PRP Records

Probable Primes Top 10000

(294113 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 ?
9751(24728^21751-1)/2472795552Serge Batalov06/2022
9752(49764^20341-1)/4976395536Serge Batalov06/2022
9753(36155^20959-1)/3615495531Serge Batalov06/2022
9754(7725^24571-1)/772495526Serge Batalov06/2022
9755(20546^22147-1)/2054595510Serge Batalov06/2022
97562^317251+46595503Lelio R Paula03/2016
975719^74684+5895503Lelio R Paula06/2016
9758(2^317250-7)/33995500Lelio R Paula07/2013
97595*10^95498-2195499Robert Price12/2021
9760(21615^22031-1)/2161495495Serge Batalov06/2022
97616^122718-7995494Lelio R Paula05/2016
976222168^20291+20291^2216895485Hans Havermann10/2019
9763(77427^19531-1)/7742695481Serge Batalov06/2022
9764(13026^23203-1)/1302595472Serge Batalov06/2022
97652^317141-11049195469Enzo Doria05/2014
9766(2^317097+3014)/295456Stefano Morozzi09/2020
97672^317094+7630995455Enzo Doria05/2016
97682^317085+9595453Lelio R Paula11/2012
9769(17*10^95451-377)/995452Robert Price11/2017
97702^317057-10955195444Enzo Doria04/2014
97713^200026+2895437Lelio R Paula05/2016
97722^317024+9395434Donovan Johnson06/2008
9773(86*10^95428-437)/995429Robert Price03/2021
977410^95427+19259195428Patrick De Geest05/2021
97772^316999+160595427Lelio R Paula03/2016
9776(2^317000+3210)/295427Stefano Morozzi09/2020
977510^95427-1000195427Robert Price02/2021
97782^316995-11042795426Enzo Doria05/2014
9779(69841^19699-1)/6984095420Serge Batalov06/2022
9780(59242^19993-1)/5924195415Serge Batalov06/2022
978222300^18987+18987^2230095410Hans Havermann06/2020
9781(9478^23993-1)/947795410Serge Batalov06/2022
97842^316937+17795408Lelio R Paula11/2012
97834*10^95407+9195408Robert Price11/2017
9785(94085^19321-1)/(94085^139-1)95403Ryan Propper11/2023
97862^316908+191595399Lelio R Paula03/2016
97872^316894+9995395Lelio R Paula11/2012
9788(2^316887+2546)/295393Stefano Morozzi09/2020
97892*10^95374-2195375Robert Price09/2020
97906^122547+1195361Lelio R Paula05/2016
97912^316771+8287595358Lelio R Paula03/2016
9792(15609^22741-1)/1560895358Serge Batalov06/2022
9793(2^316765+3102)/295356Stefano Morozzi09/2020
9794(2267^28411-1)/226695329Serge Batalov06/2022
9795(824^32693-1)/82395328Serge Batalov06/2022
9796(23*10^95326+1)/395327Serge Batalov05/2009
97971*10^95326+5795327Robert Price03/2011
979810^95326-39368795326Patrick De Geest09/2013
9799(3^199803+4)/47953995325Lelio R Paula04/2013
98002^316654-10948195323Enzo Doria04/2014
98018*10^95316+5195317Robert Price05/2017
9802(50^56099+43^56099)/9395309Serge Batalov12/2016
9803(23*2^316559+1)/392595292Lelio R Paula09/2013
9804(71*10^95277-539)/995278Robert Price11/2017
980523422^11691+11691^2342295278Hans Havermann10/2019
980619^74503-5695271Lelio R Paula06/2016
9807(5038^25733-1)/503795267Serge Batalov06/2022
980811^91475-438095262Enzo Doria01/2013
9809(62*10^95251-611)/995252Robert Price05/2017
9810(160090^18301-1)/16008995240Serge Batalov06/2022
9811(173205^18181-1)/17320495238Serge Batalov06/2022
9812(158710^18313-1)/15870995234Serge Batalov06/2022
9813(9979^23813-1)/997895227Serge Batalov06/2022
9814(57376^20011-1)/5737595223Serge Batalov06/2022
9815(2^316321-509203)/6937795218Lelio R Paula06/2013
981626541^3868+3868^2654195216Hans Havermann07/2020
9817(79*10^95214-43)/995215Erik Branger11/2013
9818(7176^24691-1)/717595202Anonymous11/2020
9819(9*2^316233-1)/175195194Lelio R Paula02/2014
98205*2^316213+995191Lelio R Paula08/2014
98212*10^95188-9195189Robert Price04/2020
98222^316205-184816395188Enzo Doria07/2015
98232^316185-278791395182Enzo Doria04/2016
9824(2^316174+3538)/295178Stefano Morozzi09/2020
9825(9787*2^316142-1)/395172Lelio R Paula04/2015
98262^316140-595168Henri Lifchitz02/2006
9827(15185*2^316117-1)/395165Lelio R Paula04/2015
9828(34*10^95153-7)/9/19/1915795149Makoto Morimoto05/2016
98292^316069+7681795147Enzo Doria05/2016
9830(199*10^95134-7)/395136Robert Price02/2017
98312^316027-9730595134Lelio R Paula03/2016
98322^316006-279805195128Enzo Doria04/2016
983324994^6397+6397^2499495127Hans Havermann02/2020
98352^315921-279760395102Enzo Doria04/2016
9834(2^315921+1314)/295102Stefano Morozzi02/2021
98362*10^95095+6395096Robert Price10/2017
98372^315857+129995083Lelio R Paula03/2016
9838(2^315858+2598)/295083Stefano Morozzi09/2020
984014^82955-4395078Lelio R Paula06/2016
9839(8*10^95078-269)/995078Robert Price09/2021
9841(23*10^95074-101)/395075Robert Price04/2021
98422^315827-93307595074Paul Bourdelais04/2021
9843(2*10^95072-17)/395072Robert Price08/2014
9844(286*10^95059-1)/395061Robert Price11/2020
9845(2^315779+1610)/295059Stefano Morozzi09/2020
98462^315775-11154643595058Paul Bourdelais10/2021
984721938^21513+21513^2193895051Hans Havermann09/2020
98482^315727+6595044Lelio R Paula11/2012
98492^315725+188575795043Enzo Doria03/2017
985010^(2*47509+1)-10^47509-195019Robert Price07/2023
985123277^12058+12058^2327795000Hans Havermann09/2020
98521*10^94983+2194984Robert Price03/2011
985310^94983-71794983Patrick De Geest08/2013
985417^77187-8294975Lelio R Paula07/2016
98553*10^94964+3794965Robert Price10/2017
9856(2^315481-1017)/2062728594962Lelio R Paula06/2013
98572^315423-11032994952Enzo Doria05/2014
98582^315420+349394951Riley Fisher08/2023
985911^91169-723094943Enzo Doria02/2013
98607*10^94938+6194939Robert Price02/2017
98612^315351+102594931Lelio R Paula03/2016
98622^315350-11225394930Enzo Doria06/2014
9863(2^315343+1766)/294928Stefano Morozzi09/2020
9864(2^315343+3066)/294928Stefano Morozzi09/2020
9866((1001327^(15817)+1)/1001328)94906Faysal YAtim10/2010
98652^315268+794906Lelio R Paula10/2012
986711^91133+6294906Lelio R Paula05/2016
9868(2^315264+1558)/294904Stefano Morozzi09/2020
986930^64244+4194897Lelio R Paula08/2012
9870(151*10^94885-7)/994887Robert Price07/2017
9871fibonacci(453998)+294880Jon Grantham08/2023
98724^157583+2214794875Mike Oakes01/2011
9873(14*32^63026-190819)/3194864Eric Chen04/2023
98742^315123+2051394862Enzo Doria07/2023
98752^315098+12394854Lelio R Paula11/2012
98763^198791-3494848Robert Price11/2013
98773*2^315067+794846Lelio R Paula08/2014
9878(9*2^315057+1)/7394841Lelio R Paula09/2013
987922576^15875+15875^2257694836Hans Havermann09/2020
9880(16*10^94822+53)/394823Robert Price12/2016
98818*6^121849-794818Lelio R Paula10/2014
9882(85*10^94802+473)/994803Robert Price03/2017
988321767^21852-21852^2176794790Norbert Schneider06/2020
9884(2*34^61893-647)/394788Eric Chen03/2023
98852^314870-10876194786Enzo Doria03/2014
98865*2^314841-394778Lelio R Paula08/2014
9888(2^314842+550)/294777Stefano Morozzi09/2020
988711738^23289-23289^1173894777Norbert Schneider05/2022
9889(2^314787+2630)/294761Stefano Morozzi09/2020
98906^121772+11394758Lelio R Paula05/2016
9891(19812^22201-1)/(19812^149-1)94756Ryan Propper11/2023
98922^314751+22187394750Enzo Doria09/2023
9893(2^314740+3642)/294746Stefano Morozzi09/2020
98946^121756-1625394745Enzo Doria02/2013
9895(5*25^67773-2267)/694743Eric Chen04/2023
98962^314718-11279394740Enzo Doria06/2014
98972^314697-184729394734Enzo Doria07/2015
989822836^14065+14065^2283694727Hans Havermann09/2020
98992^314548-24994689Yves Minet02/2012
99005^135469+4294689Lelio R Paula04/2016
99012^314545+2269794688Enzo Doria09/2023
9902gcd(V(1137755),5*F(227551)*(F(227551)-1)+1)94676Serge Batalov04/2015
990325773^4712+4712^2577394670Hans Havermann08/2020
9904(2^314485+3614)/294670Stefano Morozzi09/2020
9905(2*10^94604+547)/994604Robert Price10/2017
9906(2^314164+2562)/294573Stefano Morozzi09/2020
99073*2^314152+594570Lelio R Paula08/2014
99082*6^121530-594570Lelio R Paula10/2014
99097*10^94563+8794564Robert Price11/2016
99102^314114-10967794558Enzo Doria04/2014
9911(218389#+240867)/(3*11*811)94557Makoto Morimoto10/2017
99122^314059+7658394542Enzo Doria05/2016
99132^314041-403594536Lelio R Paula03/2016
9914(2^314028+3102)/294532Stefano Morozzi09/2020
9915(807*33^62250-7)/3294529Eric Chen05/2023
9916(2^314012+618)/294527Stefano Morozzi09/2020
9917(7*2^314003-11)/1594524Renaud Lifchitz03/2011
991811^90760-471094517Enzo Doria01/2013
991921675^21796+21796^2167594507Norbert Schneider04/2020
99202^313942+10028024506594506Paul Bourdelais10/2021
9921(457829*27^66017-385)/2694499Eric Chen02/2023
9922(7*2^313926-1)/14882194497Lelio R Paula02/2014
992394*10^94493-394495Robert Price11/2016
9924(1000547^15749+1)/100054894492Faysal YAtim12/2008
9925(2^313859+2706)/294481Stefano Morozzi09/2020
9926(F(3*75345)^2+L(3*75345)^2)/494477Henri Lifchitz10/2017
99277^111792-3294476Lelio R Paula04/2016
9928(2^313800+822)/294463Stefano Morozzi01/2021
99299*10^94462-4794463Robert Price11/2021
993011*10^94460+394462Robert Price07/2021
9931(202*10^94441-1)/394443Robert Price05/2020
993211^90680-585094434Enzo Doria01/2013
9933(752^32833-1)/75194432Michael Stocker05/2020
99342^313675-11012594426Enzo Doria04/2014
9935(2999*29^64556-2427)/494410Curtis Bright05/2015
99362^313609-11222594406Enzo Doria06/2014
99372^313584+7290194399Enzo Doria04/2016
9938(2^313567+1310)/294393Stefano Morozzi02/2021
9939(2^313562+730)/294392Stefano Morozzi09/2020
99402^313510-11286594376Enzo Doria06/2014
99417*10^94373+8794374Robert Price11/2016
9942(9^98897+8^98897)/1794371Robert Price12/2012
99432^313453-11470394359Enzo Doria04/2015
99448*10^94357-5194358Robert Price10/2017
994525903^4392+4392^2590394356Hans Havermann09/2020
994631706^945+945^3170694340Hans Havermann09/2020
9947(379*10^94337-1)/994339Robert Price08/2017
99482^313344-313344+194326Robert Price10/2014
9949(2^313313+3662)/294317Stefano Morozzi09/2020
995020^72481-4994300Lelio R Paula05/2016
9951(34*10^94293-259)/994294Robert Price12/2021
995244725!2+12894289Robert Price03/2015
99534*10^94286+994287Robert Price05/2015
995417^76621+2494279Lelio R Paula07/2016
995526274^3875+3875^2627494279Hans Havermann09/2020
99564*10^94270-3394271Robert Price04/2021
99572^313156-11285994270Enzo Doria06/2014
9958(49*10^94262-211)/994263Robert Price06/2022
99596^121130-5994258Lelio R Paula05/2016
99603^197542+2894252Robert Price11/2013
9961(2^313076+3550)/294245Stefano Morozzi09/2020
9962(81822^19321-1)/(81822^139-1)94239Ryan Propper11/2023
9963(3^197521+2)/5165594237Lelio R Paula04/2013
99642^313045-595594236Lelio R Paula03/2016
996522099^18358+18358^2209994227Hans Havermann08/2020
9966(9*33^62046+53831)/1694218Eric Chen05/2023
9967(67*10^94212+23)/994213Ray Chandler02/2011
99682^312909-186520394195Enzo Doria03/2016
996925013^5830+5830^2501394191Hans Havermann09/2020
99702^312848-14994177Lelio R Paula11/2012
9971(2^312819+3278)/294168Stefano Morozzi02/2021
99724^156403-7759794164Mike Oakes04/2011
997318^75004-8594151Lelio R Paula06/2016
9974(19573*10^94146-7)/994150Patrick De Geest05/2023
997519^73622-4894145Lelio R Paula06/2016
9976(11^90397-3^90397)/894138Robert Price04/2011
9977(3^197287+5)/1694129Lelio R Paula04/2013
9978(23*10^94123-29)/394124Robert Price03/2022
997924220^7691+7691^2422094119Hans Havermann09/2020
998012^87212-3794118Lelio R Paula06/2016
998111^90376+7694117Lelio R Paula05/2016
9982(6^120946-11)/594114Paul Bourdelais11/2011
9983(2^312622+534)/294109Stefano Morozzi09/2020
9984(10^94096+191)/394096Robert Price11/2017
998523794^9005+9005^2379494093Hans Havermann09/2020
99862^312562-11268594091Enzo Doria06/2014
9987137^44026-294072Lelio R Paula10/2017
9988s(164441)94052Robert Price05/2020
99892^312404-86968810594043Lelio R Paula09/2016
99902^312387+279353394038Enzo Doria03/2016
999210^94016+9194017Robert Price04/2011
9991(15*2^312325-1)/720194017Lelio R Paula02/2014
999310^94016-18896394016Patrick De Geest08/2013
9994(17*2^312315-1)/4594016Lelio R Paula02/2014
9995(401*10^94010+13)/994012Robert Price09/2021
999623866^8691+8691^2386694010Hans Havermann08/2020
99976^120802+766194003Mike Oakes04/2011
9998(67607*2^312254+1)/17794001Lelio R Paula06/2014
9999(2^312245+702)/293995Stefano Morozzi09/2020
10000(56*10^93993+493)/993994Robert Price10/2021


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Created by  Henri Lifchitz & Renaud Lifchitz : October, 26 2000, last modification: December, 05 2023 08:12 (Time in France)

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