PRP Records

Probable Primes Top 10000

(294627 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 ?
926125206!+p(4114)100001Henri Lifchitz09/2005
926225206!-p(5447)100001Henri Lifchitz10/2005
926325206!-p(12402)100001Henri Lifchitz04/2006
926425206!-p(16290)100001Henri Lifchitz09/2006
926525206!-p(19647)100001Henri Lifchitz02/2007
92662^332194+11473100001Henri Lifchitz03/2007
925610^100000+342909100001Milton L. Brown12/2007
925710^100000+346579100001Robert Price04/2012
925810^100000+829767100001Robert Price05/2012
925910^100000+871899100001Robert Price05/2012
926010^100000+1475997100001Robert Price07/2012
925110^100000+2483527100001Robert Price12/2012
925210^100000+2503087100001Robert Price12/2012
925310^100000+2686179100001Robert Price12/2012
925410^100000+2688933100001Robert Price12/2012
925510^100000+3667159100001Robert Price08/2013
926710^99999+309403100000Daniel Heuer01/2004
926810^100000-260199100000Patrick De Geest01/2010
92692^332192+10192681100000Sujan Das06/2022
92701610172603059^8192+1610172602878^8192100000Youcef Lemsafer01/2023
927210^99999-5951199999Patrick De Geest07/2009
927110^99998+23543799999Patrick De Geest02/2020
927310^99998-28658799998Patrick De Geest02/2020
927410^99997+7229799998Patrick De Geest02/2020
927510^99997-40262799997Patrick De Geest02/2020
927610^99996+27985399997Patrick De Geest02/2020
927710^99997-50000000199997Robert Price12/2020
927810^99996-9496199996Patrick De Geest02/2020
927910^99995+5463399996Patrick De Geest02/2020
928010^99995-10142999995Patrick De Geest02/2020
928110^99994+11727199995Patrick De Geest02/2020
928210^99994-45228999994Patrick De Geest02/2020
928310^99993+37131199994Patrick De Geest02/2020
928410^99993-18649199993Patrick De Geest02/2020
928510^99992+1743199993Patrick De Geest02/2020
928610^99992-2860799992Patrick De Geest02/2020
928710^99991+12539199992Patrick De Geest02/2020
928810^99991-20457399991Patrick De Geest02/2020
928910^99990+1389999991Patrick De Geest02/2020
929010^99990-811199990Patrick De Geest02/2020
92912^332141-11307399985Enzo Doria07/2014
9292(1610172603037^8192+1610172602919^8192)/1711094812747366699983Youcef Lemsafer01/2023
92936*10^99979-7999980Robert Price03/2022
9295(3^209561+2)/72810125599978Lelio R Paula09/2013
929423827^15702+15702^2382799978Hans Havermann04/2018
92962^332085+186589799968Enzo Doria03/2016
9297(9787*2^332070-1)/93640236999959Lelio R Paula05/2015
92982^332023+19199949Lelio R Paula02/2011
9299(6271^26321-1)/627099946Serge Batalov06/2022
93007*10^99944+2799945Robert Price11/2020
93013188^28523-28523^318899931Norbert Schneider06/2023
93022^331938+7114999924Enzo Doria04/2016
93032^331932-7879599922Lelio R Paula09/2016
93042^331921+77199919Lelio R Paula01/2013
93057947^25618-25618^794799916Norbert Schneider08/2023
9306(3^209419-2)/513275599912Lelio R Paula09/2013
93072^331860-11498999900Enzo Doria05/2015
93082^331746-1165599866Lelio R Paula09/2016
930911^95891-2899861Lelio R Paula08/2016
9310(2^331694-5)/1199849Lelio R Paula10/2013
9311(3^209246+7)/6499834Lelio R Paula09/2013
931225062^9617+9617^2506299823Hans Havermann04/2018
931315^84866-5299811Lelio R Paula08/2016
931413^89600+3099810Lelio R Paula08/2016
93152^331527+10028024506599800Paul Bourdelais10/2021
931622950^22309+22309^2295099798Hans Havermann03/2018
93175^142772-3899794Lelio R Paula08/2016
9318(7482^25759-1)/748199787Serge Batalov06/2022
9319(23*2^331459+1)/47599778Lelio R Paula11/2013
93202^331416-331416+199767Robert Price10/2014
93212^331256-5799718Lelio R Paula12/2012
932228192^3443+3443^2819299714Hans Havermann03/2018
93232^331185+73799697Lelio R Paula01/2013
9324(4*10^99693+149)/999693Robert Price03/2017
93252^331154+188052799688Enzo Doria10/2016
9327(19^77951+1)/2099679Paul Bourdelais03/2010
932624354^12385+12385^2435499679Hans Havermann03/2018
93282^331110+187045999675Enzo Doria05/2016
93295*2^331075+799665Lelio R Paula08/2014
933025776^7351+7351^2577699659Hans Havermann02/2018
9331(16*10^99656-31)/399657Robert Price03/2016
9332(6059^26347-1)/605899652Serge Batalov06/2022
9333(15544^23773-1)/1554399642Serge Batalov06/2022
93352^330968+34599632Lelio R Paula09/2016
9334(2^330969+690)/299632Stefano Morozzi09/2020
93372*5^142528-799624Lelio R Paula11/2014
93362^330942+7732999624Enzo Doria05/2016
933814^86914-9999615Lelio R Paula08/2016
9339(19*2^330902+1)/7799611Lelio R Paula11/2013
934022971^21692+21692^2297199610Hans Havermann03/2018
93412^330845+7168799595Enzo Doria04/2016
9342(26667^22501-1)/2666699585Serge Batalov06/2022
9343(23*2^330770+1)/399573Lelio R Paula11/2013
934424494^11613+11613^2449499567Hans Havermann03/2018
93452^330735+841599562Lelio R Paula09/2016
93462^330720+7407199557Enzo Doria04/2016
9347(10405^24781-1)/1040499548Serge Batalov06/2022
934931^66738-299531Lelio R Paula09/2013
9348(9002^25171-1)/900199531Serge Batalov06/2022
9350(5023^26893-1)/502299527Serge Batalov06/2022
93517*3^208567+499513Lelio R Paula08/2014
9352(15881^23689-1)/1588099511Serge Batalov06/2022
9353(13*10^99508+47)/399509Robert Price01/2017
93542^330553+77999507Lelio R Paula01/2013
935515^84606-9499505Lelio R Paula08/2016
9356(10^99497+173)/399497Robert Price05/2021
93579*10^99493-4399494Robert Price09/2021
93586^127858+4799493Lelio R Paula08/2016
93595^142337+4899490Lelio R Paula08/2016
93607^117724-2099489Lelio R Paula08/2016
9361(559^36209-1)/55899479Serge Batalov06/2022
9362(13470^24091-1)/1346999477Serge Batalov06/2022
9363(29*10^99474-17)/399475Erik Branger09/2014
9364(185*10^99466-11)/399468Robert Price10/2020
9365(2^330410+2038)/299464Stefano Morozzi09/2020
9366(9*2^330407-1)/799463Lelio R Paula03/2014
9367(516*32^66077-175)/3199458Eric Chen04/2023
9368(2863^28771-1)/286299453Serge Batalov06/2022
9369(2^330373+2114)/299452Stefano Morozzi09/2020
9370(68*10^99441+7)/399443Robert Price03/2016
937110^99434+15557199435Patrick De Geest04/2020
937210^99434-12345678999434Robert Price02/2020
937310^99434-19123799434Patrick De Geest04/2020
937446^59791-45^5979199418Jean-Louis Charton01/2013
937523839^14802+14802^2383999417Hans Havermann02/2018
9376(2*10^99408+529)/999408Robert Price01/2017
9377(2^330216+3510)/299405Stefano Morozzi09/2020
937853^57646-299398Lelio R Paula09/2013
93792^330165+187002599390Enzo Doria05/2016
93807*10^99383+9799384Robert Price09/2021
93812^330142-15599383Lelio R Paula12/2012
93822^330088-11525999367Enzo Doria06/2015
938324216^12671+12671^2421699354Hans Havermann01/2018
9384Phi(200548,10)/320876999354Makoto Kamada04/2019
9385(746*10^99303+1)/999305Robert Price02/2017
93863^208107+4099293Lelio R Paula08/2016
93872^329843+21134399293Enzo Doria08/2023
9388(3939^27617-1)/393899291Serge Batalov06/2022
9389(5*2^329833-1)/36999288Lelio R Paula02/2014
93908*3^208093+599287Lelio R Paula08/2014
93915^142043+5699284Lelio R Paula08/2016
9392(13*10^99282-157)/999283Robert Price05/2021
9393(10^99284+7)/53/6799281Alfred Reich06/2021
939422*10^99275+799277Robert Price04/2016
93952^329778+187618999274Enzo Doria07/2016
9396(149557^19321-1)/(149557^139-1)99264Ryan Propper11/2023
9397(6580^25997-1)/657999259Serge Batalov06/2022
9398(2249^29611-1)/224899253Serge Batalov06/2022
9399(10^99239-13)/399239Robert Price02/2017
9400(1199^32233-1)/119899237Serge Batalov06/2022
94023^207987+6299236Lelio R Paula08/2016
9401(62*10^99235+91)/999236Robert Price07/2021
94032^329638+4999231Lelio R Paula12/2012
94047^117413-1899226Lelio R Paula08/2016
94052^329586-45890399216Enzo Doria04/2015
9406(6290^26119-1)/628999214Serge Batalov06/2022
94082^329553+10199206Lelio R Paula12/2012
9407(21297^22921-1)/2129699206Serge Batalov06/2022
94092^329551-11289799205Enzo Doria06/2014
9410(3^207925+7)/5099204Lelio R Paula09/2013
94116^127458-1799399182Enzo Doria03/2013
941227197^4428+4428^2719799166Hans Havermann10/2017
9413(46*10^99143-1)/999144Robert Price12/2014
9414(64*10^99135+161)/999136Robert Price08/2022
94157*10^99133+6999134Robert Price10/2017
9416(21701^22861-1)/2170099132Serge Batalov06/2022
941718^78968-306599127Enzo Doria03/2013
941925927^6654+6654^2592799122Hans Havermann10/2017
941887915!4+1699122Robert Price09/2019
94202^329259+18999117Lelio R Paula12/2012
94218*10^99113+3999114Robert Price01/2017
94226^127364+7799109Lelio R Paula08/2016
9423(82*10^99103+143)/999104Robert Price06/2021
9424(11414^24421-1)/1141399083Serge Batalov06/2022
9425(2^329135+1110)/299080Stefano Morozzi09/2020
9426(22089^22807-1)/2208899074Serge Batalov06/2022
9427(59*10^99069+391)/999070Robert Price03/2021
9428(797*10^99061-41)/999063Robert Price04/2022
94292^329058-28768199057Harrison Mesh06/2022
94306^127285+1399047Lelio R Paula08/2016
9431(228581#+235862)/(2^3*11*71*151)99044Makoto Morimoto10/2017
94322^329007+7328399041Enzo Doria04/2016
9433(145413^19321-1)/(145413^139-1)99030Ryan Propper11/2023
94345*3^207543-899024Lelio R Paula08/2014
9435(2^328930+570)/299018Stefano Morozzi09/2020
94362^328885+14999005Lelio R Paula12/2012
943823392^17075+17075^2339299004Hans Havermann09/2017
9437(7424^25579-1)/742399004Serge Batalov06/2022
9439(2^328879-9)/11999001Lelio R Paula10/2013
94405^141618+5498987Lelio R Paula08/2016
94412^328824+2439198986Enzo Doria10/2023
94428*10^98982+5198983Robert Price05/2017
9443(21*2^328809-1)/770998979Lelio R Paula03/2014
94442^328794-279760198977Enzo Doria04/2016
9445(88331^20011-1)/8833098972Serge Batalov06/2022
94466^127176+598963Lelio R Paula11/2014
94472*10^98961-2198962Robert Price09/2020
944824262^11989+11989^2426298960Hans Havermann09/2017
9449(60138^20707-1)/6013798958Serge Batalov06/2022
94502^328700-10970998949Enzo Doria04/2014
9451(2^328698+1810)/298948Stefano Morozzi01/2021
9452(1014^32917-1)/101398947Serge Batalov06/2022
945387771!4-12898944Robert Price11/2019
9454(4576^27031-1)/457598943Serge Batalov06/2022
9455(2^328658+3042)/298936Stefano Morozzi09/2020
9456(1933^30103-1)/193298923Serge Batalov06/2022
945746711!2-2^4671198916Robert Price09/2015
94589*7^117037+498909Lelio R Paula11/2014
9459127^47012+12698905Norbert Schneider01/2019
9460(93826^19891-1)/9382598900Serge Batalov06/2022
9461(2^328525+1250)/298896Stefano Morozzi09/2020
9462(10^98890+149)/398890Serge Batalov12/2014
946322775^21978+21978^2277598889Hans Havermann08/2017
94642^328497-21693398888Enzo Doria05/2014
94652^328487+3276998885Lelio R Paula08/2016
94663^207250-11235898884Enzo Doria06/2014
946713^88754-9098867Lelio R Paula08/2016
94682^328406+70998861Lelio R Paula02/2013
94692*10^98860-2198861Robert Price09/2020
9470(17*2^328413-1)/1617398860Lelio R Paula03/2014
94717^116976+7698857Lelio R Paula08/2016
9472(2^328378+2710)/298852Stefano Morozzi09/2020
9473(25411^22441-1)/2541098849Serge Batalov06/2022
9474(18668^23143-1)/1866798842Serge Batalov06/2022
94762^328335+115598839Lelio R Paula08/2016
94752^328333-34900398839Harrison Mesh06/2022
9478(3*2^328311+1)/598832Lelio R Paula11/2013
9477287^40210+40210^28798832Norbert Schneider11/2014
9479(2^328284+9)/132598821Lelio R Paula10/2013
9480(21*2^328258+1)/212598814Lelio R Paula11/2013
9481(28623^22171-1)/2862298806Serge Batalov06/2022
948224746^9825+9825^2474698795Hans Havermann07/2020
948326620^5143+5143^2662098793Hans Havermann07/2020
948465^54491+4898788Lelio R Paula04/2016
94853^207042+9898785Lelio R Paula08/2016
9486(2^328121+3110)/298774Stefano Morozzi09/2020
948710^98754+7338398755Patrick De Geest02/2021
94903^206977-11275698754Enzo Doria07/2014
948910^98754-4000000000198754Robert Price09/2020
948810^98754-16934398754Patrick De Geest02/2021
94917^116846-5098747Lelio R Paula08/2016
9492(19152^23059-1)/1915198740Serge Batalov06/2022
949323267^17512+17512^2326798730Hans Havermann04/2020
94942^327967-2863598728Lelio R Paula08/2016
9495707^34642+34642^70798710Norbert Schneider12/2017
9496(10771^24481-1)/1077098710Serge Batalov06/2022
94976^126850-4798709Lelio R Paula08/2016
9498(2^327886+2170)/298704Stefano Morozzi09/2020
9499(22*10^98697+47)/398698Robert Price06/2021
9500(139706^19321-1)/(139706^139-1)98696Ryan Propper11/2023


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Created by  Henri Lifchitz & Renaud Lifchitz : October, 26 2000, last modification: March, 12 2024 13:37 (Time in France)

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