PRP Records

Probable Primes Top 10000

(291910 PRPs in the top)


What is a PRP ?

A PRP is a probable prime number, a number that nobody knows how to prove or disprove its primality.
Here are some criterions that can be used to recognize these numbers :

- N does not have any prime factor up to 2^32.
- N cannot be trivially written into a product.
- Take 3 square-free consecutive bases such that (b1/N)=(b2/N)=(b3/N)= -1. N should be such that b1^((N-1)/2)=b2^((N-1)/2)=b3^((N-1)/2)= -1 (mod N).
- Take a prime base such that (b/N)= -1 and b<>b1<>b2<>b3. N should pass the strong test in base b.
- or more (if someone has got an idea) !!!


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1-250   251-500   501-750   751-1000   1001-1250   1251-1500   1501-1750   1751-2000   
2001-2250   2251-2500   2501-2750   2751-3000   3001-3250   3251-3500   3501-3750   3751-4000   
4001-4250   4251-4500   4501-4750   4751-5000   5001-5250   5251-5500   5501-5750   5751-6000   
6001-6250   6251-6500   6501-6750   6751-7000   7001-7250   7251-7500   7501-7750   7751-8000   
8001-8250   8251-8500   8501-8750   8751-9000   9001-9250   9251-9500   9501-9750   9751-10000   


Rank Probable prime Digits (> 50000) Who ? When ?
50012^369081-55111105Lelio R Paula02/2013
5002(2^369047+3618)/2111094Stefano Morozzi09/2020
500388^57124-87111077Norbert Schneider11/2015
50042^368980+753111075Lelio R Paula05/2013
50052^368946-3623111064Yves Minet03/2017
50062^368929+29835111059Lelio R Paula05/2017
50074^184463-3^184463111058Jean-Louis Charton12/2004
5008111^54298+110111057Norbert Schneider04/2017
5009(4*10^111032-7)/3111033Ray Chandler04/2011
501035799^1262+1262^35799111015Hans Havermann10/2020
5011(298*10^111004+11)/3111006Robert Price11/2020
501227648^10349+10349^27648111004Hans Havermann11/2020
501328899^6932+6932^28899110997Hans Havermann11/2020
50142^368641-460303110972Enzo Doria06/2015
50152^368619-109087110966Enzo Doria04/2014
5016(74*10^110961+313)/9110962Robert Price06/2019
501725258^24711+24711^25258110956Hans Havermann11/2020
5018(2^368539+1290)/2110941Stefano Morozzi01/2021
50193*2^368489+7110927Lelio R Paula09/2014
5020(14*10^110922+61)/3110923Robert Price12/2018
502197411!4-2110913Robert Price07/2017
5022(301*10^110903+23)/9110905Robert Price06/2021
5023(9179*2^368330-1)/35110881Lelio R Paula05/2015
502425830^19619+19619^25830110880Hans Havermann10/2020
5025(34*10^110882-7)/9/13/29/1019374319110871Makoto Morimoto05/2016
502626022^18191+18191^26022110850Hans Havermann10/2020
5027(2^368211+2250)/2110843Stefano Morozzi01/2021
5028(37*10^110813+251)/9110814Robert Price09/2021
50292^368050-64875110795Lelio R Paula05/2017
50302^368048+25110794Lelio R Paula02/2013
5031(2^368017+2262)/2110784Stefano Morozzi02/2021
503269^60239-2110771Lelio R Paula10/2013
5033(23*2^367952+1)/15717110762Lelio R Paula03/2014
50342^367924-69110757Lelio R Paula02/2013
5035(23*10^110738+61)/3110739Robert Price01/2022
5036(2^367779+3750)/2110713Stefano Morozzi01/2021
50372^367709-109723110692Enzo Doria04/2014
5038(3*2^367644-1)/107110671Lelio R Paula03/2014
5039(2^367626+3514)/2110667Stefano Morozzi09/2020
5040(23*2^367398+1)/57963110595Lelio R Paula03/2014
5041140^51515-139110558Norbert Schneider04/2019
50422^367215+1879223110543Enzo Doria09/2016
504325782^19375+19375^25782110534Hans Havermann10/2020
504426117^17058+17058^26117110526Hans Havermann10/2020
50452^367141+41110521Lelio R Paula02/2013
50462^367126+29835110516Lelio R Paula05/2017
5047(10^110503-1)/9+2*(10^59183-1)/9*10^25660110503Makoto Morimoto09/2020
5048(10^110503-1)/9+2*(10^65511-1)/9*10^22496110503Makoto Morimoto09/2020
5049(10^110503-1)/9+2*10^108327+2*10^2175110503Makoto Morimoto09/2020
5050(10^110503-1)/9+2*10^66251+2*10^44251110503Makoto Morimoto09/2020
5051(10^110503-1)/9+3*(10^28813-1)/9*10^40845110503Makoto Morimoto09/2020
5052(10^110503-1)/9+3*(10^82573-1)/9*10^13965110503Makoto Morimoto09/2020
5053(10^110503-1)/9+4*(10^43305-1)/9*10^33599110503Makoto Morimoto09/2020
5054(10^110503-1)/9+5*10^70327+5*10^40175110503Makoto Morimoto09/2020
5055(10^110503-1)/9+5*10^99423+5*10^11079110503Makoto Morimoto09/2020
5056(10^110503-1)/9+7*(10^23617-1)/9*10^43443110503Makoto Morimoto09/2020
5057(10^110503-1)/9+8*(10^30251-1)/9*10^40126110503Makoto Morimoto09/2020
50583*(10^110503-1)/9+1*10^106036+1*10^4466110503Makoto Morimoto09/2020
50593*(10^110503-1)/9+1*10^58962+1*10^51540110503Makoto Morimoto09/2020
50603*(10^110503-1)/9+1*10^78213+1*10^32289110503Makoto Morimoto09/2020
50613*(10^110503-1)/9+2*10^76898+2*10^33604110503Makoto Morimoto09/2020
50623*(10^110503-1)/9-1*10^100802-1*10^9700110503Makoto Morimoto09/2020
50633*(10^110503-1)/9-1*10^76355-1*10^34147110503Makoto Morimoto09/2020
50643*(10^110503-1)/9-2*10^105704-2*10^4798110503Makoto Morimoto09/2020
50657*(10^110503-1)/9+1*(10^27685-1)/9*10^41409110503Makoto Morimoto09/2020
50667*(10^110503-1)/9+1*(10^91035-1)/9*10^9734110503Makoto Morimoto09/2020
50677*(10^110503-1)/9-1*(10^23717-1)/9*10^43393110503Makoto Morimoto09/2020
50687*(10^110503-1)/9-1*10^57906-1*10^52596110503Makoto Morimoto09/2020
50697*(10^110503-1)/9-1*10^72287-1*10^38215110503Makoto Morimoto09/2020
50707*(10^110503-1)/9-2*(10^53823-1)/9*10^28340110503Makoto Morimoto09/2020
50717*(10^110503-1)/9-2*(10^88659-1)/9*10^10922110503Makoto Morimoto09/2020
50727*(10^110503-1)/9-3*(10^79921-1)/9*10^15291110503Makoto Morimoto09/2020
50737*(10^110503-1)/9-3*10^60024-3*10^50478110503Makoto Morimoto09/2020
50747*(10^110503-1)/9-4*(10^103091-1)/9*10^3706110503Makoto Morimoto09/2020
50757*(10^110503-1)/9-4*10^103658-4*10^6844110503Makoto Morimoto09/2020
50767*(10^110503-1)/9-4*10^78188-4*10^32314110503Makoto Morimoto09/2020
50777*(10^110503-1)/9-5*(10^35035-1)/9*10^37734110503Makoto Morimoto09/2020
50787*(10^110503-1)/9-6*(10^67347-1)/9*10^21578110503Makoto Morimoto09/2020
50797*(10^110503-1)/9-6*10^60391-6*10^50111110503Makoto Morimoto09/2020
5080(10^110503-1)-4*(10^96247-1)/9*10^7128110503Makoto Morimoto09/2020
5081(10^110503-1)-4*10^74037-4*10^36465110503Makoto Morimoto09/2020
5082(10^110503-1)-4*10^77787-4*10^32715110503Makoto Morimoto09/2020
5083(10^110503-1)-4*10^91179-4*10^19323110503Makoto Morimoto09/2020
5084(10^110503-1)-5*(10^99143-1)/9*10^5680110503Makoto Morimoto09/2020
5085(10^110503-1)-7*(10^85075-1)/9*10^12714110503Makoto Morimoto09/2020
5086(10^110503-1)-7*10^100712-7*10^9790110503Makoto Morimoto09/2020
5087(10^110503-1)-7*10^76427-7*10^34075110503Makoto Morimoto09/2020
5088(10^110503-1)-7*10^90451-7*10^20051110503Makoto Morimoto09/2020
5089(10^110503-1)-8*10^106252-8*10^4250110503Makoto Morimoto09/2020
5090(11*10^110496+49)/3110497Robert Price07/2018
509125447^21958+21958^25447110481Hans Havermann11/2020
5092(31*2^366976+1)/7110472Lelio R Paula03/2014
50937*10^110468-23110469Robert Price07/2019
50942^366853+5711110434Lelio R Paula05/2017
5095(21181*2^366833+1)/3110432Lelio R Paula07/2014
50962^366816+315110423Lelio R Paula05/2017
50972^366775-2787037110411Enzo Doria03/2016
5098(112*10^110405-1)/3110407Serge Batalov12/2014
50992^366751+2797553110404Enzo Doria03/2016
510025276^23331+23331^25276110404Hans Havermann10/2020
51012^366748+255110403Lelio R Paula05/2017
51022^366738-2985110400Yves Minet09/2014
5103(23*2^366739+1)/74575110396Lelio R Paula03/2014
5104(2^366722+1314)/2110395Stefano Morozzi02/2021
51052^366716+1871791110393Enzo Doria05/2016
51062^366649+1871687110373Enzo Doria05/2016
51072^366629-351205110367Enzo Doria06/2015
5108(31*10^110363+257)/9110364Robert Price12/2021
5109(17*19^86292-215)/18110347Eric Chen01/2023
51112^366558+1874479110345Enzo Doria06/2016
511025132^24581+24581^25132110345Hans Havermann10/2020
5112(2^366539+770)/2110339Stefano Morozzi09/2020
511326368^15285+15285^26368110331Hans Havermann10/2020
5114(23*10^110290+19)/3110291Robert Price07/2019
511518^87853-4409110280Enzo Doria03/2013
511628490^7419+7419^28490110267Hans Havermann11/2020
51172^366218-23110243Lelio R Paula02/2013
5118(21*2^366193-1)/197110235Lelio R Paula03/2014
51192^366178-343991110231Enzo Doria07/2015
512025777^18798+18798^25777110174Hans Havermann10/2020
51212^365944+1871341110161Enzo Doria05/2016
51222^365838-461267110129Enzo Doria07/2015
512330152^4491+4491^30152110126Hans Havermann11/2020
512410^110111+464019110112Patrick De Geest05/2021
512510^110111-40001110111Robert Price01/2021
51262^365763-6555110106Lelio R Paula04/2017
5127(2^365689+2^182845+1)/511008311/2006
51282^365666-459161110077Enzo Doria05/2015
51293*10^110076-7110077Robert Price08/2015
513013^98785-72110041Lelio R Paula03/2017
5131(25^78707+1)/26110027Robert Price06/2013
5132(7*10^110027-277)/9110027Robert Price02/2022
5133(16*10^110014-73)/3110015Robert Price07/2020
5134(7*10^110006-151)/9110006Robert Price02/2018
51356^141361-7110001Lelio R Paula11/2014
513620^84536+81109984Lelio R Paula03/2017
51375*2^365347-9109982Lelio R Paula09/2014
51389*6^141303+7109957Lelio R Paula11/2014
513927635^9522+9522^27635109953Hans Havermann11/2020
514078^58099+77109929Norbert Schneider02/2015
51412*10^109928-7109929Robert Price10/2015
514230580^3933+3933^30580109927Hans Havermann11/2020
514326380^14689+14689^26380109926Hans Havermann11/2020
5144(2^365161+1130)/2109925Stefano Morozzi09/2020
5145(27*2^365137-1)/2021109916Lelio R Paula03/2014
5146(4441*29^75152-24)/7109905Curtis Bright05/2015
5147(2^365087+7)/6015109899Lelio R Paula01/2014
5148(2^365069+3774)/2109897Stefano Morozzi02/2021
514929652^5083+5083^29652109894Mark Rodenkirch10/2020
5150(2^365049+722)/2109891Stefano Morozzi09/2020
5151(35*10^109888-89)/9109889Robert Price02/2022
515218^87533-11109878Lelio R Paula04/2017
51532^364982-5109871Henri Lifchitz04/2006
51543*10^109861+59109862Robert Price08/2018
51555*10^109860-69109861Robert Price02/2021
51562^364936-1867979109857Enzo Doria04/2016
515727013^11652+11652^27013109846Hans Havermann10/2020
51582^364867-112087109836Enzo Doria06/2014
51594^182415-85061109825Mike Oakes06/2011
5160(2^364809+1034)/2109819Stefano Morozzi09/2020
5161(53*10^109809-287)/9109810Robert Price02/2022
5162(52*10^109807-133)/9109808Robert Price09/2021
516325708^18675+18675^25708109806Hans Havermann10/2020
5164(17^89227+16^89227)/33109788Robert Price08/2013
51652^364687-187109782Lelio R Paula01/2012
51662^364644+67109769Lelio R Paula01/2012
5167(9787*2^364625-1)/24947109763Lelio R Paula05/2015
5168(2^364616+5)/9109760Lelio R Paula01/2014
5169(55*10^109759+89)/9109760Robert Price03/2019
517012^101694+73109747Lelio R Paula03/2017
517113^98518-66109744Lelio R Paula03/2017
5172(8*10^109721-269)/9109721Robert Price09/2021
51732^364478-113261109719Enzo Doria07/2014
5174(2^364513+1)/(3*44290516579)109719Gord Palameta08/2018
5175(24737*2^364454+1)/3109716Lelio R Paula07/2014
517627814^8777+8777^27814109681Hans Havermann10/2020
5177(62*10^109673+1)/9109674Serge Batalov11/2010
51783^229824+340109654Lelio R Paula03/2017
5179(2*10^109645-71)/3109645Robert Price12/2017
51802^364169-112813109626Enzo Doria06/2014
518128822^6359+6359^28822109622Hans Havermann11/2020
518210^109615+21109616Lelio R Paula03/2017
518310^109615-456267109615Patrick De Geest03/2017
51842^364094-113109604Lelio R Paula01/2012
518525251^21898+21898^25251109600Hans Havermann11/2020
5186(4^182026+11)/3109591Robert Price02/2017
51872^364041-6883109588Lelio R Paula09/2011
518812^101545+11109586Lelio R Paula03/2017
518926536^13475+13475^26536109582Hans Havermann11/2020
51902^363842-2787101109528Enzo Doria03/2016
5191(2^363812+3570)/2109519Stefano Morozzi09/2020
5192(22699*2^363782+1)/763109511Lelio R Paula07/2014
51932^363769+5711109506Lelio R Paula04/2017
5194(31*2^363748+1)/49109499Lelio R Paula03/2014
5195(2^363670+100280245065)109476Paul Bourdelais05/2022
5196p(22245)#/2-8109462Robert Price01/2017
51972^363556+55109442Lelio R Paula01/2012
5198(509*10^109414+31)/9109416Robert Price08/2022
5199(2^363437+1682)/2109406Stefano Morozzi09/2020
5200(55459*2^363411+1)/81109401Lelio R Paula07/2014
52012^363406+1871569109397Enzo Doria05/2016
5202(2^363370+1338)/2109385Stefano Morozzi02/2021
5203(2^363349+7)/9109378Lelio R Paula01/2014
52043^229236+100109374Lelio R Paula03/2017
5205(2^363315+3258)/2109369Stefano Morozzi02/2021
52062^363268-58695109355Lelio R Paula04/2017
52072^363191-112321109332Enzo Doria06/2014
520826231^14718+14718^26231109327Hans Havermann10/2020
520925461^19672+19672^25461109326Hans Havermann10/2020
52104*10^109316-63109317Robert Price10/2018
52112^363120+3109311Donovan Johnson04/2006
5212(10^109297-1)/9109297Paul Bourdelais, Harvey Dubner04/2007
52132^363042-114641109287Enzo Doria04/2015
52142^363020-112793109280Enzo Doria06/2014
5215(85*10^109253+203)/9109254Robert Price09/2020
521624990^23431+23431^24990109202Hans Havermann10/2020
5217(2^362746+3738)/2109198Stefano Morozzi09/2020
5218(2^362716+1282)/2109189Stefano Morozzi01/2021
5219(67607*2^362695+1)/70499109183Lelio R Paula07/2014
522025060^22737+22737^25060109180Hans Havermann10/2020
5221(9*2^362644+1)/5109167Lelio R Paula03/2014
52225^156181+38109166Lelio R Paula02/2017
5223(2^362623+3618)/2109161Stefano Morozzi09/2020
522425138^21993+21993^25138109157Hans Havermann10/2020
52254*10^109142+91109143Robert Price08/2018
52263^228750+68109142Lelio R Paula03/2017
5227(2^362561+786)/2109142Stefano Morozzi09/2020
5228(23*10^109113+61)/3109114Robert Price01/2022
52292*10^109100-49109101Robert Price09/2020
5230(10223*2^362376+1)/9109090Lelio R Paula07/2014
523165^60167-64^60167109078Robert Price08/2013
52327*3^228589-2109066Lelio R Paula09/2014
523324874^24243+24243^24874109063Hans Havermann11/2020
5234(17*10^109059-161)/9109060Robert Price02/2021
523529158^5495+5495^29158109050Hans Havermann11/2020
5236(78557*2^362188+1)/189109033Lelio R Paula07/2014
52372*7^129008+9109025Lelio R Paula11/2014
523888*10^109022+7109024Robert Price03/2020
523928194^7337+7337^28194108985Hans Havermann10/2020
5240(5*10^108960+91)/3108961Robert Price04/2018
52412^361957+76367108960Enzo Doria05/2016
52422^361873-1411108935Yves Minet01/2013
5243(24737*2^361857+1)/35108933Lelio R Paula07/2014
5244115^52842-114108892Norbert Schneider07/2018
524513^97745-24108883Lelio R Paula03/2017
5246(2^361696+2562)/2108882Stefano Morozzi09/2020
524717^88475+8108864Lelio R Paula04/2017
52482^361567+51108843Lelio R Paula01/2012
52492^361563-109501108842Enzo Doria04/2014
525012^100852+83108838Lelio R Paula03/2017


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Created by  Henri Lifchitz & Renaud Lifchitz : October, 26 2000, last modification: February, 02 2023 13:22 (Time in France)

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