PRP Records

Probable Primes Top 10000

(301692 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(21181*2^366833+1)/3110432Lelio R Paula07/2014
7002(4^231439)%(3^231439)110425Henri Lifchitz06/2025
70032^366816+315110423Lelio R Paula05/2017
7004(11^2667520)/(10^2667520)110416Henri Lifchitz06/2025
70052^366775-2787037110411Enzo Doria03/2016
7006(112*10^110405-1)/3110407Serge Batalov12/2014
70072^366751+2797553110404Enzo Doria03/2016
700825276^23331+23331^25276110404Hans Havermann10/2020
70092^366748+255110403Lelio R Paula05/2017
70102^366738-2985110400Yves Minet09/2014
7011(23*2^366739+1)/74575110396Lelio R Paula03/2014
7012(2^366722+1314)/2110395Stefano Morozzi02/2021
70132^366716+1871791110393Enzo Doria05/2016
7014(239*23^81066-349)/22110391Eric Chen08/2023
70152^366695+1334025110387Henri Lifchitz10/2024
7016(5^528189)%F(528189)110385Henri Lifchitz06/2025
70172^366649+1871687110373Enzo Doria05/2016
70182^366629-351205110367Enzo Doria06/2015
7019(31*10^110363+257)/9110364Robert Price12/2021
7020(5^183291)%(4^183291)110353Henri Lifchitz06/2025
7021(17*19^86292-215)/18110347Eric Chen01/2023
70232^366558+1874479110345Enzo Doria06/2016
702225132^24581+24581^25132110345Hans Havermann10/2020
7024(2^366539+770)/2110339Stefano Morozzi09/2020
702526368^15285+15285^26368110331Hans Havermann10/2020
7026(23*10^110290+19)/3110291Robert Price07/2019
702718^87853-4409110280Enzo Doria03/2013
702828490^7419+7419^28490110267Hans Havermann11/2020
70292^366218-23110243Lelio R Paula02/2013
7030(21*2^366193-1)/197110235Lelio R Paula03/2014
70312^366178-343991110231Enzo Doria07/2015
703212^102123-11110210Riley Fisher09/2023
7033(725*35^71368+16649)/34110199Eric Chen05/2025
703425777^18798+18798^25777110174Hans Havermann10/2020
70352^365944+1871341110161Enzo Doria05/2016
70362^365838-461267110129Enzo Doria07/2015
703730152^4491+4491^30152110126Hans Havermann11/2020
70382^365802+23359110118Enzo Doria10/2023
703910^110111+464019110112Patrick De Geest05/2021
704010^110111-40001110111Robert Price01/2021
70412^365763-6555110106Lelio R Paula04/2017
7042(2^365689+2^182845+1)/511008311/2006
7043(83^57367-1)/3536509644718110080Paul Vanderveen05/2025
70442^365666-459161110077Enzo Doria05/2015
70453*10^110076-7110077Robert Price08/2015
704613^98785-72110041Lelio R Paula03/2017
7048(25^78707+1)/26110027Robert Price06/2013
7047(7*10^110027-277)/9110027Robert Price02/2022
7049(16*10^110014-73)/3110015Robert Price07/2020
7050(7*10^110006-151)/9110006Robert Price02/2018
70516^141361-7110001Lelio R Paula11/2014
705210^110000+8029681110001Hayden Chesnut11/2024
705310^110000+2044477110001Hayden Chesnut11/2024
705410^110000+76407110001Hayden Chesnut11/2024
705510^110000+167311110001Hayden Chesnut11/2024
705620^84536+81109984Lelio R Paula03/2017
70575*2^365347-9109982Lelio R Paula09/2014
70589*6^141303+7109957Lelio R Paula11/2014
705927635^9522+9522^27635109953Hans Havermann11/2020
706078^58099+77109929Norbert Schneider02/2015
70612*10^109928-7109929Robert Price10/2015
706230580^3933+3933^30580109927Hans Havermann11/2020
706326380^14689+14689^26380109926Hans Havermann11/2020
7064(2^365161+1130)/2109925Stefano Morozzi09/2020
7065(27*2^365137-1)/2021109916Lelio R Paula03/2014
706629^75157-30109910Anonymous09/2024
7067(4441*29^75152-24)/7109905Curtis Bright05/2015
7068(2^365087+7)/6015109899Lelio R Paula01/2014
7069(2^365069+3774)/2109897Stefano Morozzi02/2021
707029652^5083+5083^29652109894Mark Rodenkirch10/2020
7071(2^365049+722)/2109891Stefano Morozzi09/2020
7072(35*10^109888-89)/9109889Robert Price02/2022
707318^87533-11109878Lelio R Paula04/2017
70742^364982-5109871Henri Lifchitz04/2006
70753*10^109861+59109862Robert Price08/2018
70765*10^109860-69109861Robert Price02/2021
70772^364936-1867979109857Enzo Doria04/2016
707827013^11652+11652^27013109846Hans Havermann10/2020
70792^364867-112087109836Enzo Doria06/2014
70804^182415-85061109825Mike Oakes06/2011
7081(2^364809+1034)/2109819Stefano Morozzi09/2020
708224972^24972-8323^8323109814Henri Lifchitz10/2024
7083(53*10^109809-287)/9109810Robert Price02/2022
7084(52*10^109807-133)/9109808Robert Price09/2021
708525708^18675+18675^25708109806Hans Havermann10/2020
7086(17^89227+16^89227)/33109788Robert Price08/2013
70872^364687-187109782Lelio R Paula01/2012
70882^364644+67109769Lelio R Paula01/2012
7089(9787*2^364625-1)/24947109763Lelio R Paula05/2015
7090(2^364616+5)/9109760Lelio R Paula01/2014
7091(55*10^109759+89)/9109760Robert Price03/2019
7092(14*32^72921+4171)/31109757Eric Chen04/2023
709312^101694+73109747Lelio R Paula03/2017
709413^98518-66109744Lelio R Paula03/2017
7095(35^71069+2^71069)/37109734Robert Price01/2025
7096(8*10^109721-269)/9109721Robert Price09/2021
70972^364478-113261109719Enzo Doria07/2014
7098(2^364513+1)/(3*44290516579)109719Gord Palameta08/2018
7099(24737*2^364454+1)/3109716Lelio R Paula07/2014
710027814^8777+8777^27814109681Hans Havermann10/2020
7101(62*10^109673+1)/9109674Serge Batalov11/2010
71023^229824+340109654Lelio R Paula03/2017
7103(16623*33^72206-8095)/16109649Eric Chen05/2023
7104(2*10^109645-71)/3109645Robert Price12/2017
7105V(786978)109644Serge Batalov07/2024
71062^364169-112813109626Enzo Doria06/2014
710728822^6359+6359^28822109622Hans Havermann11/2020
710810^109615+21109616Lelio R Paula03/2017
710910^109615-456267109615Patrick De Geest03/2017
7110522^40331-40331^522109607Norman Luhn09/2024
71112^364094-113109604Lelio R Paula01/2012
711225251^21898+21898^25251109600Hans Havermann11/2020
7113(4^182026+11)/3109591Robert Price02/2017
71142^364041-6883109588Lelio R Paula09/2011
711512^101545+11109586Lelio R Paula03/2017
711626536^13475+13475^26536109582Hans Havermann11/2020
71172^363842-2787101109528Enzo Doria03/2016
7118(2^363812+3570)/2109519Stefano Morozzi09/2020
7119(996^36527+1)/997109515Jinyuan Wang12/2024
7120(22699*2^363782+1)/763109511Lelio R Paula07/2014
71212^363769+5711109506Lelio R Paula04/2017
7122(31*2^363748+1)/49109499Lelio R Paula03/2014
712326^77372+25109480Anonymous09/2024
7124(2^363670+100280245065)109476Paul Bourdelais05/2022
7125p(22245)#/2-8109462Robert Price01/2017
71262^363556+55109442Lelio R Paula01/2012
7127(509*10^109414+31)/9109416Robert Price08/2022
7128(2^363437+1682)/2109406Stefano Morozzi09/2020
7129(55459*2^363411+1)/81109401Lelio R Paula07/2014
71302^363406+1871569109397Enzo Doria05/2016
7131(129^51829-1)/128109388Anonymous06/2024
7132(2^363370+1338)/2109385Stefano Morozzi02/2021
7133(2^363349+7)/9109378Lelio R Paula01/2014
7134(13869^26569-1)/(13869^163-1)109375Ryan Propper11/2023
71353^229236+100109374Lelio R Paula03/2017
7136(2^363315+3258)/2109369Stefano Morozzi02/2021
71372^363268-58695109355Lelio R Paula04/2017
71382^363191-112321109332Enzo Doria06/2014
713926231^14718+14718^26231109327Hans Havermann10/2020
714025461^19672+19672^25461109326Hans Havermann10/2020
71414*10^109316-63109317Robert Price10/2018
71422^363120+3109311Donovan Johnson04/2006
7143(10^109297-1)/9109297Paul Bourdelais, Harvey Dubner04/2007
71442^363042-114641109287Enzo Doria04/2015
71452^363020-112793109280Enzo Doria06/2014
7146(8732^27889-1)/(8732^167-1)109256Ryan Propper11/2023
7147(85*10^109253+203)/9109254Robert Price09/2020
714824990^23431+23431^24990109202Hans Havermann10/2020
7149(2^362746+3738)/2109198Stefano Morozzi09/2020
7150(2^362716+1282)/2109189Stefano Morozzi01/2021
7151(67607*2^362695+1)/70499109183Lelio R Paula07/2014
715225060^22737+22737^25060109180Hans Havermann10/2020
7153(9*2^362644+1)/5109167Lelio R Paula03/2014
71545^156181+38109166Lelio R Paula02/2017
7155(2^362623+3618)/2109161Stefano Morozzi09/2020
715625138^21993+21993^25138109157Hans Havermann10/2020
71574*10^109142+91109143Robert Price08/2018
71583^228750+68109142Lelio R Paula03/2017
7159(2^362561+786)/2109142Stefano Morozzi09/2020
7160578*29^74623+7109132Eric Chen06/2025
7161(23*10^109113+61)/3109114Robert Price01/2022
71622*10^109100-49109101Robert Price09/2020
7163(10223*2^362376+1)/9109090Lelio R Paula07/2014
716465^60167-64^60167109078Robert Price08/2013
71657*3^228589-2109066Lelio R Paula09/2014
716624874^24243+24243^24874109063Hans Havermann11/2020
7167(17*10^109059-161)/9109060Robert Price02/2021
716829158^5495+5495^29158109050Hans Havermann11/2020
7169(78557*2^362188+1)/189109033Lelio R Paula07/2014
71702*7^129008+9109025Lelio R Paula11/2014
717188*10^109022+7109024Robert Price03/2020
717228194^7337+7337^28194108985Hans Havermann10/2020
7173(5*10^108960+91)/3108961Robert Price04/2018
71742^361957+76367108960Enzo Doria05/2016
7175(11*29^74504-245655)/28108955Eric Chen06/2025
71762^361873-1411108935Yves Minet01/2013
7177(24737*2^361857+1)/35108933Lelio R Paula07/2014
7178216^216^216+91^91^91108917Henri Lifchitz03/2025
717947^65132-65132^47108908Norman Luhn09/2024
7180115^52842-114108892Norbert Schneider07/2018
718113^97745-24108883Lelio R Paula03/2017
7182(2^361696+2562)/2108882Stefano Morozzi09/2020
718317^88475+8108864Lelio R Paula04/2017
71842^361567+51108843Lelio R Paula01/2012
71852^361563-109501108842Enzo Doria04/2014
718612^100852+83108838Lelio R Paula03/2017
71872^361497+767108822Lelio R Paula01/2012
7188L(520691)/78103651/1057002731/42794551909108791Serge Batalov07/2024
718928019^7630+7630^28019108785Hans Havermann10/2020
719024723^24758-24758^24723108765Norbert Schneider11/2020
71912^361280-112349108757Enzo Doria06/2014
71922^361271-5955108754Lelio R Paula04/2017
719312^100757+19108736Lelio R Paula03/2017
719425368^19333+19333^25368108735Hans Havermann11/2020
7195(2^361195+3618)/2108731Stefano Morozzi09/2020
71962^361153-111546435108718Paul Bourdelais10/2021
719714^94849-61108710Lelio R Paula05/2017
719827267^9700+9700^27267108708Hans Havermann11/2020
7199(19^85009-5^85009)/14108705Robert Price07/2013
720024832^23853+23853^24832108704Hans Havermann11/2020
720127502^8963+8963^27502108701Hans Havermann11/2020
7202(130^51419-1)/129108695Anonymous06/2024
720325807^16278+16278^25807108689Hans Havermann11/2020
7204(11*2^361027+1)/40463108677Lelio R Paula03/2014
72052^360973+1299108664Lelio R Paula04/2017
720624^78728+23108662Anonymous09/2024
72072^360959-109101108660Enzo Doria04/2014
72086*5^155454+7108659Lelio R Paula11/2014
720910^108656+79108657Lelio R Paula02/2017
721010^108656-50001108656Patrick De Geest03/2017
72112^360918-35108648Lelio R Paula01/2012
72124*10^108646-47108647Robert Price10/2021
7213(11*2^360886-1)/7108638Lelio R Paula03/2014
72143*10^108624-49108625Robert Price07/2018
7215(2^360831+666)/2108621Stefano Morozzi09/2020
7216(134*10^108610+7)/3108612Robert Price02/2020
72172*10^108609+29108610Robert Price02/2021
7218(10^108604+7)/71/191108600Alfred Reich06/2021
7219(2^360742+3222)/2108594Stefano Morozzi09/2020
72202^360706-458903108584Enzo Doria04/2015
722131112^3087+3087^31112108567Hans Havermann11/2020
72222^360641-113185108564Enzo Doria07/2014
7223(29*10^108559-71)/3108560Robert Price07/2021
72252^360618+75019108557Enzo Doria04/2016
72242^360618+2025108557Henri Lifchitz01/2025
72262^360607-216367108554Harrison Mesh06/2022
722729^74228+556108551Eric Chen06/2025
7228(14*10^108545-221)/9108546Robert Price04/2018
7229(44*10^108544-233)/9108545Robert Price01/2019
72303*5^155286+2108541Lelio R Paula11/2014
72317^128422+4108530Lelio R Paula11/2014
72327^128421-80108529Lelio R Paula03/2017
72332^360497+53807108521Yves Minet07/2010
72342^360468-4559108512Yves Minet03/2019
7235(2^360451+578)/2108507Stefano Morozzi09/2020
72362^360366+1459108481Lelio R Paula09/2011
72372^360364-1499108481Yves Minet05/2013
723825662^16871+16871^25662108477Hans Havermann10/2020
723925009^21748+21748^25009108475Hans Havermann10/2020
724014^94642-23108472Lelio R Paula05/2017
7241(197*10^108446-11)/3108448Robert Price03/2020
7242(2^360229+1290)/2108440Stefano Morozzi01/2021
72434*10^108412+9108413Robert Price05/2015
7244(259*10^108409-1)/3108411Robert Price12/2020
7245(2^360122+1194)/2108408Stefano Morozzi09/2020
7246133^51042-132108406Norbert Schneider02/2019
72472^360093-351103108399Enzo Doria06/2015
72482^360042+723108384Lelio R Paula01/2012
724985^56164-2108364Lelio R Paula10/2013
72502^359937-29323108352Enzo Doria07/2015


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Created by  Henri Lifchitz & Renaud Lifchitz : October, 26 2000, last modification: July, 05 2025 13:49 (Time in France)

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