PRP Records

Probable Primes Top 10000

(301723 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 ?
70017*(10^110503-1)/9+1*(10^27685-1)/9*10^41409110503Makoto Morimoto09/2020
70027*(10^110503-1)/9+1*(10^91035-1)/9*10^9734110503Makoto Morimoto09/2020
70037*(10^110503-1)/9-1*(10^23717-1)/9*10^43393110503Makoto Morimoto09/2020
70047*(10^110503-1)/9-1*10^57906-1*10^52596110503Makoto Morimoto09/2020
70057*(10^110503-1)/9-1*10^72287-1*10^38215110503Makoto Morimoto09/2020
70067*(10^110503-1)/9-2*(10^53823-1)/9*10^28340110503Makoto Morimoto09/2020
70077*(10^110503-1)/9-2*(10^88659-1)/9*10^10922110503Makoto Morimoto09/2020
70087*(10^110503-1)/9-3*(10^79921-1)/9*10^15291110503Makoto Morimoto09/2020
70097*(10^110503-1)/9-3*10^60024-3*10^50478110503Makoto Morimoto09/2020
70107*(10^110503-1)/9-4*(10^103091-1)/9*10^3706110503Makoto Morimoto09/2020
70117*(10^110503-1)/9-4*10^103658-4*10^6844110503Makoto Morimoto09/2020
70127*(10^110503-1)/9-4*10^78188-4*10^32314110503Makoto Morimoto09/2020
70137*(10^110503-1)/9-5*(10^35035-1)/9*10^37734110503Makoto Morimoto09/2020
70147*(10^110503-1)/9-6*(10^67347-1)/9*10^21578110503Makoto Morimoto09/2020
70157*(10^110503-1)/9-6*10^60391-6*10^50111110503Makoto Morimoto09/2020
7016(10^110503-1)-4*(10^96247-1)/9*10^7128110503Makoto Morimoto09/2020
7017(10^110503-1)-4*10^74037-4*10^36465110503Makoto Morimoto09/2020
7018(10^110503-1)-4*10^77787-4*10^32715110503Makoto Morimoto09/2020
7019(10^110503-1)-4*10^91179-4*10^19323110503Makoto Morimoto09/2020
7020(10^110503-1)-5*(10^99143-1)/9*10^5680110503Makoto Morimoto09/2020
7021(10^110503-1)-7*(10^85075-1)/9*10^12714110503Makoto Morimoto09/2020
7022(10^110503-1)-7*10^100712-7*10^9790110503Makoto Morimoto09/2020
7023(10^110503-1)-7*10^76427-7*10^34075110503Makoto Morimoto09/2020
7024(10^110503-1)-7*10^90451-7*10^20051110503Makoto Morimoto09/2020
7025(10^110503-1)-8*10^106252-8*10^4250110503Makoto Morimoto09/2020
7026(11*10^110496+49)/3110497Robert Price07/2018
702725447^21958+21958^25447110481Hans Havermann11/2020
7028(31*2^366976+1)/7110472Lelio R Paula03/2014
70297*10^110468-23110469Robert Price07/2019
70305*3^231464-2^231464110438Jon Grantham08/2023
70312^366853+5711110434Lelio R Paula05/2017
7032(21181*2^366833+1)/3110432Lelio R Paula07/2014
7033(4^231439)%(3^231439)110425Henri Lifchitz06/2025
70342^366816+315110423Lelio R Paula05/2017
7035(11^2667520)/(10^2667520)110416Henri Lifchitz06/2025
70362^366775-2787037110411Enzo Doria03/2016
7037(112*10^110405-1)/3110407Serge Batalov12/2014
70382^366751+2797553110404Enzo Doria03/2016
703925276^23331+23331^25276110404Hans Havermann10/2020
70402^366748+255110403Lelio R Paula05/2017
70412^366738-2985110400Yves Minet09/2014
7042(23*2^366739+1)/74575110396Lelio R Paula03/2014
7043(2^366722+1314)/2110395Stefano Morozzi02/2021
70442^366716+1871791110393Enzo Doria05/2016
7045(239*23^81066-349)/22110391Eric Chen08/2023
70462^366695+1334025110387Henri Lifchitz10/2024
7047(5^528189)%F(528189)110385Henri Lifchitz06/2025
70482^366649+1871687110373Enzo Doria05/2016
70492^366629-351205110367Enzo Doria06/2015
7050(31*10^110363+257)/9110364Robert Price12/2021
7051(5^183291)%(4^183291)110353Henri Lifchitz06/2025
7052(17*19^86292-215)/18110347Eric Chen01/2023
70542^366558+1874479110345Enzo Doria06/2016
705325132^24581+24581^25132110345Hans Havermann10/2020
7055(2^366539+770)/2110339Stefano Morozzi09/2020
705626368^15285+15285^26368110331Hans Havermann10/2020
7057(23*10^110290+19)/3110291Robert Price07/2019
705818^87853-4409110280Enzo Doria03/2013
705928490^7419+7419^28490110267Hans Havermann11/2020
70602^366218-23110243Lelio R Paula02/2013
7061(21*2^366193-1)/197110235Lelio R Paula03/2014
70622^366178-343991110231Enzo Doria07/2015
706312^102123-11110210Riley Fisher09/2023
7064(725*35^71368+16649)/34110199Eric Chen05/2025
706525777^18798+18798^25777110174Hans Havermann10/2020
70662^365944+1871341110161Enzo Doria05/2016
70672^365838-461267110129Enzo Doria07/2015
706830152^4491+4491^30152110126Hans Havermann11/2020
70692^365802+23359110118Enzo Doria10/2023
707010^110111+464019110112Patrick De Geest05/2021
707110^110111-40001110111Robert Price01/2021
70722^365763-6555110106Lelio R Paula04/2017
7073(2^365689+2^182845+1)/511008311/2006
7074(83^57367-1)/3536509644718110080Paul Vanderveen05/2025
70752^365666-459161110077Enzo Doria05/2015
70763*10^110076-7110077Robert Price08/2015
707713^98785-72110041Lelio R Paula03/2017
7079(25^78707+1)/26110027Robert Price06/2013
7078(7*10^110027-277)/9110027Robert Price02/2022
7080(16*10^110014-73)/3110015Robert Price07/2020
7081(7*10^110006-151)/9110006Robert Price02/2018
70826^141361-7110001Lelio R Paula11/2014
708310^110000+8029681110001Hayden Chesnut11/2024
708410^110000+2044477110001Hayden Chesnut11/2024
708510^110000+76407110001Hayden Chesnut11/2024
708610^110000+167311110001Hayden Chesnut11/2024
708720^84536+81109984Lelio R Paula03/2017
70885*2^365347-9109982Lelio R Paula09/2014
70899*6^141303+7109957Lelio R Paula11/2014
709027635^9522+9522^27635109953Hans Havermann11/2020
709178^58099+77109929Norbert Schneider02/2015
70922*10^109928-7109929Robert Price10/2015
709330580^3933+3933^30580109927Hans Havermann11/2020
709426380^14689+14689^26380109926Hans Havermann11/2020
7095(2^365161+1130)/2109925Stefano Morozzi09/2020
7096(27*2^365137-1)/2021109916Lelio R Paula03/2014
709729^75157-30109910Anonymous09/2024
7098(4441*29^75152-24)/7109905Curtis Bright05/2015
7099(2^365087+7)/6015109899Lelio R Paula01/2014
7100(2^365069+3774)/2109897Stefano Morozzi02/2021
710129652^5083+5083^29652109894Mark Rodenkirch10/2020
7102(2^365049+722)/2109891Stefano Morozzi09/2020
7103(35*10^109888-89)/9109889Robert Price02/2022
710418^87533-11109878Lelio R Paula04/2017
71052^364982-5109871Henri Lifchitz04/2006
71063*10^109861+59109862Robert Price08/2018
71075*10^109860-69109861Robert Price02/2021
71082^364936-1867979109857Enzo Doria04/2016
710927013^11652+11652^27013109846Hans Havermann10/2020
71102^364867-112087109836Enzo Doria06/2014
71114^182415-85061109825Mike Oakes06/2011
7112(2^364809+1034)/2109819Stefano Morozzi09/2020
711324972^24972-8323^8323109814Henri Lifchitz10/2024
7114(53*10^109809-287)/9109810Robert Price02/2022
7115(52*10^109807-133)/9109808Robert Price09/2021
711625708^18675+18675^25708109806Hans Havermann10/2020
7117(17^89227+16^89227)/33109788Robert Price08/2013
71182^364687-187109782Lelio R Paula01/2012
71192^364644+67109769Lelio R Paula01/2012
7120(9787*2^364625-1)/24947109763Lelio R Paula05/2015
7121(2^364616+5)/9109760Lelio R Paula01/2014
7122(55*10^109759+89)/9109760Robert Price03/2019
7123(14*32^72921+4171)/31109757Eric Chen04/2023
712412^101694+73109747Lelio R Paula03/2017
712513^98518-66109744Lelio R Paula03/2017
7126(35^71069+2^71069)/37109734Robert Price01/2025
7127(8*10^109721-269)/9109721Robert Price09/2021
71282^364478-113261109719Enzo Doria07/2014
7129(2^364513+1)/(3*44290516579)109719Gord Palameta08/2018
7130(24737*2^364454+1)/3109716Lelio R Paula07/2014
713127814^8777+8777^27814109681Hans Havermann10/2020
7132(62*10^109673+1)/9109674Serge Batalov11/2010
71333^229824+340109654Lelio R Paula03/2017
7134(16623*33^72206-8095)/16109649Eric Chen05/2023
7135(2*10^109645-71)/3109645Robert Price12/2017
7136V(786978)109644Serge Batalov07/2024
71372^364169-112813109626Enzo Doria06/2014
713828822^6359+6359^28822109622Hans Havermann11/2020
713910^109615+21109616Lelio R Paula03/2017
714010^109615-456267109615Patrick De Geest03/2017
7141522^40331-40331^522109607Norman Luhn09/2024
71422^364094-113109604Lelio R Paula01/2012
714325251^21898+21898^25251109600Hans Havermann11/2020
7144(4^182026+11)/3109591Robert Price02/2017
71452^364041-6883109588Lelio R Paula09/2011
714612^101545+11109586Lelio R Paula03/2017
714726536^13475+13475^26536109582Hans Havermann11/2020
71482^363842-2787101109528Enzo Doria03/2016
7149(2^363812+3570)/2109519Stefano Morozzi09/2020
7150(996^36527+1)/997109515Jinyuan Wang12/2024
7151(22699*2^363782+1)/763109511Lelio R Paula07/2014
71522^363769+5711109506Lelio R Paula04/2017
7153(31*2^363748+1)/49109499Lelio R Paula03/2014
715426^77372+25109480Anonymous09/2024
7155(2^363670+100280245065)109476Paul Bourdelais05/2022
7156p(22245)#/2-8109462Robert Price01/2017
71572^363556+55109442Lelio R Paula01/2012
7158(509*10^109414+31)/9109416Robert Price08/2022
7159(2^363437+1682)/2109406Stefano Morozzi09/2020
7160(55459*2^363411+1)/81109401Lelio R Paula07/2014
71612^363406+1871569109397Enzo Doria05/2016
7162(129^51829-1)/128109388Anonymous06/2024
7163(2^363370+1338)/2109385Stefano Morozzi02/2021
7164(2^363349+7)/9109378Lelio R Paula01/2014
7165(13869^26569-1)/(13869^163-1)109375Ryan Propper11/2023
71663^229236+100109374Lelio R Paula03/2017
7167(2^363315+3258)/2109369Stefano Morozzi02/2021
71682^363268-58695109355Lelio R Paula04/2017
71692^363191-112321109332Enzo Doria06/2014
717026231^14718+14718^26231109327Hans Havermann10/2020
717125461^19672+19672^25461109326Hans Havermann10/2020
71724*10^109316-63109317Robert Price10/2018
71732^363120+3109311Donovan Johnson04/2006
7174(10^109297-1)/9109297Paul Bourdelais, Harvey Dubner04/2007
71752^363042-114641109287Enzo Doria04/2015
71762^363020-112793109280Enzo Doria06/2014
7177(8732^27889-1)/(8732^167-1)109256Ryan Propper11/2023
7178(85*10^109253+203)/9109254Robert Price09/2020
717924990^23431+23431^24990109202Hans Havermann10/2020
7180(2^362746+3738)/2109198Stefano Morozzi09/2020
7181(2^362716+1282)/2109189Stefano Morozzi01/2021
7182(67607*2^362695+1)/70499109183Lelio R Paula07/2014
718325060^22737+22737^25060109180Hans Havermann10/2020
7184(9*2^362644+1)/5109167Lelio R Paula03/2014
71855^156181+38109166Lelio R Paula02/2017
7186(2^362623+3618)/2109161Stefano Morozzi09/2020
718725138^21993+21993^25138109157Hans Havermann10/2020
71884*10^109142+91109143Robert Price08/2018
71893^228750+68109142Lelio R Paula03/2017
7190(2^362561+786)/2109142Stefano Morozzi09/2020
7191578*29^74623+7109132Eric Chen06/2025
7192(23*10^109113+61)/3109114Robert Price01/2022
71932*10^109100-49109101Robert Price09/2020
7194(10223*2^362376+1)/9109090Lelio R Paula07/2014
719565^60167-64^60167109078Robert Price08/2013
71967*3^228589-2109066Lelio R Paula09/2014
719724874^24243+24243^24874109063Hans Havermann11/2020
7198(17*10^109059-161)/9109060Robert Price02/2021
719929158^5495+5495^29158109050Hans Havermann11/2020
7200(78557*2^362188+1)/189109033Lelio R Paula07/2014
72012*7^129008+9109025Lelio R Paula11/2014
720288*10^109022+7109024Robert Price03/2020
720328194^7337+7337^28194108985Hans Havermann10/2020
7204(5*10^108960+91)/3108961Robert Price04/2018
72052^361957+76367108960Enzo Doria05/2016
7206(11*29^74504-245655)/28108955Eric Chen06/2025
72072^361873-1411108935Yves Minet01/2013
7208(24737*2^361857+1)/35108933Lelio R Paula07/2014
7209216^216^216+91^91^91108917Henri Lifchitz03/2025
721047^65132-65132^47108908Norman Luhn09/2024
7211115^52842-114108892Norbert Schneider07/2018
721213^97745-24108883Lelio R Paula03/2017
7213(2^361696+2562)/2108882Stefano Morozzi09/2020
721417^88475+8108864Lelio R Paula04/2017
72152^361567+51108843Lelio R Paula01/2012
72162^361563-109501108842Enzo Doria04/2014
721712^100852+83108838Lelio R Paula03/2017
72182^361497+767108822Lelio R Paula01/2012
7219L(520691)/78103651/1057002731/42794551909108791Serge Batalov07/2024
722028019^7630+7630^28019108785Hans Havermann10/2020
722124723^24758-24758^24723108765Norbert Schneider11/2020
72222^361280-112349108757Enzo Doria06/2014
72232^361271-5955108754Lelio R Paula04/2017
722412^100757+19108736Lelio R Paula03/2017
722525368^19333+19333^25368108735Hans Havermann11/2020
7226(2^361195+3618)/2108731Stefano Morozzi09/2020
72272^361153-111546435108718Paul Bourdelais10/2021
722814^94849-61108710Lelio R Paula05/2017
722927267^9700+9700^27267108708Hans Havermann11/2020
7230(19^85009-5^85009)/14108705Robert Price07/2013
723124832^23853+23853^24832108704Hans Havermann11/2020
723227502^8963+8963^27502108701Hans Havermann11/2020
7233(130^51419-1)/129108695Anonymous06/2024
723425807^16278+16278^25807108689Hans Havermann11/2020
7235(11*2^361027+1)/40463108677Lelio R Paula03/2014
72362^360973+1299108664Lelio R Paula04/2017
723724^78728+23108662Anonymous09/2024
72382^360959-109101108660Enzo Doria04/2014
72396*5^155454+7108659Lelio R Paula11/2014
724010^108656+79108657Lelio R Paula02/2017
724110^108656-50001108656Patrick De Geest03/2017
72422^360918-35108648Lelio R Paula01/2012
72434*10^108646-47108647Robert Price10/2021
7244(11*2^360886-1)/7108638Lelio R Paula03/2014
72453*10^108624-49108625Robert Price07/2018
7246(2^360831+666)/2108621Stefano Morozzi09/2020
7247(134*10^108610+7)/3108612Robert Price02/2020
72482*10^108609+29108610Robert Price02/2021
7249(10^108604+7)/71/191108600Alfred Reich06/2021
7250(2^360742+3222)/2108594Stefano Morozzi09/2020


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Created by  Henri Lifchitz & Renaud Lifchitz : October, 26 2000, last modification: July, 10 2025 14:11 (Time in France)

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