PRP Records

Probable Primes Top 10000

(294613 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 ?
925125206!-p(16290)100001Henri Lifchitz09/2006
925225206!-p(19647)100001Henri Lifchitz02/2007
92532^332194+11473100001Henri Lifchitz03/2007
925410^99999+309403100000Daniel Heuer01/2004
925510^100000-260199100000Patrick De Geest01/2010
92562^332192+10192681100000Sujan Das06/2022
92571610172603059^8192+1610172602878^8192100000Youcef Lemsafer01/2023
925910^99999-5951199999Patrick De Geest07/2009
925810^99998+23543799999Patrick De Geest02/2020
926010^99998-28658799998Patrick De Geest02/2020
926110^99997+7229799998Patrick De Geest02/2020
926210^99997-40262799997Patrick De Geest02/2020
926310^99996+27985399997Patrick De Geest02/2020
926410^99997-50000000199997Robert Price12/2020
926510^99996-9496199996Patrick De Geest02/2020
926610^99995+5463399996Patrick De Geest02/2020
926710^99995-10142999995Patrick De Geest02/2020
926810^99994+11727199995Patrick De Geest02/2020
926910^99994-45228999994Patrick De Geest02/2020
927010^99993+37131199994Patrick De Geest02/2020
927110^99993-18649199993Patrick De Geest02/2020
927210^99992+1743199993Patrick De Geest02/2020
927310^99992-2860799992Patrick De Geest02/2020
927410^99991+12539199992Patrick De Geest02/2020
927510^99991-20457399991Patrick De Geest02/2020
927610^99990+1389999991Patrick De Geest02/2020
927710^99990-811199990Patrick De Geest02/2020
92782^332141-11307399985Enzo Doria07/2014
9279(1610172603037^8192+1610172602919^8192)/1711094812747366699983Youcef Lemsafer01/2023
92806*10^99979-7999980Robert Price03/2022
9282(3^209561+2)/72810125599978Lelio R Paula09/2013
928123827^15702+15702^2382799978Hans Havermann04/2018
92832^332085+186589799968Enzo Doria03/2016
9284(9787*2^332070-1)/93640236999959Lelio R Paula05/2015
92852^332023+19199949Lelio R Paula02/2011
9286(6271^26321-1)/627099946Serge Batalov06/2022
92877*10^99944+2799945Robert Price11/2020
92883188^28523-28523^318899931Norbert Schneider06/2023
92892^331938+7114999924Enzo Doria04/2016
92902^331932-7879599922Lelio R Paula09/2016
92912^331921+77199919Lelio R Paula01/2013
92927947^25618-25618^794799916Norbert Schneider08/2023
9293(3^209419-2)/513275599912Lelio R Paula09/2013
92942^331860-11498999900Enzo Doria05/2015
92952^331746-1165599866Lelio R Paula09/2016
929611^95891-2899861Lelio R Paula08/2016
9297(2^331694-5)/1199849Lelio R Paula10/2013
9298(3^209246+7)/6499834Lelio R Paula09/2013
929925062^9617+9617^2506299823Hans Havermann04/2018
930015^84866-5299811Lelio R Paula08/2016
930113^89600+3099810Lelio R Paula08/2016
93022^331527+10028024506599800Paul Bourdelais10/2021
930322950^22309+22309^2295099798Hans Havermann03/2018
93045^142772-3899794Lelio R Paula08/2016
9305(7482^25759-1)/748199787Serge Batalov06/2022
9306(23*2^331459+1)/47599778Lelio R Paula11/2013
93072^331416-331416+199767Robert Price10/2014
93082^331256-5799718Lelio R Paula12/2012
930928192^3443+3443^2819299714Hans Havermann03/2018
93102^331185+73799697Lelio R Paula01/2013
9311(4*10^99693+149)/999693Robert Price03/2017
93122^331154+188052799688Enzo Doria10/2016
9314(19^77951+1)/2099679Paul Bourdelais03/2010
931324354^12385+12385^2435499679Hans Havermann03/2018
93152^331110+187045999675Enzo Doria05/2016
93165*2^331075+799665Lelio R Paula08/2014
931725776^7351+7351^2577699659Hans Havermann02/2018
9318(16*10^99656-31)/399657Robert Price03/2016
9319(6059^26347-1)/605899652Serge Batalov06/2022
9320(15544^23773-1)/1554399642Serge Batalov06/2022
93222^330968+34599632Lelio R Paula09/2016
9321(2^330969+690)/299632Stefano Morozzi09/2020
93242*5^142528-799624Lelio R Paula11/2014
93232^330942+7732999624Enzo Doria05/2016
932514^86914-9999615Lelio R Paula08/2016
9326(19*2^330902+1)/7799611Lelio R Paula11/2013
932722971^21692+21692^2297199610Hans Havermann03/2018
93282^330845+7168799595Enzo Doria04/2016
9329(26667^22501-1)/2666699585Serge Batalov06/2022
9330(23*2^330770+1)/399573Lelio R Paula11/2013
933124494^11613+11613^2449499567Hans Havermann03/2018
93322^330735+841599562Lelio R Paula09/2016
93332^330720+7407199557Enzo Doria04/2016
9334(10405^24781-1)/1040499548Serge Batalov06/2022
933631^66738-299531Lelio R Paula09/2013
9335(9002^25171-1)/900199531Serge Batalov06/2022
9337(5023^26893-1)/502299527Serge Batalov06/2022
93387*3^208567+499513Lelio R Paula08/2014
9339(15881^23689-1)/1588099511Serge Batalov06/2022
9340(13*10^99508+47)/399509Robert Price01/2017
93412^330553+77999507Lelio R Paula01/2013
934215^84606-9499505Lelio R Paula08/2016
9343(10^99497+173)/399497Robert Price05/2021
93449*10^99493-4399494Robert Price09/2021
93456^127858+4799493Lelio R Paula08/2016
93465^142337+4899490Lelio R Paula08/2016
93477^117724-2099489Lelio R Paula08/2016
9348(559^36209-1)/55899479Serge Batalov06/2022
9349(13470^24091-1)/1346999477Serge Batalov06/2022
9350(29*10^99474-17)/399475Erik Branger09/2014
9351(185*10^99466-11)/399468Robert Price10/2020
9352(2^330410+2038)/299464Stefano Morozzi09/2020
9353(9*2^330407-1)/799463Lelio R Paula03/2014
9354(516*32^66077-175)/3199458Eric Chen04/2023
9355(2863^28771-1)/286299453Serge Batalov06/2022
9356(2^330373+2114)/299452Stefano Morozzi09/2020
9357(68*10^99441+7)/399443Robert Price03/2016
935810^99434+15557199435Patrick De Geest04/2020
935910^99434-12345678999434Robert Price02/2020
936010^99434-19123799434Patrick De Geest04/2020
936146^59791-45^5979199418Jean-Louis Charton01/2013
936223839^14802+14802^2383999417Hans Havermann02/2018
9363(2*10^99408+529)/999408Robert Price01/2017
9364(2^330216+3510)/299405Stefano Morozzi09/2020
936553^57646-299398Lelio R Paula09/2013
93662^330165+187002599390Enzo Doria05/2016
93677*10^99383+9799384Robert Price09/2021
93682^330142-15599383Lelio R Paula12/2012
93692^330088-11525999367Enzo Doria06/2015
937024216^12671+12671^2421699354Hans Havermann01/2018
9371Phi(200548,10)/320876999354Makoto Kamada04/2019
9372(746*10^99303+1)/999305Robert Price02/2017
93733^208107+4099293Lelio R Paula08/2016
93742^329843+21134399293Enzo Doria08/2023
9375(3939^27617-1)/393899291Serge Batalov06/2022
9376(5*2^329833-1)/36999288Lelio R Paula02/2014
93778*3^208093+599287Lelio R Paula08/2014
93785^142043+5699284Lelio R Paula08/2016
9379(13*10^99282-157)/999283Robert Price05/2021
9380(10^99284+7)/53/6799281Alfred Reich06/2021
938122*10^99275+799277Robert Price04/2016
93822^329778+187618999274Enzo Doria07/2016
9383(149557^19321-1)/(149557^139-1)99264Ryan Propper11/2023
9384(6580^25997-1)/657999259Serge Batalov06/2022
9385(2249^29611-1)/224899253Serge Batalov06/2022
9386(10^99239-13)/399239Robert Price02/2017
9387(1199^32233-1)/119899237Serge Batalov06/2022
93893^207987+6299236Lelio R Paula08/2016
9388(62*10^99235+91)/999236Robert Price07/2021
93902^329638+4999231Lelio R Paula12/2012
93917^117413-1899226Lelio R Paula08/2016
93922^329586-45890399216Enzo Doria04/2015
9393(6290^26119-1)/628999214Serge Batalov06/2022
93952^329553+10199206Lelio R Paula12/2012
9394(21297^22921-1)/2129699206Serge Batalov06/2022
93962^329551-11289799205Enzo Doria06/2014
9397(3^207925+7)/5099204Lelio R Paula09/2013
93986^127458-1799399182Enzo Doria03/2013
939927197^4428+4428^2719799166Hans Havermann10/2017
9400(46*10^99143-1)/999144Robert Price12/2014
9401(64*10^99135+161)/999136Robert Price08/2022
94027*10^99133+6999134Robert Price10/2017
9403(21701^22861-1)/2170099132Serge Batalov06/2022
940418^78968-306599127Enzo Doria03/2013
940625927^6654+6654^2592799122Hans Havermann10/2017
940587915!4+1699122Robert Price09/2019
94072^329259+18999117Lelio R Paula12/2012
94088*10^99113+3999114Robert Price01/2017
94096^127364+7799109Lelio R Paula08/2016
9410(82*10^99103+143)/999104Robert Price06/2021
9411(11414^24421-1)/1141399083Serge Batalov06/2022
9412(2^329135+1110)/299080Stefano Morozzi09/2020
9413(22089^22807-1)/2208899074Serge Batalov06/2022
9414(59*10^99069+391)/999070Robert Price03/2021
9415(797*10^99061-41)/999063Robert Price04/2022
94162^329058-28768199057Harrison Mesh06/2022
94176^127285+1399047Lelio R Paula08/2016
9418(228581#+235862)/(2^3*11*71*151)99044Makoto Morimoto10/2017
94192^329007+7328399041Enzo Doria04/2016
9420(145413^19321-1)/(145413^139-1)99030Ryan Propper11/2023
94215*3^207543-899024Lelio R Paula08/2014
9422(2^328930+570)/299018Stefano Morozzi09/2020
94232^328885+14999005Lelio R Paula12/2012
942523392^17075+17075^2339299004Hans Havermann09/2017
9424(7424^25579-1)/742399004Serge Batalov06/2022
9426(2^328879-9)/11999001Lelio R Paula10/2013
94275^141618+5498987Lelio R Paula08/2016
94282^328824+2439198986Enzo Doria10/2023
94298*10^98982+5198983Robert Price05/2017
9430(21*2^328809-1)/770998979Lelio R Paula03/2014
94312^328794-279760198977Enzo Doria04/2016
9432(88331^20011-1)/8833098972Serge Batalov06/2022
94336^127176+598963Lelio R Paula11/2014
94342*10^98961-2198962Robert Price09/2020
943524262^11989+11989^2426298960Hans Havermann09/2017
9436(60138^20707-1)/6013798958Serge Batalov06/2022
94372^328700-10970998949Enzo Doria04/2014
9438(2^328698+1810)/298948Stefano Morozzi01/2021
9439(1014^32917-1)/101398947Serge Batalov06/2022
944087771!4-12898944Robert Price11/2019
9441(4576^27031-1)/457598943Serge Batalov06/2022
9442(2^328658+3042)/298936Stefano Morozzi09/2020
9443(1933^30103-1)/193298923Serge Batalov06/2022
944446711!2-2^4671198916Robert Price09/2015
94459*7^117037+498909Lelio R Paula11/2014
9446127^47012+12698905Norbert Schneider01/2019
9447(93826^19891-1)/9382598900Serge Batalov06/2022
9448(2^328525+1250)/298896Stefano Morozzi09/2020
9449(10^98890+149)/398890Serge Batalov12/2014
945022775^21978+21978^2277598889Hans Havermann08/2017
94512^328497-21693398888Enzo Doria05/2014
94522^328487+3276998885Lelio R Paula08/2016
94533^207250-11235898884Enzo Doria06/2014
945413^88754-9098867Lelio R Paula08/2016
94552^328406+70998861Lelio R Paula02/2013
94562*10^98860-2198861Robert Price09/2020
9457(17*2^328413-1)/1617398860Lelio R Paula03/2014
94587^116976+7698857Lelio R Paula08/2016
9459(2^328378+2710)/298852Stefano Morozzi09/2020
9460(25411^22441-1)/2541098849Serge Batalov06/2022
9461(18668^23143-1)/1866798842Serge Batalov06/2022
94632^328335+115598839Lelio R Paula08/2016
94622^328333-34900398839Harrison Mesh06/2022
9465(3*2^328311+1)/598832Lelio R Paula11/2013
9464287^40210+40210^28798832Norbert Schneider11/2014
9466(2^328284+9)/132598821Lelio R Paula10/2013
9467(21*2^328258+1)/212598814Lelio R Paula11/2013
9468(28623^22171-1)/2862298806Serge Batalov06/2022
946924746^9825+9825^2474698795Hans Havermann07/2020
947026620^5143+5143^2662098793Hans Havermann07/2020
947165^54491+4898788Lelio R Paula04/2016
94723^207042+9898785Lelio R Paula08/2016
9473(2^328121+3110)/298774Stefano Morozzi09/2020
947410^98754+7338398755Patrick De Geest02/2021
94773^206977-11275698754Enzo Doria07/2014
947610^98754-4000000000198754Robert Price09/2020
947510^98754-16934398754Patrick De Geest02/2021
94787^116846-5098747Lelio R Paula08/2016
9479(19152^23059-1)/1915198740Serge Batalov06/2022
948023267^17512+17512^2326798730Hans Havermann04/2020
94812^327967-2863598728Lelio R Paula08/2016
9482707^34642+34642^70798710Norbert Schneider12/2017
9483(10771^24481-1)/1077098710Serge Batalov06/2022
94846^126850-4798709Lelio R Paula08/2016
9485(2^327886+2170)/298704Stefano Morozzi09/2020
9486(22*10^98697+47)/398698Robert Price06/2021
9487(139706^19321-1)/(139706^139-1)98696Ryan Propper11/2023
94888*6^126830-798694Lelio R Paula11/2014
948911^94770-27098693Enzo Doria08/2012
9490(2^327846+3250)/298692Stefano Morozzi01/2021
94912^327832+4398688Lelio R Paula12/2012
94922^327795+76198677Lelio R Paula02/2013
9493(2^327796+1522)/298677Stefano Morozzi09/2020
949410^98669+14741198670Patrick De Geest11/2016
949610^98669-9^(98669-1)98669Robert Price05/2016
949510^98669-10524998669Patrick De Geest11/2016
9497(7911^25309-1)/791098657Serge Batalov06/2022
94982^327671-10980198639Enzo Doria04/2014
949924398^11037+11037^2439898638Hans Havermann10/2019
95005^141090-1498618Lelio R Paula08/2016


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Created by  Henri Lifchitz & Renaud Lifchitz : October, 26 2000, last modification: March, 04 2024 15:31 (Time in France)

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