PRP Records

Probable Primes Top 10000

(301668 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 ?
7001(31*10^110363+257)/9110364Robert Price12/2021
7002(5^183291)%(4^183291)110353Henri Lifchitz06/2025
7003(17*19^86292-215)/18110347Eric Chen01/2023
70052^366558+1874479110345Enzo Doria06/2016
700425132^24581+24581^25132110345Hans Havermann10/2020
7006(2^366539+770)/2110339Stefano Morozzi09/2020
700726368^15285+15285^26368110331Hans Havermann10/2020
7008(23*10^110290+19)/3110291Robert Price07/2019
700918^87853-4409110280Enzo Doria03/2013
701028490^7419+7419^28490110267Hans Havermann11/2020
70112^366218-23110243Lelio R Paula02/2013
7012(21*2^366193-1)/197110235Lelio R Paula03/2014
70132^366178-343991110231Enzo Doria07/2015
701412^102123-11110210Riley Fisher09/2023
7015(725*35^71368+16649)/34110199Eric Chen05/2025
701625777^18798+18798^25777110174Hans Havermann10/2020
70172^365944+1871341110161Enzo Doria05/2016
70182^365838-461267110129Enzo Doria07/2015
701930152^4491+4491^30152110126Hans Havermann11/2020
70202^365802+23359110118Enzo Doria10/2023
702110^110111+464019110112Patrick De Geest05/2021
702210^110111-40001110111Robert Price01/2021
70232^365763-6555110106Lelio R Paula04/2017
7024(2^365689+2^182845+1)/511008311/2006
7025(83^57367-1)/3536509644718110080Paul Vanderveen05/2025
70262^365666-459161110077Enzo Doria05/2015
70273*10^110076-7110077Robert Price08/2015
702813^98785-72110041Lelio R Paula03/2017
7030(25^78707+1)/26110027Robert Price06/2013
7029(7*10^110027-277)/9110027Robert Price02/2022
7031(16*10^110014-73)/3110015Robert Price07/2020
7032(7*10^110006-151)/9110006Robert Price02/2018
70336^141361-7110001Lelio R Paula11/2014
703410^110000+8029681110001Hayden Chesnut11/2024
703510^110000+2044477110001Hayden Chesnut11/2024
703610^110000+76407110001Hayden Chesnut11/2024
703710^110000+167311110001Hayden Chesnut11/2024
703820^84536+81109984Lelio R Paula03/2017
70395*2^365347-9109982Lelio R Paula09/2014
70409*6^141303+7109957Lelio R Paula11/2014
704127635^9522+9522^27635109953Hans Havermann11/2020
704278^58099+77109929Norbert Schneider02/2015
70432*10^109928-7109929Robert Price10/2015
704430580^3933+3933^30580109927Hans Havermann11/2020
704526380^14689+14689^26380109926Hans Havermann11/2020
7046(2^365161+1130)/2109925Stefano Morozzi09/2020
7047(27*2^365137-1)/2021109916Lelio R Paula03/2014
704829^75157-30109910Anonymous09/2024
7049(4441*29^75152-24)/7109905Curtis Bright05/2015
7050(2^365087+7)/6015109899Lelio R Paula01/2014
7051(2^365069+3774)/2109897Stefano Morozzi02/2021
705229652^5083+5083^29652109894Mark Rodenkirch10/2020
7053(2^365049+722)/2109891Stefano Morozzi09/2020
7054(35*10^109888-89)/9109889Robert Price02/2022
705518^87533-11109878Lelio R Paula04/2017
70562^364982-5109871Henri Lifchitz04/2006
70573*10^109861+59109862Robert Price08/2018
70585*10^109860-69109861Robert Price02/2021
70592^364936-1867979109857Enzo Doria04/2016
706027013^11652+11652^27013109846Hans Havermann10/2020
70612^364867-112087109836Enzo Doria06/2014
70624^182415-85061109825Mike Oakes06/2011
7063(2^364809+1034)/2109819Stefano Morozzi09/2020
706424972^24972-8323^8323109814Henri Lifchitz10/2024
7065(53*10^109809-287)/9109810Robert Price02/2022
7066(52*10^109807-133)/9109808Robert Price09/2021
706725708^18675+18675^25708109806Hans Havermann10/2020
7068(17^89227+16^89227)/33109788Robert Price08/2013
70692^364687-187109782Lelio R Paula01/2012
70702^364644+67109769Lelio R Paula01/2012
7071(9787*2^364625-1)/24947109763Lelio R Paula05/2015
7072(2^364616+5)/9109760Lelio R Paula01/2014
7073(55*10^109759+89)/9109760Robert Price03/2019
7074(14*32^72921+4171)/31109757Eric Chen04/2023
707512^101694+73109747Lelio R Paula03/2017
707613^98518-66109744Lelio R Paula03/2017
7077(35^71069+2^71069)/37109734Robert Price01/2025
7078(8*10^109721-269)/9109721Robert Price09/2021
70792^364478-113261109719Enzo Doria07/2014
7080(2^364513+1)/(3*44290516579)109719Gord Palameta08/2018
7081(24737*2^364454+1)/3109716Lelio R Paula07/2014
708227814^8777+8777^27814109681Hans Havermann10/2020
7083(62*10^109673+1)/9109674Serge Batalov11/2010
70843^229824+340109654Lelio R Paula03/2017
7085(16623*33^72206-8095)/16109649Eric Chen05/2023
7086(2*10^109645-71)/3109645Robert Price12/2017
7087V(786978)109644Serge Batalov07/2024
70882^364169-112813109626Enzo Doria06/2014
708928822^6359+6359^28822109622Hans Havermann11/2020
709010^109615+21109616Lelio R Paula03/2017
709110^109615-456267109615Patrick De Geest03/2017
7092522^40331-40331^522109607Norman Luhn09/2024
70932^364094-113109604Lelio R Paula01/2012
709425251^21898+21898^25251109600Hans Havermann11/2020
7095(4^182026+11)/3109591Robert Price02/2017
70962^364041-6883109588Lelio R Paula09/2011
709712^101545+11109586Lelio R Paula03/2017
709826536^13475+13475^26536109582Hans Havermann11/2020
70992^363842-2787101109528Enzo Doria03/2016
7100(2^363812+3570)/2109519Stefano Morozzi09/2020
7101(996^36527+1)/997109515Jinyuan Wang12/2024
7102(22699*2^363782+1)/763109511Lelio R Paula07/2014
71032^363769+5711109506Lelio R Paula04/2017
7104(31*2^363748+1)/49109499Lelio R Paula03/2014
710526^77372+25109480Anonymous09/2024
7106(2^363670+100280245065)109476Paul Bourdelais05/2022
7107p(22245)#/2-8109462Robert Price01/2017
71082^363556+55109442Lelio R Paula01/2012
7109(509*10^109414+31)/9109416Robert Price08/2022
7110(2^363437+1682)/2109406Stefano Morozzi09/2020
7111(55459*2^363411+1)/81109401Lelio R Paula07/2014
71122^363406+1871569109397Enzo Doria05/2016
7113(129^51829-1)/128109388Anonymous06/2024
7114(2^363370+1338)/2109385Stefano Morozzi02/2021
7115(2^363349+7)/9109378Lelio R Paula01/2014
7116(13869^26569-1)/(13869^163-1)109375Ryan Propper11/2023
71173^229236+100109374Lelio R Paula03/2017
7118(2^363315+3258)/2109369Stefano Morozzi02/2021
71192^363268-58695109355Lelio R Paula04/2017
71202^363191-112321109332Enzo Doria06/2014
712126231^14718+14718^26231109327Hans Havermann10/2020
712225461^19672+19672^25461109326Hans Havermann10/2020
71234*10^109316-63109317Robert Price10/2018
71242^363120+3109311Donovan Johnson04/2006
7125(10^109297-1)/9109297Paul Bourdelais, Harvey Dubner04/2007
71262^363042-114641109287Enzo Doria04/2015
71272^363020-112793109280Enzo Doria06/2014
7128(8732^27889-1)/(8732^167-1)109256Ryan Propper11/2023
7129(85*10^109253+203)/9109254Robert Price09/2020
713024990^23431+23431^24990109202Hans Havermann10/2020
7131(2^362746+3738)/2109198Stefano Morozzi09/2020
7132(2^362716+1282)/2109189Stefano Morozzi01/2021
7133(67607*2^362695+1)/70499109183Lelio R Paula07/2014
713425060^22737+22737^25060109180Hans Havermann10/2020
7135(9*2^362644+1)/5109167Lelio R Paula03/2014
71365^156181+38109166Lelio R Paula02/2017
7137(2^362623+3618)/2109161Stefano Morozzi09/2020
713825138^21993+21993^25138109157Hans Havermann10/2020
71394*10^109142+91109143Robert Price08/2018
71403^228750+68109142Lelio R Paula03/2017
7141(2^362561+786)/2109142Stefano Morozzi09/2020
7142578*29^74623+7109132Eric Chen06/2025
7143(23*10^109113+61)/3109114Robert Price01/2022
71442*10^109100-49109101Robert Price09/2020
7145(10223*2^362376+1)/9109090Lelio R Paula07/2014
714665^60167-64^60167109078Robert Price08/2013
71477*3^228589-2109066Lelio R Paula09/2014
714824874^24243+24243^24874109063Hans Havermann11/2020
7149(17*10^109059-161)/9109060Robert Price02/2021
715029158^5495+5495^29158109050Hans Havermann11/2020
7151(78557*2^362188+1)/189109033Lelio R Paula07/2014
71522*7^129008+9109025Lelio R Paula11/2014
715388*10^109022+7109024Robert Price03/2020
715428194^7337+7337^28194108985Hans Havermann10/2020
7155(5*10^108960+91)/3108961Robert Price04/2018
71562^361957+76367108960Enzo Doria05/2016
7157(11*29^74504-245655)/28108955Eric Chen06/2025
71582^361873-1411108935Yves Minet01/2013
7159(24737*2^361857+1)/35108933Lelio R Paula07/2014
7160216^216^216+91^91^91108917Henri Lifchitz03/2025
716147^65132-65132^47108908Norman Luhn09/2024
7162115^52842-114108892Norbert Schneider07/2018
716313^97745-24108883Lelio R Paula03/2017
7164(2^361696+2562)/2108882Stefano Morozzi09/2020
716517^88475+8108864Lelio R Paula04/2017
71662^361567+51108843Lelio R Paula01/2012
71672^361563-109501108842Enzo Doria04/2014
716812^100852+83108838Lelio R Paula03/2017
71692^361497+767108822Lelio R Paula01/2012
7170L(520691)/78103651/1057002731/42794551909108791Serge Batalov07/2024
717128019^7630+7630^28019108785Hans Havermann10/2020
717224723^24758-24758^24723108765Norbert Schneider11/2020
71732^361280-112349108757Enzo Doria06/2014
71742^361271-5955108754Lelio R Paula04/2017
717512^100757+19108736Lelio R Paula03/2017
717625368^19333+19333^25368108735Hans Havermann11/2020
7177(2^361195+3618)/2108731Stefano Morozzi09/2020
71782^361153-111546435108718Paul Bourdelais10/2021
717914^94849-61108710Lelio R Paula05/2017
718027267^9700+9700^27267108708Hans Havermann11/2020
7181(19^85009-5^85009)/14108705Robert Price07/2013
718224832^23853+23853^24832108704Hans Havermann11/2020
718327502^8963+8963^27502108701Hans Havermann11/2020
7184(130^51419-1)/129108695Anonymous06/2024
718525807^16278+16278^25807108689Hans Havermann11/2020
7186(11*2^361027+1)/40463108677Lelio R Paula03/2014
71872^360973+1299108664Lelio R Paula04/2017
718824^78728+23108662Anonymous09/2024
71892^360959-109101108660Enzo Doria04/2014
71906*5^155454+7108659Lelio R Paula11/2014
719110^108656+79108657Lelio R Paula02/2017
719210^108656-50001108656Patrick De Geest03/2017
71932^360918-35108648Lelio R Paula01/2012
71944*10^108646-47108647Robert Price10/2021
7195(11*2^360886-1)/7108638Lelio R Paula03/2014
71963*10^108624-49108625Robert Price07/2018
7197(2^360831+666)/2108621Stefano Morozzi09/2020
7198(134*10^108610+7)/3108612Robert Price02/2020
71992*10^108609+29108610Robert Price02/2021
7200(10^108604+7)/71/191108600Alfred Reich06/2021
7201(2^360742+3222)/2108594Stefano Morozzi09/2020
72022^360706-458903108584Enzo Doria04/2015
720331112^3087+3087^31112108567Hans Havermann11/2020
72042^360641-113185108564Enzo Doria07/2014
7205(29*10^108559-71)/3108560Robert Price07/2021
72072^360618+75019108557Enzo Doria04/2016
72062^360618+2025108557Henri Lifchitz01/2025
72082^360607-216367108554Harrison Mesh06/2022
720929^74228+556108551Eric Chen06/2025
7210(14*10^108545-221)/9108546Robert Price04/2018
7211(44*10^108544-233)/9108545Robert Price01/2019
72123*5^155286+2108541Lelio R Paula11/2014
72137^128422+4108530Lelio R Paula11/2014
72147^128421-80108529Lelio R Paula03/2017
72152^360497+53807108521Yves Minet07/2010
72162^360468-4559108512Yves Minet03/2019
7217(2^360451+578)/2108507Stefano Morozzi09/2020
72182^360366+1459108481Lelio R Paula09/2011
72192^360364-1499108481Yves Minet05/2013
722025662^16871+16871^25662108477Hans Havermann10/2020
722125009^21748+21748^25009108475Hans Havermann10/2020
722214^94642-23108472Lelio R Paula05/2017
7223(197*10^108446-11)/3108448Robert Price03/2020
7224(2^360229+1290)/2108440Stefano Morozzi01/2021
72254*10^108412+9108413Robert Price05/2015
7226(259*10^108409-1)/3108411Robert Price12/2020
7227(2^360122+1194)/2108408Stefano Morozzi09/2020
7228133^51042-132108406Norbert Schneider02/2019
72292^360093-351103108399Enzo Doria06/2015
72302^360042+723108384Lelio R Paula01/2012
723185^56164-2108364Lelio R Paula10/2013
72322^359937-29323108352Enzo Doria07/2015
723322^80712-23108350Anonymous09/2024
7234(2^359922+1762)/2108348Stefano Morozzi09/2020
7235(2^359903+758)/2108342Stefano Morozzi09/2020
72362^359898-19997108341Enzo Doria06/2013
7237(2^359886+2122)/2108337Stefano Morozzi09/2020
72382*5^154948-7108305Lelio R Paula11/2014
723910^108303+13108304Lelio R Paula02/2017
724010^108303-207959108303Patrick De Geest03/2017
72417*10^108300+69108301Robert Price07/2019
7242198^47155-47155^198108300Norman Luhn09/2024
72432^359730+753108290Lelio R Paula12/2011
7244(8*10^108273+13)/3108274Robert Price06/2018
72452^359650-19797108266Enzo Doria06/2013
7246(47*10^108261+259)/9108262Robert Price03/2022
724791^55259-90^55259108255Robert Price07/2015
724810^108251+85749108252Patrick De Geest02/2021
724910^108251-50000000001108251Robert Price12/2020
725010^108251-252081108251Patrick De Geest02/2021


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Created by  Henri Lifchitz & Renaud Lifchitz : October, 26 2000, last modification: June, 20 2025 15:18 (Time in France)

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