001April 8, 2011Ray Chandler
5942048 9w59999999102048-40000001April 8, 2011Ray Chandler
5952021 9w299999999102021-700000001April 8, 2011Ray Chandler
5991991 9w499101991-501April 8, 2011Ray Chandler
6011946 9w19999999999101946-80000000001April 8, 2011Ray Chandler
6051931 9w79999101931-20001April 8, 2011Ray Chandler
6071914 9w7999101914-2001April 8, 2011Ray Chandler
6131851 9w29999101851-70001April 8, 2011Ray Chandler
6141844 9w1999999999101844-8000000001April 8, 2011Ray Chandler
6161810 9w49999999101810-50000001April 8, 2011Ray Chandler
6171805 9w4999999999101805-5000000001April 8, 2011Ray Chandler
6191729 9w79999999999101729-20000000001April 8, 2011Ray Chandler
6201726 9w2999999101726-7000001April 8, 2011Ray Chandler
6211676 9w799101676-201April 8, 2011Ray Chandler
6221676 9w59999101676-40001April 8, 2011Ray Chandler
6231674 9w1999101674-8001April 8, 2011Ray Chandler
6241629 9w499999999101629-500000001April 8, 2011Ray Chandler
6251621 9w199999101621-800001April 8, 2011Ray Chandler
6261617 9w79999999999101617-20000000001April 8, 2011Ray Chandler
6271585 9w499999101585-500001April 8, 2011Ray Chandler
6281562 9w19999101562-80001April 8, 2011Ray Chandler
6291532 9w5999101532-4001April 8, 2011Ray Chandler
6301513 9w799999999101513-200000001April 8, 2011Ray Chandler
6311485 9w599999999101485-400000001April 8, 2011Ray Chandler
6321483 9w49999999101483-50000001April 8, 2011Ray Chandler
6331441 9w499101441-501April 8, 2011Ray Chandler
6341420 9w799999999101420-200000001April 8, 2011Ray Chandler
6351415 9w2999999101415-7000001April 8, 2011Ray Chandler
6361392 9w59999999999101392-40000000001April 8, 2011Ray Chandler
6371348 9w199101348-801April 8, 2011Ray Chandler
6381332 9w199999999101332-800000001April 8, 2011Ray Chandler
6391322 9w299999101322-700001April 8, 2011Ray Chandler
6401303 9w199999101303-800001April 8, 2011Ray Chandler
6411283 9w4999101283-5001April 8, 2011Ray Chandler
6421275 9w199999999101275-800000001April 8, 2011Ray Chandler
6431270 9w299101270-701April 8, 2011Ray Chandler
6441251 9w199999999101251-800000001April 8, 2011Ray Chandler
6451249 9w19999999101249-80000001April 8, 2011Ray Chandler
6461240 9w7999999999101240-2000000001April 8, 2011Ray Chandler
6471210 9w19999101210-80001April 8, 2011Ray Chandler
6481178 9w199999101178-800001April 8, 2011Ray Chandler
6491171 9w5999999101171-4000001April 8, 2011Ray Chandler
6501161 9w599101161-401April 8, 2011Ray Chandler
6511147 9w2999999101147-7000001April 8, 2011Ray Chandler
6521139 9w499999999101139-500000001April 8, 2011Ray Chandler
6531138 9w199999999101138-800000001April 8, 2011Ray Chandler
6541108 9w599999101108-400001April 8, 2011Ray Chandler
6551106 9w7999101106-2001April 8, 2011Ray Chandler
6561106 9w29999999101106-70000001April 8, 2011Ray Chandler
6571101 9w7999999101101-2000001April 8, 2011Ray Chandler
6581089 9w2999999999101089-7000000001April 8, 2011Ray Chandler
6591087 9w599999999101087-400000001April 8, 2011Ray Chandler
6601079 9w29999101079-70001April 8, 2011Ray Chandler
6611068 9w799999999101068-200000001April 8, 2011Ray Chandler
6621043 9w199101043-801April 8, 2011Ray Chandler
6631034 9w59999101034-40001April 8, 2011Ray Chandler
6641024 9w29999999101024-70000001April 8, 2011Ray Chandler
6651009 9w2999101009-7001April 8, 2011Ray Chandler
6661007 9w499101007-501April 8, 2011Ray Chandler
6671000 9w499999101000-500001April 8, 2011Ray Chandler
668992 9w19910992-801April 8, 2011Ray Chandler
669990 9w4999910990-50001April 8, 2011Ray Chandler
670987 9w29999910987-700001April 8, 2011Ray Chandler
671979 9w29910979-701April 8, 2011Ray Chandler
672979 9w49999999910979-500000001April 8, 2011Ray Chandler
673958 9w19910958-801April 8, 2011Ray Chandler
674946 9w29910946-701April 8, 2011Ray Chandler
675899 9w19910899-801April 8, 2011Ray Chandler
676896 9w199910896-8001April 8, 2011Ray Chandler
677888 9w199910888-8001April 8, 2011Ray Chandler
678883 9w19999910883-800001April 8, 2011Ray Chandler
679869 9w29999999910869-700000001April 8, 2011Ray Chandler
680845 9w29999910845-700001April 8, 2011Ray Chandler
681843 9w79999999910843-200000001April 8, 2011Ray Chandler
682828 9w1999999910828-80000001April 8, 2011Ray Chandler
683824 9w29999999910824-700000001April 8, 2011Ray Chandler
684820 9w599999910820-4000001April 8, 2011Ray Chandler
685805 9w1999999999910805-80000000001April 8, 2011Ray Chandler
686794 9w49910794-501April 8, 2011Ray Chandler
687787 9w4999999999910787-50000000001April 8, 2011Ray Chandler
688768 9w599910768-4001April 8, 2011Ray Chandler
689748 9w19910748-801April 8, 2011Ray Chandler
690738 9w599999999910738-4000000001April 8, 2011Ray Chandler
691737 9w599999999910737-4000000001April 8, 2011Ray Chandler
692733 9w2999999999910733-70000000001April 8, 2011Ray Chandler
693729 9w499910729-5001April 8, 2011Ray Chandler
694715 9w1999999910715-80000001April 8, 2011Ray Chandler
695713 9w19910713-801April 8, 2011Ray Chandler
696707 9w7999910707-20001April 8, 2011Ray Chandler
697695 9w5999999999910695-40000000001April 8, 2011Ray Chandler
698692 9w299999999910692-7000000001April 8, 2011Ray Chandler
699646 9w59910646-401April 8, 2011Ray Chandler
700642 9w5999999999910642-40000000001April 8, 2011Ray Chandler
701638 9w599999999910638-4000000001April 8, 2011Ray Chandler
702623 9w499999999910623-5000000001April 8, 2011Ray Chandler
703622 9w7999910622-20001April 8, 2011Ray Chandler
704617 9w2999999910617-70000001April 8, 2011Ray Chandler
705615 9w5999999999910615-40000000001April 8, 2011Ray Chandler
706613 9w29999910613-700001April 8, 2011Ray Chandler

April 6, 2011

Ray Chandler found the 51st prime number of the form 6355977888567929342·10n-1.

Prime numbers of the form k·10n-1 (including 45 known prime numbers at least)
 digitsflabelwlabelexpressionwhenwho
3439617 63559778885679293419w6355977888567929342·1039598-1April 6, 2011Ray Chandler

Ray Chandler found 10 quasi-repdigit PRPs and 22 near-repdigit-related PRPs in the range 25001≤n≤26000.

Unprovable quasi-repdigit PRPs (except pd)
 digitsflabelwlabelexpressionwhenwho
1822559037339373w9(112·1025588+17)/3April 6, 2011Ray Chandler
1842554364667646w7(194·1025541+1)/3April 6, 2011Ray Chandler
1852551364333643w(193·1025511-1)/3April 6, 2011Ray Chandler
1872529916333163w(49·1025297-1)/3April 6, 2011Ray Chandler
188252806334363w43(19·1025279+29)/3April 6, 2011Ray Chandler
189252521336313w63(4·1025251+89)/3April 6, 2011Ray Chandler
1912521120333203w(61·1025209-1)/3April 6, 2011Ray Chandler
1922518561333613w(184·1025183-1)/3April 6, 2011Ray Chandler
1932515176333763w(229·1025149-1)/3April 6, 2011Ray Chandler
197250488336383w63(25·1025047+89)/3April 6, 2011Ray Chandler
Unprovable near-repdigit-related PRPs (except ru/nr/pd/qr)
 digitsflabelwlabelexpressionwhenwho
131259796336763w67(19·1025978+101)/3April 6, 2011Ray Chandler
132259779665396w53(29·1025976-41)/3April 6, 2011Ray Chandler
134259056339763w97(19·1025904+191)/3April 6, 2011Ray Chandler
136258467662176w21(23·1025845-137)/3April 6, 2011Ray Chandler
138257726337963w79(19·1025771+137)/3April 6, 2011Ray Chandler
14425712 43w99(13·1025711+197)/3April 6, 2011Ray Chandler
145256981660316w03(5·1025697-191)/3April 6, 2011Ray Chandler
146256894336743w67(13·1025688+101)/3April 6, 2011Ray Chandler
148256841663716w37(5·1025683-89)/3April 6, 2011Ray Chandler
150256492335723w57(7·1025648+71)/3April 6, 2011Ray Chandler
151255957667976w79(23·1025594+37)/3April 6, 2011Ray Chandler
152255762335723w57(7·1025575+71)/3April 6, 2011Ray Chandler
15425502 553w1(166·1025500-7)/3April 6, 2011Ray Chandler
162253602668326w83(8·1025359+49)/3April 6, 2011Ray Chandler
163253148338983w89(25·1025313+167)/3April 6, 2011Ray Chandler
16525283 23w11(7·1025282-67)/3April 6, 2011Ray Chandler
16725242 883w9(265·1025240+17)/3April 6, 2011Ray Chandler
171252049664996w49(29·1025203-53)/3April 6, 2011Ray Chandler
177251224336943w69(13·1025121+107)/3April 6, 2011Ray Chandler
179250729331993w19(28·1025071-43)/3April 6, 2011Ray Chandler
181250209667396w73(29·1025019+19)/3April 6, 2011Ray Chandler
183250108332983w29(25·1025009-13)/3April 6, 2011Ray Chandler

April 4, 2011

Ray Chandler found the 46th-50th prime number of the form 6355977888567929342·10n-1.

Prime numbers of the form k·10n-1 (including 45 known prime numbers at least)
 digitsflabelwlabelexpressionwhenwho
7822028 63559778885679293419w6355977888567929342·1022009-1April 4, 2011Ray Chandler
9318083 63559778885679293419w6355977888567929342·1018064-1April 4, 2011Ray Chandler
11614408 63559778885679293419w6355977888567929342·1014389-1April 4, 2011Ray Chandler
13112149 63559778885679293419w6355977888567929342·1012130-1April 4, 2011Ray Chandler
13911247 63559778885679293419w6355977888567929342·1011228-1April 4, 2011Ray Chandler

April 3, 2011

Ray Chandler found 2 near-repdigit PRPs, 21 quasi-repdigit PRPs and 24 near-repdigit-related PRPs in the range 24001≤n≤25000.

Unprovable near-repdigit PRPs
 digitsflabelwlabelexpressionwhenwho
702475034333343w(103·1024748-1)/3April 3, 2011Ray Chandler
7424048333533w53(1024048+59)/3April 3, 2011Ray Chandler
Unprovable quasi-repdigit PRPs (except pd)
 digitsflabelwlabelexpressionwhenwho
19124996666976w97(2·1024996+91)/3April 3, 2011Ray Chandler
1922499469661696w1(209·1024992-17)/3April 3, 2011Ray Chandler
1952493239337393w7(118·1024930+11)/3April 3, 2011Ray Chandler
1972486671333713w(214·1024864-1)/3April 3, 2011Ray Chandler
200248432339323w93(7·1024842+179)/3April 3, 2011Ray Chandler
202248312336323w63(7·1024830+89)/3April 3, 2011Ray Chandler
20324804333413w41(1024804+23)/3April 3, 2011Ray Chandler
205247376337363w73(19·1024736+119)/3April 3, 2011Ray Chandler
2062473434331343w1(103·1024732-7)/3April 3, 2011Ray Chandler
2082468629333293w(88·1024684-1)/3April 3, 2011Ray Chandler
209246709334393w43(28·1024669+29)/3April 3, 2011Ray Chandler
2102460261669616w9(185·1024600+7)/3April 3, 2011Ray Chandler
214243982339323w93(7·1024397+179)/3April 3, 2011Ray Chandler
2162431967667676w7(203·1024317+1)/3April 3, 2011Ray Chandler
21724308666596w59(2·1024308-23)/3April 3, 2011Ray Chandler
218242765338353w83(16·1024275+149)/3April 3, 2011Ray Chandler
2192426129333293w(88·1024259-1)/3April 3, 2011Ray Chandler
220242174336343w63(13·1024216+89)/3April 3, 2011Ray Chandler
2242412246333463w(139·1024120-1)/3April 3, 2011Ray Chandler
225240272338323w83(7·1024026+149)/3April 3, 2011Ray Chandler
2262401961663616w3(185·1024017-11)/3April 3, 2011Ray Chandler
Unprovable near-repdigit-related PRPs (except ru/nr/pd/qr)
 digitsflabelwlabelexpressionwhenwho
162249931667316w73(5·1024992+19)/3April 3, 2011Ray Chandler
164249565334153w41(16·1024955+23)/3April 3, 2011Ray Chandler
16824919 76w99(23·1024918+97)/3April 3, 2011Ray Chandler
170248715332953w29(16·1024870-13)/3April 3, 2011Ray Chandler
174248105332153w21(16·1024809-37)/3April 3, 2011Ray Chandler
176247943667336w73(11·1024793+19)/3April 3, 2011Ray Chandler
180247288664186w41(26·1024727-77)/3April 3, 2011Ray Chandler
182247064667346w73(14·1024705+19)/3April 3, 2011Ray Chandler
184246731335713w57(4·1024672+71)/3April 3, 2011Ray Chandler
185246379668996w89(29·1024636+67)/3April 3, 2011Ray Chandler
187245829661396w13(29·1024581-161)/3April 3, 2011Ray Chandler
190244368662386w23(26·1024435-131)/3April 3, 2011Ray Chandler
191244175334153w41(16·1024416+23)/3April 3, 2011Ray Chandler
192244133662336w23(11·1024412-131)/3April 3, 2011Ray Chandler
19824322 223w7(67·1024320+11)/3April 3, 2011Ray Chandler
199243221335713w57(4·1024321+71)/3April 3, 2011Ray Chandler
201242894660346w03(14·1024288-191)/3April 3, 2011Ray Chandler
203242599334193w41(28·1024258+23)/3April 3, 2011Ray Chandler
204242543667336w73(11·1024253+19)/3April 3, 2011Ray Chandler
206242049668996w89(29·1024203+67)/3April 3, 2011Ray Chandler
208241644339743w97(13·1024163+191)/3April 3, 2011Ray Chandler
212240702334123w41(7·1024069+23)/3April 3, 2011Ray Chandler
21524036 46w99(14·1024035+97)/3April 3, 2011Ray Chandler
21624030 46w33(14·1024029-101)/3April 3, 2011Ray Chandler

Ray Chandler found the 52nd-53rd prime number of the form 5695466050858800153·10n-1.

Prime numbers of the form k·10n-1 (including 45 known prime numbers at least)
 digitsflabelwlabelexpressionwhenwho
3737738 56954660508588001529w5695466050858800153·1037719-1April 3, 2011Ray Chandler
4534878 56954660508588001529w5695466050858800153·1034859-1April 3, 2011Ray Chandler

April 2, 2011

Ray Chandler found the 50th-51st prime number of the form 5695466050858800153·10n-1.

Prime numbers of the form k·10n-1 (including 45 known prime numbers at least)
 digitsflabelwlabelexpressionwhenwho
4830299 56954660508588001529w5695466050858800153·1030280-1April 2, 2011Ray Chandler
5029926 56954660508588001529w5695466050858800153·1029907-1April 2, 2011Ray Chandler

April 1, 2011

Ray Chandler found a plateau and depression PRP.

Unprovable plateau and depression PRPs
 digitsflabelwlabelexpressionwhenwho
21199317999779w78·10119930-3April 1, 2011Ray Chandler

Ray Chandler found the 58th prime number of the form 5166409399321812845·10n-1.

Prime numbers of the form k·10n-1 (including 45 known prime numbers at least)
 digitsflabelwlabelexpressionwhenwho
2843306 51664093993218128449w5166409399321812845·1043287-1April 1, 2011Ray Chandler

Ray Chandler found 1 near-repdigit PRP, 12 quasi-repdigit PRPs and 21 near-repdigit-related PRPs in the range 23001≤n≤24000.

Unprovable near-repdigit PRPs
 digitsflabelwlabelexpressionwhenwho
752399532333323w(97·1023993-1)/3April 1, 2011Ray Chandler
Unprovable quasi-repdigit PRPs (except pd)
 digitsflabelwlabelexpressionwhenwho
2072389434339343w9(103·1023892+17)/3April 1, 2011Ray Chandler
2082388694333943w(283·1023884-1)/3April 1, 2011Ray Chandler
21123789333173w17(1023789-49)/3April 1, 2011Ray Chandler
21223782666736w73(2·1023782+19)/3April 1, 2011Ray Chandler
215236918336383w63(25·1023690+89)/3April 1, 2011Ray Chandler
2202363165669656w9(197·1023629+7)/3April 1, 2011Ray Chandler
221235307337373w73(22·1023529+119)/3April 1, 2011Ray Chandler
223234702338323w83(7·1023469+149)/3April 1, 2011Ray Chandler
22623347666016w01(2·1023347-197)/3April 1, 2011Ray Chandler
22823245666016w01(2·1023245-197)/3April 1, 2011Ray Chandler
2292312234331343w1(103·1023120-7)/3April 1, 2011Ray Chandler
23323009666736w73(2·1023009+19)/3April 1, 2011Ray Chandler
Unprovable near-repdigit-related PRPs (except ru/nr/pd/qr)
 digitsflabelwlabelexpressionwhenwho
19323957 16w99(5·1023956+97)/3April 1, 2011Ray Chandler
195239385662356w23(17·1023937-131)/3April 1, 2011Ray Chandler
19723906 446w9(134·1023904+7)/3April 1, 2011Ray Chandler
201238657336173w61(22·1023864+83)/3April 1, 2011Ray Chandler
207237824338743w87(13·1023781+161)/3April 1, 2011Ray Chandler
20823775 226w3(68·1023773-11)/3April 1, 2011Ray Chandler
20923772 53w99(16·1023771+197)/3April 1, 2011Ray Chandler
213237208662386w23(26·1023719-131)/3April 1, 2011Ray Chandler
215236622334723w47(7·1023661+41)/3April 1, 2011Ray Chandler
216236608664186w41(26·1023659-77)/3April 1, 2011Ray Chandler
218236328665386w53(26·1023631-41)/3April 1, 2011Ray Chandler
219236095665356w53(17·1023608-41)/3April 1, 2011Ray Chandler
22023609 56w11(17·1023608-167)/3April 1, 2011Ray Chandler
222235556339163w91(19·1023554+173)/3April 1, 2011Ray Chandler
224234247668176w81(23·1023423+43)/3April 1, 2011Ray Chandler
225234161664916w49(5·1023415-53)/3April 1, 2011Ray Chandler
23023301 886w3(266·1023299-11)/3April 1, 2011Ray Chandler
231232895660356w03(17·1023288-191)/3April 1, 2011Ray Chandler
234232383660736w07(11·1023237-179)/3April 1, 2011Ray Chandler
235232264663746w37(14·1023225-89)/3April 1, 2011Ray Chandler
237231696331963w19(19·1023168-43)/3April 1, 2011Ray Chandler

Ray Chandler found the 49th prime number of the form 5695466050858800153·10n-1.

Prime numbers of the form k·10n-1 (including 45 known prime numbers at least)
 digitsflabelwlabelexpressionwhenwho
9216669 56954660508588001529w5695466050858800153·1016650-1April 1, 2011Ray Chandler

March 2011

March 31, 2011

Ray Chandler found the 57th prime number of the form 5166409399321812845·10n-1, 55th of 2297132757314548041·10n-1 and 52nd of 3252520491594488226·10n-1.

Prime numbers of the form k·10n-1 (including 45 known prime numbers at least)
 digitsflabelwlabelexpressionwhenwho
2346157 32525204915944882259w3252520491594488226·1046138-1March 31, 2011Ray Chandler
2644106 22971327573145480409w2297132757314548041·1044087-1March 31, 2011Ray Chandler
4035488 51664093993218128449w5166409399321812845·1035469-1March 31, 2011Ray Chandler

March 29, 2011

Ray Chandler found 2 near-repdigit PRPs, 14 quasi-repdigit PRPs and 14 near-repdigit-related PRPs in the range 22001≤n≤23000.

Unprovable near-repdigit PRPs
 digitsflabelwlabelexpressionwhenwho
8622287333733w73(1022287+119)/3March 29, 2011Ray Chandler
8922078333133w13(1022078-61)/3March 29, 2011Ray Chandler
Unprovable quasi-repdigit PRPs (except pd)
 digitsflabelwlabelexpressionwhenwho
223230015332353w23(16·1023000-31)/3March 29, 2011Ray Chandler
224229841337313w73(4·1022983+119)/3March 29, 2011Ray Chandler
22522979333293w29(1022979-13)/3March 29, 2011Ray Chandler
23122772333713w71(1022772+113)/3March 29, 2011Ray Chandler
2382258239331393w1(118·1022580-7)/3March 29, 2011Ray Chandler
23922536666836w83(2·1022536+49)/3March 29, 2011Ray Chandler
2412247210333103w(31·1022470-1)/3March 29, 2011Ray Chandler
2442234968669686w9(206·1022347+7)/3March 29, 2011Ray Chandler
2452230267333673w(202·1022300-1)/3March 29, 2011Ray Chandler
24622296666476w47(2·1022296-59)/3March 29, 2011Ray Chandler
2492223761669616w9(185·1022235+7)/3March 29, 2011Ray Chandler
25022231666896w89(2·1022231+67)/3March 29, 2011Ray Chandler
251222102339323w93(7·1022209+179)/3March 29, 2011Ray Chandler
253221917337373w73(22·1022190+119)/3March 29, 2011Ray Chandler
Unprovable near-repdigit-related PRPs (except ru/nr/pd/qr)
 digitsflabelwlabelexpressionwhenwho
221230008665186w51(26·1022999-47)/3March 29, 2011Ray Chandler
227227989330193w01(28·1022797-97)/3March 29, 2011Ray Chandler
228227885334753w47(16·1022787+41)/3March 29, 2011Ray Chandler
229227476336763w67(19·1022746+101)/3March 29, 2011Ray Chandler
236226139337193w71(28·1022612+113)/3March 29, 2011Ray Chandler
239225141339113w91(4·1022513+173)/3March 29, 2011Ray Chandler
240225071334913w49(4·1022506+47)/3March 29, 2011Ray Chandler
244223739663796w37(29·1022372-89)/3March 29, 2011Ray Chandler
250223282335723w57(7·1022327+71)/3March 29, 2011Ray Chandler
252222878662986w29(26·1022286-113)/3March 29, 2011Ray Chandler
25322279 993w1(298·1022277-7)/3March 29, 2011Ray Chandler
259221918668186w81(26·1022190+43)/3March 29, 2011Ray Chandler
262221272669326w93(8·1022126+79)/3March 29, 2011Ray Chandler
266220858332983w29(25·1022084-13)/3March 29, 2011Ray Chandler

March 28, 2011

Ray Chandler found the 52nd-56th prime number of the form 5166409399321812845·10n-1.

Prime numbers of the form k·10n-1 (including 45 known prime numbers at least)
 digitsflabelwlabelexpressionwhenwho
5227404 51664093993218128449w5166409399321812845·1027385-1March 28, 2011Ray Chandler
5327198 51664093993218128449w5166409399321812845·1027179-1March 28, 2011Ray Chandler
5625551 51664093993218128449w5166409399321812845·1025532-1March 28, 2011Ray Chandler
6423260 51664093993218128449w5166409399321812845·1023241-1March 28, 2011Ray Chandler
7420593 51664093993218128449w5166409399321812845·1020574-1March 28, 2011Ray Chandler

Ray Chandler found 18 quasi-repdigit PRPs and 21 near-repdigit-related PRPs in the range 21001≤n≤22000..

Unprovable quasi-repdigit PRPs (except pd)
 digitsflabelwlabelexpressionwhenwho
2442199369661696w1(209·1021991-17)/3March 28, 2011Ray Chandler
24521993333973w97(1021993+191)/3March 28, 2011Ray Chandler
2482185239331393w1(118·1021850-7)/3March 28, 2011Ray Chandler
24921851666076w07(2·1021851-179)/3March 28, 2011Ray Chandler
25021836333413w41(1021836+23)/3March 28, 2011Ray Chandler
2522174417333173w(52·1021742-1)/3March 28, 2011Ray Chandler
2572164852333523w(157·1021646-1)/3March 28, 2011Ray Chandler
2612156819333193w(58·1021566-1)/3March 28, 2011Ray Chandler
2632155263661636w1(191·1021550-17)/3March 28, 2011Ray Chandler
2642144449333493w(148·1021442-1)/3March 28, 2011Ray Chandler
266214235330353w03(16·1021422-91)/3March 28, 2011Ray Chandler
2672140689333893w(268·1021404-1)/3March 28, 2011Ray Chandler
2692125964661646w1(194·1021257-17)/3March 28, 2011Ray Chandler
270211908338383w83(25·1021189+149)/3March 28, 2011Ray Chandler
2722111982333823w(247·1021117-1)/3March 28, 2011Ray Chandler
27321081666596w59(2·1021081-23)/3March 28, 2011Ray Chandler
27421079666076w07(2·1021079-179)/3March 28, 2011Ray Chandler
2752107734337343w7(103·1021075+11)/3March 28, 2011Ray Chandler
Unprovable near-repdigit-related PRPs (except ru/nr/pd/qr)
 digitsflabelwlabelexpressionwhenwho
253219682334123w41(7·1021967+23)/3March 28, 2011Ray Chandler
25521940 16w99(5·1021939+97)/3March 28, 2011Ray Chandler
256219208664186w41(26·1021919-77)/3March 28, 2011Ray Chandler
262218021667916w79(5·1021801+37)/3March 28, 2011Ray Chandler
266217525338953w89(16·1021751+167)/3March 28, 2011Ray Chandler
26821721 223w9(67·1021719+17)/3March 28, 2011Ray Chandler
26921697 883w9(265·1021695+17)/3March 28, 2011Ray Chandler
271216579663796w37(29·1021656-89)/3March 28, 2011Ray Chandler
272216392335723w57(7·1021638+71)/3March 28, 2011Ray Chandler
273216376331963w19(19·1021636-43)/3March 28, 2011Ray Chandler
275215406337163w71(19·1021539+113)/3March 28, 2011Ray Chandler
27621531 883w1(265·1021529-7)/3March 28, 2011Ray Chandler
277215048661786w17(26·1021503-149)/3March 28, 2011Ray Chandler
278214866334963w49(19·1021485+47)/3March 28, 2011Ray Chandler
279214809660196w01(29·1021479-197)/3March 28, 2011Ray Chandler
281214768662386w23(26·1021475-131)/3March 28, 2011Ray Chandler
286214137663176w31(23·1021412-107)/3March 28, 2011Ray Chandler
30121157 86w99(26·1021156+97)/3March 28, 2011Ray Chandler
30421077 553w1(166·1021075-7)/3March 28, 2011Ray Chandler
305210289662396w23(29·1021027-131)/3March 28, 2011Ray Chandler
307210033664936w49(11·1021002-53)/3March 28, 2011Ray Chandler

March 27, 2011

Ray Chandler found 46th-51st prime number of the form 5166409399321812845·10n-1.

Prime numbers of the form k·10n-1 (including 45 known prime numbers at least)
 digitsflabelwlabelexpressionwhenwho
8217325 51664093993218128449w5166409399321812845·1017306-1March 27, 2011Ray Chandler
8317253 51664093993218128449w5166409399321812845·1017234-1March 27, 2011Ray Chandler
8616411 51664093993218128449w5166409399321812845·1016392-1March 27, 2011Ray Chandler
9016146 51664093993218128449w5166409399321812845·1016127-1March 27, 2011Ray Chandler
9315489 51664093993218128449w5166409399321812845·1015470-1March 27, 2011Ray Chandler
9515230 51664093993218128449w5166409399321812845·1015211-1March 27, 2011Ray Chandler

Ray Chandler found 54th prime number of the form 2297132757314548041·10n-1 and 51st of 3252520491594488226·10n-1.

Prime numbers of the form k·10n-1 (including 45 prime numbers at least)
 digitsflabelwlabelexpressionwhenwho
3238220 22971327573145480409w2297132757314548041·1038201-1March 27, 2011Ray Chandler
3536200 32525204915944882259w3252520491594488226·1036181-1March 27, 2011Ray Chandler

March 26, 2011

Ray Chandler found 48th-50th prime number of the form 366507756522446·10n-1.

Prime numbers of the form k·10n-1 (including 45 prime numbers at least)
 digitsflabelwlabelexpressionwhenwho
2246201 3665077565224459w366507756522446·1046186-1March 26, 2011Ray Chandler
2444520 3665077565224459w366507756522446·1044505-1March 26, 2011Ray Chandler
2642875 3665077565224459w366507756522446·1042860-1March 26, 2011Ray Chandler

Ray Chandler found 9 quasi-repdigit PRPs and 29 near-repdigit-related PRPs in the range 20001≤n≤21000.

Unprovable quasi-repdigit PRPs (except pd)
 digitsflabelwlabelexpressionwhenwho
262209265335353w53(16·1020925+59)/3March 26, 2011Ray Chandler
26320924666296w29(2·1020924-113)/3March 26, 2011Ray Chandler
26920855333593w59(1020855+77)/3March 26, 2011Ray Chandler
278206092332323w23(7·1020608-31)/3March 26, 2011Ray Chandler
279206017337373w73(22·1020600+119)/3March 26, 2011Ray Chandler
2802056639331393w1(118·1020564-7)/3March 26, 2011Ray Chandler
2812045068669686w9(206·1020448+7)/3March 26, 2011Ray Chandler
2852033261669616w9(185·1020330+7)/3March 26, 2011Ray Chandler
2882017361661616w1(185·1020171-17)/3March 26, 2011Ray Chandler
Unprovable near-repdigit-related PRPs (except ru/nr/pd/qr)
 digitsflabelwlabelexpressionwhenwho
288209289330793w07(28·1020927-79)/3March 26, 2011Ray Chandler
28920910 93w77(28·1020909+131)/3March 26, 2011Ray Chandler
29220840 993w1(298·1020838-7)/3March 26, 2011Ray Chandler
294208347664976w49(23·1020833-53)/3March 26, 2011Ray Chandler
29520827 86w33(26·1020826-101)/3March 26, 2011Ray Chandler
297208092668726w87(8·1020808+61)/3March 26, 2011Ray Chandler
300207577339773w97(22·1020756+191)/3March 26, 2011Ray Chandler
30220720 226w7(68·1020718+1)/3March 26, 2011Ray Chandler
304206871336713w67(4·1020686+101)/3March 26, 2011Ray Chandler
306206671668116w81(5·1020666+43)/3March 26, 2011Ray Chandler
309206145669356w93(17·1020613+79)/3March 26, 2011Ray Chandler
310206047665176w51(23·1020603-47)/3March 26, 2011Ray Chandler
311205926339763w97(19·1020591+191)/3March 26, 2011Ray Chandler
312205714336143w61(13·1020570+83)/3March 26, 2011Ray Chandler
314205245338153w81(16·1020523+143)/3March 26, 2011Ray Chandler
31720455 86w99(26·1020454+97)/3March 26, 2011Ray Chandler
31820426 883w7(265·1020424+11)/3March 26, 2011Ray Chandler
319204087335773w57(22·1020407+71)/3March 26, 2011Ray Chandler
320203905665356w53(17·1020389-41)/3March 26, 2011Ray Chandler
321203701339113w91(4·1020369+173)/3March 26, 2011Ray Chandler
324202376331763w17(19·1020236-49)/3March 26, 2011Ray Chandler
325201917338773w87(22·1020190+161)/3March 26, 2011Ray Chandler
328201554663146w31(14·1020154-107)/3March 26, 2011Ray Chandler
330201389664196w41(29·1020137-77)/3March 26, 2011Ray Chandler
333200944335143w51(13·1020093+53)/3March 26, 2011Ray Chandler
334200892663926w39(8·1020088-83)/3March 26, 2011Ray Chandler
335200862668326w83(8·1020085+49)/3March 26, 2011Ray Chandler
339200438665986w59(26·1020042-23)/3March 26, 2011Ray Chandler
340200327663976w39(23·1020031-83)/3March 26, 2011Ray Chandler

March 25, 2011

Ray Chandler proved primality of 3 near-repdigit prime numbers by Primo 3.0.9.

Proven near-repdigit primes
 digitsflabelwlabelexpressionwhenwho
6781173 9w899999999101173-100000001March 25, 2011Ray Chandler
731951 9w899999999910951-1000000001March 25, 2011Ray Chandler
789757 9w899999999910757-1000000001March 25, 2011Ray Chandler

Ray Chandler found 53rd prime number of the form 2297132757314548041·10n-1, 50th of 3252520491594488226·10n-1 and 46th-47th of 366507756522446·10n-1.

Prime numbers of the form k·10n-1 (including 45 prime numbers at least)
 digitsflabelwlabelexpressionwhenwho
2938011 3665077565224459w366507756522446·1037996-1March 25, 2011Ray Chandler
3335343 3665077565224459w366507756522446·1035328-1March 25, 2011Ray Chandler
4329249 32525204915944882259w3252520491594488226·1029230-1March 25, 2011Ray Chandler
5224404 22971327573145480409w2297132757314548041·1024385-1March 25, 2011Ray Chandler

Bob Price found 2 PRPs of the form 10n+<2-digit>.

Unprovable near-repdigit-related PRPs (except ru/nr/pd/qr)
 digitsflabelwlabelexpressionwhenwho
1953271005710w571095326+57March 25, 2011Bob Price
2949841002110w211094983+21March 25, 2011Bob Price

March 24, 2011

Ray Chandler found 49th-52nd prime number of the form 2297132757314548041·10n-1 and 46th-49th of 3252520491594488226·10n-1.

Prime numbers of the form k·10n-1 (including 45 prime numbers at least)
 digitsflabelwlabelexpressionwhenwho
7516347 22971327573145480409w2297132757314548041·1016328-1March 24, 2011Ray Chandler
7616256 32525204915944882259w3252520491594488226·1016237-1March 24, 2011Ray Chandler
7716161 32525204915944882259w3252520491594488226·1016142-1March 24, 2011Ray Chandler
8214948 32525204915944882259w3252520491594488226·1014929-1March 24, 2011Ray Chandler
9013465 32525204915944882259w3252520491594488226·1013446-1March 24, 2011Ray Chandler
9712499 22971327573145480409w2297132757314548041·1012480-1March 24, 2011Ray Chandler
10411320 22971327573145480409w2297132757314548041·1011301-1March 24, 2011Ray Chandler
10511273 22971327573145480409w2297132757314548041·1011254-1March 24, 2011Ray Chandler

Serge Batalov proved primality of a near-repdigit prime number by using Primo 3.0.9 and PFGW.

Proven near-repdigit primes
 digitsflabelwlabelexpressionwhenwho
4074127 9w8999999999104127-1000000001March 24, 2011Serge Batalov

March 22, 2011

Ray Chandler found 22 near-repdigit PRPs.

Unprovable near-repdigit PRPs
 digitsflabelwlabelexpressionwhenwho
5528566 9w8999999991028566-100000001March 22, 2011Ray Chandler
6625628 9w89999999991025628-1000000001March 22, 2011Ray Chandler
9320670 9w899999999991020670-10000000001March 22, 2011Ray Chandler
9919960 9w899999999991019960-10000000001March 22, 2011Ray Chandler
21811991 9w899999999991011991-10000000001March 22, 2011Ray Chandler
22611486 9w899999999991011486-10000000001March 22, 2011Ray Chandler
25710191 9w89999999991010191-1000000001March 22, 2011Ray Chandler
3207025 9w8999999999107025-1000000001March 22, 2011Ray Chandler
3286725 9w8999999999106725-1000000001March 22, 2011Ray Chandler
3446074 9w8999999999106074-1000000001March 22, 2011Ray Chandler
3605637 9w8999999999105637-1000000001March 22, 2011Ray Chandler
3854557 9w899999999104557-100000001March 22, 2011Ray Chandler
3874490 9w8999999999104490-1000000001March 22, 2011Ray Chandler
3974289 9w899999999104289-100000001March 22, 2011Ray Chandler
4054127 9w8999999999104127-1000000001March 22, 2011Ray Chandler
4133938 9w8999999999103938-1000000001March 22, 2011Ray Chandler
4343502 9w89999999999103502-10000000001March 22, 2011Ray Chandler
4482939 9w899999999102939-100000001March 22, 2011Ray Chandler
4752006 9w8999999999102006-1000000001March 22, 2011Ray Chandler
4901173 9w899999999101173-100000001March 22, 2011Ray Chandler
491951 9w899999999910951-1000000001March 22, 2011Ray Chandler
492757 9w899999999910757-1000000001March 22, 2011Ray Chandler

March 20, 2011

Ray Chandler found the 48th prime number of the form 968779233322225668·10n-1.

Prime numbers of the form k·10n-1 (including 45 prime numbers at least)
 digitsflabelwlabelexpressionwhenwho
2146320 9687792333222256679w968779233322225668·1046302-1March 20, 2011Ray Chandler

March 18, 2011

Ray Chandler found the 50th prime number of the form 787737959968841798·10n-1.

Prime numbers of the form k·10n-1 (including 45 prime numbers at least)
 digitsflabelwlabelexpressionwhenwho
2243427 7877379599688417979w787737959968841798·1043409-1March 18, 2011Ray Chandler

March 17, 2011

Stefano D'Urso found a near-repdigit prime number.

Proven near-repdigit primes
 digitsflabelwlabelexpressionwhenwho
18218979 99999949w9999995·10218972-1March 17, 2011Stefano D'Urso

Ray Chandler found the 49th prime number of the form 787737959968841798·10n-1.

Prime numbers of the form k·10n-1 (including 45 prime numbers at least)
 digitsflabelwlabelexpressionwhenwho
2242542 7877379599688417979w787737959968841798·1042524-1March 17, 2011Ray Chandler

March 16, 2011

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

Proven near-repdigit primes
 digitsflabelwlabelexpressionwhenwho
15110574999949w5·10511056-1March 16, 2011David Broadhurst

Ray Chandler found the 51st prime number of the form 579648014999079182985219545616·10n-1.

Prime numbers of the form k·10n-1 (including 45 prime numbers at least)
 digitsflabelwlabelexpressionwhenwho
6019316 5796480149990791829852195456159w579648014999079182985219545616·1019286-1March 16, 2011Ray Chandler

March 15, 2011

Ray Chandler found the 50th, 51st and 52nd prime number of the form 579648014999079182985219545616·10n-1.

Prime numbers of the form k·10n-1 (including 45 prime numbers at least)
 digitsflabelwlabelexpressionwhenwho
5123031 5796480149990791829852195456159w579648014999079182985219545616·1023001-1March 15, 2011Ray Chandler
5322778 5796480149990791829852195456159w579648014999079182985219545616·1022748-1March 15, 2011Ray Chandler
6816587 5796480149990791829852195456159w579648014999079182985219545616·1016557-1March 15, 2011Ray Chandler

Gary Barnes found 3 near-repdigit prime numbers.

Proven near-repdigit primes
 digitsflabelwlabelexpressionwhenwho
13225003 9999989w999999·10224997-1March 15, 2011Gary Barnes
15223474 999989w99999·10223469-1March 15, 2011Gary Barnes
16223167 999929w99993·10223162-1March 15, 2011Gary Barnes

Ray Chandler found 20 quasi-repdigit prime numbers of the form <2-digit>·10n-1.

Proven quasi-repdigit primes (except pd)
 digitsflabelwlabelexpressionwhenwho
94915637999379w38·1049154-1March 15, 2011Ray Chandler
104826758999589w59·1048265-1March 15, 2011Ray Chandler
114797028999289w29·1047968-1March 15, 2011Ray Chandler
124789223999239w24·1047890-1March 15, 2011Ray Chandler
134736610999109w11·1047364-1March 15, 2011Ray Chandler
144690765999659w66·1046905-1March 15, 2011Ray Chandler
154634123999239w24·1046339-1March 15, 2011Ray Chandler
164612561999619w62·1046123-1March 15, 2011Ray Chandler
174576326999269w27·1045761-1March 15, 2011Ray Chandler
184449223999239w24·1044490-1March 15, 2011Ray Chandler
194365838999389w39·1043656-1March 15, 2011Ray Chandler
204305780999809w81·1043055-1March 15, 2011Ray Chandler
214272046999469w47·1042718-1March 15, 2011Ray Chandler
224237352999529w53·1042371-1March 15, 2011Ray Chandler
234213485999859w86·1042132-1March 15, 2011Ray Chandler
244196328999289w29·1041961-1March 15, 2011Ray Chandler
264102332999329w33·1041021-1March 15, 2011Ray Chandler
274100025999259w26·1040998-1March 15, 2011Ray Chandler
284093283999839w84·1040930-1March 15, 2011Ray Chandler
294066085999859w86·1040658-1March 15, 2011Ray Chandler

March 14, 2011

Ray Chandler found the 52nd prime number of the form 985166751434757822·10n-1 and 46th, 47th, 48th and 49th of 579648014999079182985219545616·10n-1.

Prime numbers of the form k·10n-1 (including 45 prime numbers at least)
 digitsflabelwlabelexpressionwhenwho
2637583 9851667514347578219w985166751434757822·1037565-1March 14, 2011Ray Chandler
8113181 5796480149990791829852195456159w579648014999079182985219545616·1013151-1March 14, 2011Ray Chandler
8511859 5796480149990791829852195456159w579648014999079182985219545616·1011829-1March 14, 2011Ray Chandler
9110964 5796480149990791829852195456159w579648014999079182985219545616·1010934-1March 14, 2011Ray Chandler
9810205 5796480149990791829852195456159w579648014999079182985219545616·1010175-1March 14, 2011Ray Chandler

Erik Branger found 3 near-repdigit PRPs.

Unprovable near-repdigit PRPs
 digitsflabelwlabelexpressionwhenwho
793497222232w3(2·1093497+7)/9March 14, 2011Erik Branger
988545222232w3(2·1088545+7)/9March 14, 2011Erik Branger
1763117222232w3(2·1063117+7)/9March 14, 2011Erik Branger

March 13, 2011

Tokyo Electric Power Company starts the rotating power stoppage for three hours per day from March 14, 2011. Contributors working in Kanto region of Japan will be affected.

March 11, 2011

No data of this page was lost even though a big earthquake forced me to stop immediately my computer. Tokyo is far from the earthquake center but shook badly. Fortunately no one injured in my family. Thank you.

March 10, 2011

Ray Chandler found the 48th prime number of the form 77930499731·10n-1, 51st of 985166751434757822·10n-1 and 48th of 787737959968841798·10n-1.

Prime numbers of the form k·10n-1 (including 45 prime numbers at least)
 digitsflabelwlabelexpressionwhenwho
2145849 779304997309w77930499731·1045838-1March 10, 2011Ray Chandler
2933866 9851667514347578219w985166751434757822·1033848-1March 10, 2011Ray Chandler
3033833 7877379599688417979w787737959968841798·1033815-1March 10, 2011Ray Chandler

March 9, 2011

Ray Chandler found the 50th prime number of the form 985166751434757822·10n-1.

Prime numbers of the form k·10n-1
 digitsflabelwlabelexpressionwhenwho
20129273 9851667514347578219w985166751434757822·1029255-1March 9, 2011Ray Chandler

March 8, 2011

Ray Chandler found the 49th prime number of the form 985166751434757822·10n-1.

Prime numbers of the form k·10n-1
 digitsflabelwlabelexpressionwhenwho
24224545 9851667514347578219w985166751434757822·1024527-1March 8, 2011Ray Chandler

March 7, 2011

Ray Chandler found the 51st prime number of the form 50565314252240396·10n-1, 49th of 1328671701593119457·10n-1, 46th and 47th of 787737959968841798·10n-1 and 46th, 47th and 48th of 985166751434757822·10n-1.

Prime numbers of the form k·10n-1
 digitsflabelwlabelexpressionwhenwho
13942461 505653142522403959w50565314252240396·1042444-1March 7, 2011Ray Chandler
14839659 13286717015931194569w1328671701593119457·1039640-1March 7, 2011Ray Chandler
28319632 7877379599688417979w787737959968841798·1019614-1March 7, 2011Ray Chandler
34714785 9851667514347578219w985166751434757822·1014767-1March 7, 2011Ray Chandler
36214020 9851667514347578219w985166751434757822·1014002-1March 7, 2011Ray Chandler
36413843 7877379599688417979w787737959968841798·1013825-1March 7, 2011Ray Chandler
43010553 9851667514347578219w985166751434757822·1010535-1March 7, 2011Ray Chandler

March 5, 2011

Gary Barnes found 2 near-repdigit primes.

Proven near-repdigit primes
 digitsflabelwlabelexpressionwhenwho
14214373 9999919w999992·10214367-1March 5, 2011Gary Barnes
15214340 9949w995·10214337-1March 5, 2011Gary Barnes

March 4, 2011

Ray Chandler found 47th prime number of the form 77930499731·10n-1.

Proven near-repdigit-related primes (except ru/nr/pd/qr)
 digitsflabelwlabelexpressionwhenwho
8436108 779304997309w77930499731·1036097-1March 4, 2011Ray Chandler

Bob Price found 11 PRPs of the form 10n+/-c.

Unprovable near-repdigit PRPs
 digitsflabelwlabelexpressionwhenwho
1953558999799w791053558-21March 4, 2011Bob Price
Unprovable quasi-repdigit PRPs (except pd)
 digitsflabelwlabelexpressionwhenwho
14982891000310w31098288+3March 4, 2011Bob Price
16926921000910w91092691+9March 4, 2011Bob Price
Unprovable near-repdigit-related PRPs (except ru/nr/pd/qr)
 digitsflabelwlabelexpressionwhenwho
1874091005710w571087408+57March 4, 2011Bob Price
2817791003910w391081778+39March 4, 2011Bob Price
3808841004910w491080883+49March 4, 2011Bob Price
4786331008110w811078632+81March 4, 2011Bob Price
577727 10w991077726+99March 4, 2011Bob Price
6768021006910w691076801+69March 4, 2011Bob Price
8763751003110w311076374+31March 4, 2011Bob Price
11742551009110w911074254+91March 4, 2011Bob Price

March 2, 2011

Ray Chandler found 15 quasi-repdigit primes of the form <2-digit>·10n-1.

Proven quasi-repdigit primes (except pd)
 digitsflabelwlabelexpressionwhenwho
103979783999839w84·1039795-1March 2, 2011Ray Chandler
113780628999289w29·1037804-1March 2, 2011Ray Chandler
133741850999509w51·1037416-1March 2, 2011Ray Chandler
143711683999839w84·1037114-1March 2, 2011Ray Chandler
1636951 229w23·1036949-1March 2, 2011Ray Chandler
173610773999739w74·1036105-1March 2, 2011Ray Chandler
183496514999149w15·1034963-1March 2, 2011Ray Chandler
193441220999209w21·1034410-1March 2, 2011Ray Chandler
203429335999359w36·1034291-1March 2, 2011Ray Chandler
213403980999809w81·1034037-1March 2, 2011Ray Chandler
223346114999149w15·1033459-1March 2, 2011Ray Chandler
233328910999109w11·1033287-1March 2, 2011Ray Chandler
243316431999319w32·1033162-1March 2, 2011Ray Chandler
263087247999479w48·1030870-1March 2, 2011Ray Chandler
273067325999259w26·1030671-1March 2, 2011Ray Chandler

February 2011

February 28, 2011

Ray Chandler found 46th prime number of the form 77930499731·10n-1 and 46th, 47th and 48th prime number of the form 1328671701593119457·10n-1.

Proven near-repdigit-related primes (except ru/nr/pd/qr)
 digitsflabelwlabelexpressionwhenwho
10325715 779304997309w77930499731·1025704-1February 28, 2011Ray Chandler
11223260 13286717015931194569w1328671701593119457·1023241-1February 28, 2011Ray Chandler
13818629 13286717015931194569w1328671701593119457·1018610-1February 28, 2011Ray Chandler
16515276 13286717015931194569w1328671701593119457·1015257-1February 28, 2011Ray Chandler

February 27, 2011

Ray Chandler found 49th and 50th prime number of the form 50565314252240396·10n-1.

Proven near-repdigit-related primes (except ru/nr/pd/qr)
 digitsflabelwlabelexpressionwhenwho
8829930 505653142522403959w50565314252240396·1029913-1February 27, 2011Ray Chandler
16514657 505653142522403959w50565314252240396·1014640-1February 27, 2011Ray Chandler

Gary Barnes found a near-repdigit prime.

Proven near-repdigit primes
 digitsflabelwlabelexpressionwhenwho
17205963 99919w9992·10205959-1February 27, 2011Gary Barnes

February 26, 2011

Ray Chandler found 12 near-repdigit prime numbers.

Proven near-repdigit primes
 digitsflabelwlabelexpressionwhenwho
13638369 9999999929w999999993·1038360-1February 26, 2011Ray Chandler
14136452 9999999959w999999996·1036443-1February 26, 2011Ray Chandler
15033591 9999999959w999999996·1033582-1February 26, 2011Ray Chandler
15931006 9999999929w999999993·1030997-1February 26, 2011Ray Chandler
16330043 9999999919w999999992·1030034-1February 26, 2011Ray Chandler
19424522 9999999919w999999992·1024513-1February 26, 2011Ray Chandler
23217256 9999999959w999999996·1017247-1February 26, 2011Ray Chandler
24115910 9999999949w999999995·1015901-1February 26, 2011Ray Chandler
25314174 9999999949w999999995·1014165-1February 26, 2011Ray Chandler
25514081 9999999949w999999995·1014072-1February 26, 2011Ray Chandler
25613903 9999999929w999999993·1013894-1February 26, 2011Ray Chandler
29010172 9999999959w999999996·1010163-1February 26, 2011Ray Chandler

Ray Chandler found 46th, 47th and 48th prime number of the form 50565314252240396·10n-1.

Proven near-repdigit-related primes (except ru/nr/pd/qr)
 digitsflabelwlabelexpressionwhenwho
17413333 505653142522403959w50565314252240396·1013316-1February 26, 2011Ray Chandler
17513218 505653142522403959w50565314252240396·1013201-1February 26, 2011Ray Chandler
19810875 505653142522403959w50565314252240396·1010858-1February 26, 2011Ray Chandler

February 24, 2011

David Broadhurst found 48th, 49th and 50th prime of the form 725852933715·10n-1.

Proven near-repdigit-related primes (except ru/nr/pd/qr)
 digitsflabelwlabelexpressionwhenwho
1282240 7258529337149w725852933715·1082228-1February 24, 2011David Broadhurst
3267150 7258529337149w725852933715·1067138-1February 24, 2011David Broadhurst
4162684 7258529337149w725852933715·1062672-1February 24, 2011David Broadhurst

Factorizations of 44...447 have been extended up to n=250. Composite numbers that appeared newly got through ECM 118 times at level 35. Most unknown factors are supposed to be greater than 1030.

February 22, 2011

Ray Chandler proved 9 primes by Primo.

Proven near-repdigit primes
 digitsflabelwlabelexpressionwhenwho
5541626 9w8999999101626-1000001February 22, 2011Ray Chandler
5581595 9w899999101595-100001February 22, 2011Ray Chandler
5721475 9w89999999101475-10000001February 22, 2011Ray Chandler
5781444 9w8999999101444-1000001February 22, 2011Ray Chandler
6011338 9w899999101338-100001February 22, 2011Ray Chandler
6141308 9w89999999101308-10000001February 22, 2011Ray Chandler
6511125 9w89999101125-10001February 22, 2011Ray Chandler
830600 7v87w(7·10600+9·10440-7)/9February 22, 2011Ray Chandler
Proven near-repdigit-related primes (except ru/nr/pd/qr)
 digitsflabelwlabelexpressionwhenwho
11781376 5813w2751(1744·101373-1747)/3February 22, 2011Ray Chandler

Ray Chandler found 47th prime number of the form 19178079668730696804601623·10n-1.

Proven near-repdigit-related primes (except ru/nr/pd/qr)
 digitsflabelwlabelexpressionwhenwho
2629015 191780796687306968046016229w19178079668730696804601623·1028989-1February 22, 2011Ray Chandler

Ray Chandler found 4 near-repdigit primes.

Proven near-repdigit primes
 digitsflabelwlabelexpressionwhenwho
13837224 99999959w9999996·1037217-1February 22, 2011Ray Chandler
15132517 999999929w99999993·1032509-1February 22, 2011Ray Chandler
15331599 99999959w9999996·1031592-1February 22, 2011Ray Chandler
15431293 99999959w9999996·1031286-1February 22, 2011Ray Chandler

Ray Chandler proved (1744·101333-1747)/3 by Primo and PFGW.

Proven near-repdigit-related primes (except ru/nr/pd/qr)
 digitsflabelwlabelexpressionwhenwho
12501336 5813w2751(1744·101333-1747)/3February 22, 2011Ray Chandler

Ray Chandler proved 68 600-digit near-repdigit prime numbers by Primo.

Ray Chandler found an unprovable plateau and depression PRP.

Unprovable plateau and depression PRPs
 digitsflabelwlabelexpressionwhenwho
3942137444774w7(67·1094212+23)/9February 22, 2011Ray Chandler

February 21, 2011

Stefano D'Urso found a near-repdigit prime.

Proven near-repdigit primes
 digitsflabelwlabelexpressionwhenwho
17195538 99999929w9999993·10195531-1February 21, 2011Stefano D'Urso

Ray Chandler proved 188 prime numbers between 1700-digit and 1800-digit by Primo. Primality certifications are available.

February 20, 2011

Ray Chandler found 45th and 46th prime number of the form 19178079668730696804601623·10n-1.

Proven near-repdigit-related primes (except ru/nr/pd/qr)
 digitsflabelwlabelexpressionwhenwho
4423157 191780796687306968046016229w19178079668730696804601623·1023131-1February 20, 2011Ray Chandler
6020077 191780796687306968046016229w19178079668730696804601623·1020051-1February 20, 2011Ray Chandler

February 19, 2011

Ray Chandler proved 4237 near-repdigit prime number between 501-digit and 599-digit.

Alexander Gramolin found a near-repdigit PRP.

Unprovable near-repdigit PRPs
 digitsflabelwlabelexpressionwhenwho
2221631999919w110221631-9February 2011Alexander Gramolin

Ray Chandler found 43rd and 44th prime number of the form 19178079668730696804601623·10n-1.

Proven near-repdigit-related primes (except ru/nr/pd/qr)
6119142 191780796687306968046016229w19178079668730696804601623·1019116-1February 19, 2011Ray Chandler
6518680 191780796687306968046016229w19178079668730696804601623·1018654-1February 19, 2011Ray Chandler

February 18, 2011

Ray Chandler found 42nd prime number of the form 19178079668730696804601623·10n-1.

Proven near-repdigit-related primes (except ru/nr/pd/qr)
 digitsflabelwlabelexpressionwhenwho
11112572 191780796687306968046016229w19178079668730696804601623·1012546-1February 18, 2011Ray Chandler

February 16, 2011

Factorizations of 99...99799...99 have been extended up to n=100. Composite numbers that appeared newly got through ECM 118 times at level 35. Most unknown factors are supposed to be greater than 1030.

February 15, 2011

Ray Chandler proved 4192 near-repdigit prime number between 401-digit and 500-digit.

Factorizations of 99...99499...99 and Factorizations of 99...99599...99 have been extended up to n=100. Composite numbers that appeared newly got through ECM 118 times at level 35. Most unknown factors are supposed to be greater than 1030.

February 14, 2011

Factorizations of 99...99299...99 have been extended up to n=100. Composite numbers that appeared newly got through ECM 118 times at level 35. Most unknown factors are supposed to be greater than 1030.

February 13, 2011

Ray Chandler proved 4192 near-repdigit prime number between 301-digit and 400-digit.

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

Proven near-repdigit primes
 digitsflabelwlabelexpressionwhenwho
14648444999949w5·10464843-1February 13, 2011David Broadhurst

Factorizations of 99...99199...99 have been extended up to n=100. Composite numbers that appeared newly got through ECM 118 times at level 35. Most unknown factors are supposed to be greater than 1030.

February 12, 2011

Ray Chandler proved 403 near-repdigit-related prime numbers between 1500-digit and 1699-digit by Primo. Certifications are available.

Factorizations of 77...77877...77 and Factorizations of 77...77977...77 have been extended up to n=100. Composite numbers that appeared newly got through ECM 118 times at level 35. Most unknown factors are supposed to be greater than 1030.

David Broadhurst found the 66th prime number of the form 198720403123163585927608716·10n-1. See also primecount.txt.

Proven near-repdigit-related primes (except ru/nr/pd/qr)
 digitsflabelwlabelexpressionwhenwho
1099534 1987204031231635859276087159w198720403123163585927608716·1099507-1February 12, 2011David Broadhurst

February 11, 2011

Gary Barnes found a near-repdigit prime.

Proven near-repdigit primes
 digitsflabelwlabelexpressionwhenwho
16189587 9989w999·10189584-1February 11, 2011Gary Barnes

February 10, 2011

Factorizations of 77...77677...77 have been extended up to n=100. Composite numbers that appeared newly got through ECM 118 times at level 35. Most unknown factors are supposed to be greater than 1030.

February 9, 2011

Factorizations of 77...77577...77 have been extended up to n=100. Composite numbers that appeared newly got through ECM 118 times at level 35. Most unknown factors are supposed to be greater than 1030.

February 8, 2011

Factorizations of 77...77477...77 have been extended up to n=100. Composite numbers that appeared newly got through ECM 118 times at level 35. Most unknown factors are supposed to be greater than 1030.

February 7, 2011

Factorizations of 99...99899...99 have been extended up to n=150 by Serge Batalov. Most unknown factors are supposed to be greater than 1033.

Factorizations of 77...77377...77 have been extended up to n=100. Composite numbers that appeared newly got through ECM 118 times at level 35. Most unknown factors are supposed to be greater than 1030.

February 5, 2011

David Broadhust found 2 primes.

Proven near-repdigit-related primes (except ru/nr/pd/qr)
 digitsflabelwlabelexpressionwhenwho
2255862 451328423796179w45132842379618·10255848-1February 4, 2011David Broadhurst
1098404 854085679w85408568·1098396-1February 5, 2011David Broadhurst

Factorizations of 77...77277...77 have been extended up to n=100. Composite numbers that appeared newly got through ECM 118 times at level 35. Most unknown factors are supposed to be greater than 1030.

February 4, 2011

Factorizations of 33...33833...33 and Factorizations of 77...77177...77 have been extended up to n=100. Composite numbers that appeared newly got through ECM 118 times at level 35. Most unknown factors are supposed to be greater than 1030.

February 3, 2011

Stefano D'Urso found a near-repdigit prime.

Proven near-repdigit primes
 digitsflabelwlabelexpressionwhenwho
17181176 99999979w9999998·10181169-1February 3, 2011Stefano D'Urso

Factorizations of 33...33733...33 have been extended up to n=100. Composite numbers that appeared newly got through ECM 118 times at level 35. Most unknown factors are supposed to be greater than 1030.

February 2, 2011

David Broadhust found 3 near-repdigit-related primes.

Proven near-repdigit-related primes (except ru/nr/pd/qr)
 digitsflabelwlabelexpressionwhenwho
1071384 854085679w85408568·1071376-1February 2, 2011David Broadhurst
1265330 1987204031231635859276087159w198720403123163585927608716·1065303-1February 2, 2011David Broadhurst
1549740 854085679w85408568·1049732-1February 2, 2011David Broadhurst

Factorizations of 33...33133...33 and Factorizations of 33...33533...33 have been extended up to n=100. Composite numbers that appeared newly got through ECM 118 times at level 35. Most unknown factors are supposed to be greater than 1030.

February 1, 2011

David Broadhust found 4 primes of the form 85408568·10n-1.

Proven near-repdigit-related primes (except ru/nr/pd/qr)
 digitsflabelwlabelexpressionwhenwho
3723342 854085679w85408568·1023334-1February 1, 2011David Broadhurst
8015966 854085679w85408568·1015958-1February 1, 2011David Broadhurst
9513652 854085679w85408568·1013644-1February 1, 2011David Broadhurst
11111774 854085679w85408568·1011766-1February 1, 2011David Broadhurst

Serge Batalov found 4 primes of the form 19178079668730696804601623·10n-1.

Proven near-repdigit-related primes (except ru/nr/pd/qr)
 digitsflabelwlabelexpressionwhenwho
12310126 191780796687306968046016229w19178079668730696804601623·1010100-1February 1, 2011Serge Batalov
1557916 191780796687306968046016229w19178079668730696804601623·107890-1February 1, 2011Serge Batalov
1776549 191780796687306968046016229w19178079668730696804601623·106523-1February 1, 2011Serge Batalov
1836391 191780796687306968046016229w19178079668730696804601623·106365-1February 1, 2011Serge Batalov

January 2011

January 31, 2011

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

Proven near-repdigit primes
 digitsflabelwlabelexpressionwhenwho
14457744999949w5·10445773-1January 31, 2011David Broadhurst

David Broadhurst found the 64th prime number of the form 198720403123163585927608716·10n-1.

Proven near-repdigit-related primes (except ru/nr/pd/qr)
 digitsflabelwlabelexpressionwhenwho
1053964 1987204031231635859276087159w198720403123163585927608716·1053937-1January 31, 2011David Broadhurst
1141670 1987204031231635859276087159w198720403123163585927608716·1041643-1January 31, 2011David Broadhurst

Factorizations of 11...11911...11 have been extended up to n=100. Composite numbers that appeared newly got through ECM 118 times at level 35. Most unknown factors are supposed to be greater than 1030.

January 30, 2011

Gary Barnes found a near-repdigit prime.

Proven near-repdigit primes
 digitsflabelwlabelexpressionwhenwho
19171167 999929w99993·10171162-1January 30, 2011Gary Barnes

Serge Batalov proved 6 primes.

Proven near-repdigit primes
 digitsflabelwlabelexpressionwhenwho
4073042 9w899103042-101January 30, 2011Serge Batalov
5581414 9w899101414-101January 30, 2011Serge Batalov
6031235 9w8999101235-1001January 30, 2011Serge Batalov
6531007 9w8999101007-1001January 30, 2011Serge Batalov
Proven near-repdigit-related primes (except ru/nr/pd/qr)
 digitsflabelwlabelexpressionwhenwho
7931312 5813w2751(1744·101309-1747)/3January 30, 2011Serge Batalov
12991095 5813w2751(1744·101092-1747)/3January 30, 2011Serge Batalov

Bob Price found 11 PRPs.

Unprovable near-repdigit-related PRPs (except ru/nr/pd/qr)
 digitsflabelwlabelexpressionwhenwho
1767061001310w131076705+13January 30, 2011Bob Price
2754421001310w131075441+13January 30, 2011Bob Price
3746711003110w311074670+31January 30, 2011Bob Price
4726321003710w371072631+37January 30, 2011Bob Price
572268 10w331072267+33January 30, 2011Bob Price
7655381002710w271065537+27January 30, 2011Bob Price
9639871006310w631063986+63January 30, 2011Bob Price
10639171007910w791063916+79January 30, 2011Bob Price
11627511005710w571062750+57January 30, 2011Bob Price
12625241006310w631062523+63January 30, 2011Bob Price
14582511009310w931058250+93January 30, 2011Bob Price

Factorizations of 11...11711...11 and Factorizations of 11...11811...11 have been extended up to n=100. Composite numbers that appeared newly got through ECM 118 times at level 35. Most unknown factors are supposed to be greater than 1030.

January 29, 2011

Erik Branger found a near-repdigit PRP by PFGW and srsieve.

Unprovable near-repdigit PRPs
 digitsflabelwlabelexpressionwhenwho
4111706777717w1(7·10111706-61)/9January 29, 2011Erik Branger

Factorizations of 11...11611...11 have been extended up to n=100. Composite numbers that appeared newly got through ECM 118 times at level 35. Most unknown factors are supposed to be greater than 1030.

January 28, 2011

Many small near-repdigit (probable) prime numbers of the form AvBAw were added experimentally to the list. Larger known prime numbers will be added later.

David Broadhurst found the largest known prime of the form 45132842379618·10n-1. The number of primes of that form was increased to 63.

Proven near-repdigit-related primes (except ru/nr/pd/qr)
 digitsflabelwlabelexpressionwhenwho
1229218 451328423796179w45132842379618·10229204-1January 28, 2011David Broadhurst

Gary Barnes found three near-repdigit primes.

Proven near-repdigit primes
 digitsflabelwlabelexpressionwhenwho
20168728 99949w9995·10168724-1January 28, 2011Gary Barnes
2116750392999929w93·10167501-1January 28, 2011Gary Barnes
22167449 9929w993·10167446-1January 28, 2011Gary Barnes

Factorizations of 11...11511...11 have been extended up to n=100. Composite numbers that appeared newly got through ECM 118 times at level 35. Most unknown factors are supposed to be greater than 1030.

January 27, 2011

David Broadhurst found the largest known prime of the form 45132842379618·10n-1. The number of primes of that form was increased to 62.

Proven near-repdigit-related primes (except ru/nr/pd/qr)
 digitsflabelwlabelexpressionwhenwho
1225044 451328423796179w45132842379618·10225030-1January 27, 2011David Broadhurst

Factorizations of 11...11311...11 and Factorizations of 11...11411...11 have been extended up to n=100. Composite numbers that appeared newly got through ECM 118 times at level 35. Most unknown factors are supposed to be greater than 1030.

January 26, 2011

David Broadhurst found the largest known prime of the form 45132842379618·10n-1. The number of primes of that form was increased to 61.

Proven near-repdigit-related primes (except ru/nr/pd/qr)
 digitsflabelwlabelexpressionwhenwho
1218824 451328423796179w45132842379618·10218810-1January 26, 2011David Broadhurst

January 24, 2011

Gary Barnes found a near-repdigit prime.

Proven near-repdigit primes
 digitsflabelwlabelexpressionwhenwho
20161576 9999949w999995·10161570-1January 24, 2011Gary Barnes

January 22, 2011

Markus Tervooren proved 1 near-repdigit prime by Primo 3.0.9.

Proven near-repdigit primes
 digitsflabelwlabelexpressionwhenwho
2785996999979w7105996-3January 22, 2011Markus Tervooren

Factorizations of 266...669 have been extended up to n=250. Composite numbers that appeared newly got through ECM 118 times at level 35. Most unknown factors are supposed to be greater than 1030.

January 21, 2011

Stefano D'Urso found a near-repdigit prime.

Proven near-repdigit primes
 digitsflabelwlabelexpressionwhenwho
19168758 99999959w9999996·10168751-1January 21, 2011Stefano D'Urso

January 20, 2011

Gary Barnes found a near-repdigit prime.

Proven near-repdigit primes
 digitsflabelwlabelexpressionwhenwho
19154742 999919w99992·10154737-1January 20, 2011Gary Barnes

Factorizations of 988...889 have been extended up to n=250. Composite numbers that appeared newly got through ECM 118 times at level 35. Most unknown factors are supposed to be greater than 1030.

David Broadhurst found two primes of the form 45132842379618·10n-1. The number of prime numbers of that form was increased to 60.

Proven near-repdigit-related primes (except ru/nr/pd/qr)
 digitsflabelwlabelexpressionwhenwho
1173135 451328423796179w45132842379618·10173121-1January 20, 2011David Broadhurst
2172394 451328423796179w45132842379618·10172380-1January 20, 2011David Broadhurst

January 19, 2011

Gary Barnes found a near-repdigit prime.

Proven near-repdigit primes
 digitsflabelwlabelexpressionwhenwho
19153262 9999979w999998·10153256-1January 19, 2011Gary Barnes

January 18, 2011

Factorizations of 200...003 have been extended up to n=250. Composite numbers that appeared newly got through ECM 118 times at level 35. Most unknown factors are supposed to be greater than 1030.

January 17, 2011

Serge Batalov searched PRPs of the form 10n-101, 10n-1001, 10n-10001, 10n-100001, 10n-1000001, 10n-10000001 up to n=26000. See primesize.txt for details.

Unprovable near-repdigit PRPs
 digitsflabelwlabelexpressionwhenwho
5724499 9w899991024499-10001January 17, 2011Serge Batalov
6922851 9w899999991022851-10000001January 17, 2011Serge Batalov
8419812 9w8999991019812-100001January 17, 2011Serge Batalov

January 15, 2011

Ray Chandler proved 38 quasi-repdigit primes and 171 near-repdigit-related primes by Primo 3.0.9. All of them are 1400-1499 digit. See primesize.txt for details.

January 14, 2011

Gary Barnes found 3 near-repdigit primes by srsieve, sr2sieve, LLR.

Proven near-repdigit primes
 digitsflabelwlabelexpressionwhenwho
19142365 9999929w999993·10142359-1January 14, 2011Gary Barnes
20141163 9999959w999996·10141157-1January 14, 2011Gary Barnes
23138939 9959w996·10138936-1January 14, 2011Gary Barnes

January 13, 2011

Serge Batalov searched PRPs of the form (1744·10n-1747)/3 and successfully proved primality of a 39783-digit prime number by PFGW 3.4.4, Primo 3.0.9 and CHG.GP. Congratulations!

Proven near-repdigit-related primes (except ru/nr/pd/qr)
 digitsflabelwlabelexpressionwhenwho
139783 5813w2751(1744·1039780-1747)/3January 13, 2011Serge Batalov
2595680 5813w2751(1744·10677-1747)/3January 13, 2011Serge Batalov
5030320 5813w2751(1744·10317-1747)/3January 13, 2011Serge Batalov
5460280 5813w2751(1744·10277-1747)/3January 13, 2011Serge Batalov
6555196 5813w2751(1744·10193-1747)/3January 13, 2011Serge Batalov
7729135 5813w2751(1744·10132-1747)/3January 13, 2011Serge Batalov
Unprovable near-repdigit-related PRPs (except ru/nr/pd/qr)
 digitsflabelwlabelexpressionwhenwho
197612027 5813w2751(1744·1012024-1747)/3January 13, 2011Serge Batalov
41366202 5813w2751(1744·106199-1747)/3January 13, 2011Serge Batalov
78901864 5813w2751(1744·101861-1747)/3January 13, 2011Serge Batalov
85581376 5813w2751(1744·101373-1747)/3January 13, 2011Serge Batalov
85591336 5813w2751(1744·101333-1747)/3January 13, 2011Serge Batalov
85601312 5813w2751(1744·101309-1747)/3January 13, 2011Serge Batalov
85611095 5813w2751(1744·101092-1747)/3January 13, 2011Serge Batalov

January 10, 2011

Ray Chandler proved 36 quasi-repdigit primes and 166 near-repdigit-related primes by Primo 3.0.9. All of them are 1300-1399 digit. See primesize.txt for details.

Bob Price found 1 quasi-repdigit PRP and 4 near-repdigit-related PRPs by PFGW.

Unprovable quasi-repdigit PRPs
 digitsflabelwlabelexpressionwhenwho
35607771000310w31060776+3January 10, 2011Bob Price
Unprovable near-repdigit-related PRPs (except ru/nr/pd/qr)
 digitsflabelwlabelexpressionwhenwho
1660341001910w191066033+19January 10, 2011Bob Price
2654271001310w131065426+13January 10, 2011Bob Price
4558121002110w211055811+21January 10, 2011Bob Price
5553731003710w371055372+37January 10, 2011Bob Price

January 8, 2011

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

Proven near-repdigit primes
 digitsflabelwlabelexpressionwhenwho
14145095999959w6·10414508-1January 8, 2011David Broadhurst

Markus Tervooren proved 1 near-repdigit prime by Primo 3.0.9.

Proven near-repdigit primes
 digitsflabelwlabelexpressionwhenwho
32536722111121w(19·103671-1)/9January 8, 2011Markus Tervooren

Ray Chandler proved 53 quasi-repdigit primes and 195 near-repdigit-related primes by Primo 3.0.9. All of them are 1200-1300 digit. See primesize.txt for details.

January 7, 2011

David Broadhurst found the largest known near-repdigit prime number by Srsieve, LLR, NewPGen and OpenPFGW. Congratulations!

Proven near-repdigit primes
 digitsflabelwlabelexpressionwhenwho
13836448999989w9·10383643-1January 7, 2011David Broadhurst

January 6, 2011

Ray Chandler proved 120 quasi-repdigit primes and 441 near-repdigit-related primes by Primo 3.0.9. All of them are 1000-1200 digit. See primesize.txt for details.

Gary Barnes found 10 near-repdigit primes and 1 quasi-repdigit prime by srsieve, sr2sieve and LLR.

Proven near-repdigit primes
 digitsflabelwlabelexpressionwhenwho
27129024 99949w9995·10129020-1January 1, 2011Gary Barnes
2912505897999979w98·10125056-1January 1, 2011Gary Barnes
30123281 9999989w999999·10123275-1January 1, 2011Gary Barnes
34115774 999949w99995·10115769-1January 1, 2011Gary Barnes
37110608 9929w993·10110605-1January 1, 2011Gary Barnes
38108641 999989w99999·10108636-1January 1, 2011Gary Barnes
44103668 9999959w999996·10103662-1January 1, 2011Gary Barnes
45102910 9999979w999998·10102904-1January 1, 2011Gary Barnes
46101113 999959w99996·10101108-1January 1, 2011Gary Barnes
47100119 999929w99993·10100114-1January 1, 2011Gary Barnes
Proven quasi-repdigit primes
 digitsflabelwlabelexpressionwhenwho
84136334999349w35·1041361-1January 1, 2011Gary Barnes

January 5, 2011

Tyler Cadigan proved 7334-digit prime number Φ13905(10)/83431/333721 by Primo 3.0.8. It brings a proof of 27811-digit near-repdigit prime number (8·1027811-71)/9 by kppm.gp. Congratulations!

Erik Branger and Serge Batalov also proved the 7334-digit prime number by Primo 3.0.9. Congratulations!

Proven near-repdigit primes
 digitsflabelwlabelexpressionwhenwho
12627811888818w1(8·1027811-71)/9January 5, 2011Tyler Cadigan, Erik Branger, Serge Batalov

January 4, 2011

Maksym Voznyy proved 1 near-repdigit prime by Primo.

Proven near-repdigit primes
 digitsflabelwlabelexpressionwhenwho
31436288111181w(73·103627-1)/9January 4, 2011Maksym Voznyy

January 3, 2011

Gary Barnes found 1 near-repdigit prime by Srsieve and LLR.

Proven near-repdigit primes
 digitsflabelwlabelexpressionwhenwho
19134964 999989w99999·10134959-1January 3, 2011Gary Barnes

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

Unprovable plateau and depression PRPs
 digitsflabelwlabelexpressionwhenwho
3847737999779w78·1084772-3January 3, 2011Ray Chandler

Maksym Voznyy proved 3 near-repdigit primes by Primo.

Proven near-repdigit primes
 digitsflabelwlabelexpressionwhenwho
3153530999979w7103530-3January 3, 2011Maksym Voznyy
3203395999919w1103395-9January 3, 2011Maksym Voznyy
3213395888838w3(8·103395-53)/9January 3, 2011Maksym Voznyy

January 2, 2011

Gary Barnes found 2 near-repdigit primes by Srsieve and LLR.

Proven near-repdigit primes
 digitsflabelwlabelexpressionwhenwho
20132747 999929w99993·10132742-1January 2, 2011Gary Barnes
21131932 9999989w999999·10131926-1January 2, 2011Gary Barnes

January 1, 2011

Gary Barnes found 2 near-repdigit primes by Srsieve and LLR.

Proven near-repdigit primes
 digitsflabelwlabelexpressionwhenwho
2213139697999979w98·10131394-1January 1, 2011Gary Barnes
2313062294999949w95·10130620-1January 1, 2011Gary Barnes

Bob Price proved 8 near-repdigit-related primes by Primo. Two of them are greater than 105000.

Proven near-repdigit-related primes (except ru/nr/pd/qr)
 digitsflabelwlabelexpressionwhenwho
15053801003910w39105379+39January 1, 2011Bob Price
15352451003910w39105244+39January 1, 2011Bob Price
24124121004910w49102411+49January 1, 2011Bob Price
25422311003710w37102230+37January 1, 2011Bob Price
26720641001910w19102063+19January 1, 2011Bob Price
27420241004910w49102023+49January 1, 2011Bob Price
31717781004910w49101777+49January 1, 2011Bob Price
32417601001910w19101759+19January 1, 2011Bob Price

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

Proven near-repdigit-related primes (except ru/nr/pd/qr)
 digitsflabelwlabelexpressionwhenwho
16147173110931w09(28·104716-19)/9January 1, 2011Serge Batalov

Bob Price found 4 near-repdigit-related PRPs by PFGW.

Unprovable near-repdigit-related PRPs (except ru/nr/pd/qr)
 digitsflabelwlabelexpressionwhenwho
2496581003110w311049657+31January 1, 2011Bob Price
5484431005710w571048442+57January 1, 2011Bob Price
6480041002110w211048003+21January 1, 2011Bob Price
7477291007910w791047728+79January 1, 2011Bob Price
Copyright (C) 1999-2011 Makoto Kamada All Rights Reserved.