PRP Records

Probable Primes Top 10000

(293510 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 ?
87512^331746-1165599866Lelio R Paula09/2016
875211^95891-2899861Lelio R Paula08/2016
8753(2^331694-5)/1199849Lelio R Paula10/2013
8754(3^209246+7)/6499834Lelio R Paula09/2013
875525062^9617+9617^2506299823Hans Havermann04/2018
875615^84866-5299811Lelio R Paula08/2016
875713^89600+3099810Lelio R Paula08/2016
87582^331527+10028024506599800Paul Bourdelais10/2021
875922950^22309+22309^2295099798Hans Havermann03/2018
87605^142772-3899794Lelio R Paula08/2016
8761(7482^25759-1)/748199787Serge Batalov06/2022
8762(23*2^331459+1)/47599778Lelio R Paula11/2013
87632^331416-331416+199767Robert Price10/2014
87642^331256-5799718Lelio R Paula12/2012
876528192^3443+3443^2819299714Hans Havermann03/2018
87662^331185+73799697Lelio R Paula01/2013
8767(4*10^99693+149)/999693Robert Price03/2017
87682^331154+188052799688Enzo Doria10/2016
8770(19^77951+1)/2099679Paul Bourdelais03/2010
876924354^12385+12385^2435499679Hans Havermann03/2018
87712^331110+187045999675Enzo Doria05/2016
87725*2^331075+799665Lelio R Paula08/2014
877325776^7351+7351^2577699659Hans Havermann02/2018
8774(16*10^99656-31)/399657Robert Price03/2016
8775(6059^26347-1)/605899652Serge Batalov06/2022
8776(15544^23773-1)/1554399642Serge Batalov06/2022
87782^330968+34599632Lelio R Paula09/2016
8777(2^330969+690)/299632Stefano Morozzi09/2020
87802*5^142528-799624Lelio R Paula11/2014
87792^330942+7732999624Enzo Doria05/2016
878114^86914-9999615Lelio R Paula08/2016
8782(19*2^330902+1)/7799611Lelio R Paula11/2013
878322971^21692+21692^2297199610Hans Havermann03/2018
87842^330845+7168799595Enzo Doria04/2016
8785(26667^22501-1)/2666699585Serge Batalov06/2022
8786(23*2^330770+1)/399573Lelio R Paula11/2013
878724494^11613+11613^2449499567Hans Havermann03/2018
87882^330735+841599562Lelio R Paula09/2016
87892^330720+7407199557Enzo Doria04/2016
8790(10405^24781-1)/1040499548Serge Batalov06/2022
879231^66738-299531Lelio R Paula09/2013
8791(9002^25171-1)/900199531Serge Batalov06/2022
8793(5023^26893-1)/502299527Serge Batalov06/2022
87947*3^208567+499513Lelio R Paula08/2014
8795(15881^23689-1)/1588099511Serge Batalov06/2022
8796(13*10^99508+47)/399509Robert Price01/2017
87972^330553+77999507Lelio R Paula01/2013
879815^84606-9499505Lelio R Paula08/2016
8799(10^99497+173)/399497Robert Price05/2021
88009*10^99493-4399494Robert Price09/2021
88016^127858+4799493Lelio R Paula08/2016
88025^142337+4899490Lelio R Paula08/2016
88037^117724-2099489Lelio R Paula08/2016
8804(559^36209-1)/55899479Serge Batalov06/2022
8805(13470^24091-1)/1346999477Serge Batalov06/2022
8806(29*10^99474-17)/399475Erik Branger09/2014
8807(185*10^99466-11)/399468Robert Price10/2020
8808(2^330410+2038)/299464Stefano Morozzi09/2020
8809(9*2^330407-1)/799463Lelio R Paula03/2014
8810(516*32^66077-175)/3199458Eric Chen04/2023
8811(2863^28771-1)/286299453Serge Batalov06/2022
8812(2^330373+2114)/299452Stefano Morozzi09/2020
8813(68*10^99441+7)/399443Robert Price03/2016
881410^99434+15557199435Patrick De Geest04/2020
881510^99434-12345678999434Robert Price02/2020
881610^99434-19123799434Patrick De Geest04/2020
881746^59791-45^5979199418Jean-Louis Charton01/2013
881823839^14802+14802^2383999417Hans Havermann02/2018
8819(2*10^99408+529)/999408Robert Price01/2017
8820(2^330216+3510)/299405Stefano Morozzi09/2020
882153^57646-299398Lelio R Paula09/2013
88222^330165+187002599390Enzo Doria05/2016
88237*10^99383+9799384Robert Price09/2021
88242^330142-15599383Lelio R Paula12/2012
88252^330088-11525999367Enzo Doria06/2015
882624216^12671+12671^2421699354Hans Havermann01/2018
8827Phi(200548,10)/320876999354Makoto Kamada04/2019
8828(746*10^99303+1)/999305Robert Price02/2017
88293^208107+4099293Lelio R Paula08/2016
88302^329843+21134399293Enzo Doria08/2023
8831(3939^27617-1)/393899291Serge Batalov06/2022
8832(5*2^329833-1)/36999288Lelio R Paula02/2014
88338*3^208093+599287Lelio R Paula08/2014
88345^142043+5699284Lelio R Paula08/2016
8835(13*10^99282-157)/999283Robert Price05/2021
8836(10^99284+7)/53/6799281Alfred Reich06/2021
883722*10^99275+799277Robert Price04/2016
88382^329778+187618999274Enzo Doria07/2016
8839(6580^25997-1)/657999259Serge Batalov06/2022
8840(2249^29611-1)/224899253Serge Batalov06/2022
8841(10^99239-13)/399239Robert Price02/2017
8842(1199^32233-1)/119899237Serge Batalov06/2022
88443^207987+6299236Lelio R Paula08/2016
8843(62*10^99235+91)/999236Robert Price07/2021
88452^329638+4999231Lelio R Paula12/2012
88467^117413-1899226Lelio R Paula08/2016
88472^329586-45890399216Enzo Doria04/2015
8848(6290^26119-1)/628999214Serge Batalov06/2022
88502^329553+10199206Lelio R Paula12/2012
8849(21297^22921-1)/2129699206Serge Batalov06/2022
88512^329551-11289799205Enzo Doria06/2014
8852(3^207925+7)/5099204Lelio R Paula09/2013
88536^127458-1799399182Enzo Doria03/2013
885427197^4428+4428^2719799166Hans Havermann10/2017
8855(46*10^99143-1)/999144Robert Price12/2014
8856(64*10^99135+161)/999136Robert Price08/2022
88577*10^99133+6999134Robert Price10/2017
8858(21701^22861-1)/2170099132Serge Batalov06/2022
885918^78968-306599127Enzo Doria03/2013
886125927^6654+6654^2592799122Hans Havermann10/2017
886087915!4+1699122Robert Price09/2019
88622^329259+18999117Lelio R Paula12/2012
88638*10^99113+3999114Robert Price01/2017
88646^127364+7799109Lelio R Paula08/2016
8865(82*10^99103+143)/999104Robert Price06/2021
8866(11414^24421-1)/1141399083Serge Batalov06/2022
8867(2^329135+1110)/299080Stefano Morozzi09/2020
8868(22089^22807-1)/2208899074Serge Batalov06/2022
8869(59*10^99069+391)/999070Robert Price03/2021
8870(797*10^99061-41)/999063Robert Price04/2022
88712^329058-28768199057Harrison Mesh06/2022
88726^127285+1399047Lelio R Paula08/2016
8873(228581#+235862)/(2^3*11*71*151)99044Makoto Morimoto10/2017
88742^329007+7328399041Enzo Doria04/2016
88755*3^207543-899024Lelio R Paula08/2014
8876(2^328930+570)/299018Stefano Morozzi09/2020
88772^328885+14999005Lelio R Paula12/2012
887923392^17075+17075^2339299004Hans Havermann09/2017
8878(7424^25579-1)/742399004Serge Batalov06/2022
8880(2^328879-9)/11999001Lelio R Paula10/2013
88815^141618+5498987Lelio R Paula08/2016
88828*10^98982+5198983Robert Price05/2017
8883(21*2^328809-1)/770998979Lelio R Paula03/2014
88842^328794-279760198977Enzo Doria04/2016
8885(88331^20011-1)/8833098972Serge Batalov06/2022
88866^127176+598963Lelio R Paula11/2014
88872*10^98961-2198962Robert Price09/2020
888824262^11989+11989^2426298960Hans Havermann09/2017
8889(60138^20707-1)/6013798958Serge Batalov06/2022
88902^328700-10970998949Enzo Doria04/2014
8891(2^328698+1810)/298948Stefano Morozzi01/2021
8892(1014^32917-1)/101398947Serge Batalov06/2022
889387771!4-12898944Robert Price11/2019
8894(4576^27031-1)/457598943Serge Batalov06/2022
8895(2^328658+3042)/298936Stefano Morozzi09/2020
8896(1933^30103-1)/193298923Serge Batalov06/2022
889746711!2-2^4671198916Robert Price09/2015
88989*7^117037+498909Lelio R Paula11/2014
8899127^47012+12698905Norbert Schneider01/2019
8900(93826^19891-1)/9382598900Serge Batalov06/2022
8901(2^328525+1250)/298896Stefano Morozzi09/2020
8902(10^98890+149)/398890Serge Batalov12/2014
890322775^21978+21978^2277598889Hans Havermann08/2017
89042^328497-21693398888Enzo Doria05/2014
89052^328487+3276998885Lelio R Paula08/2016
89063^207250-11235898884Enzo Doria06/2014
890713^88754-9098867Lelio R Paula08/2016
89082^328406+70998861Lelio R Paula02/2013
89092*10^98860-2198861Robert Price09/2020
8910(17*2^328413-1)/1617398860Lelio R Paula03/2014
89117^116976+7698857Lelio R Paula08/2016
8912(2^328378+2710)/298852Stefano Morozzi09/2020
8913(25411^22441-1)/2541098849Serge Batalov06/2022
8914(18668^23143-1)/1866798842Serge Batalov06/2022
89162^328335+115598839Lelio R Paula08/2016
89152^328333-34900398839Harrison Mesh06/2022
8918(3*2^328311+1)/598832Lelio R Paula11/2013
8917287^40210+40210^28798832Norbert Schneider11/2014
8919(2^328284+9)/132598821Lelio R Paula10/2013
8920(21*2^328258+1)/212598814Lelio R Paula11/2013
8921(28623^22171-1)/2862298806Serge Batalov06/2022
892224746^9825+9825^2474698795Hans Havermann07/2020
892326620^5143+5143^2662098793Hans Havermann07/2020
892465^54491+4898788Lelio R Paula04/2016
89253^207042+9898785Lelio R Paula08/2016
8926(2^328121+3110)/298774Stefano Morozzi09/2020
892710^98754+7338398755Patrick De Geest02/2021
89303^206977-11275698754Enzo Doria07/2014
892910^98754-4000000000198754Robert Price09/2020
892810^98754-16934398754Patrick De Geest02/2021
89317^116846-5098747Lelio R Paula08/2016
8932(19152^23059-1)/1915198740Serge Batalov06/2022
893323267^17512+17512^2326798730Hans Havermann04/2020
89342^327967-2863598728Lelio R Paula08/2016
8935707^34642+34642^70798710Norbert Schneider12/2017
8936(10771^24481-1)/1077098710Serge Batalov06/2022
89376^126850-4798709Lelio R Paula08/2016
8938(2^327886+2170)/298704Stefano Morozzi09/2020
8939(22*10^98697+47)/398698Robert Price06/2021
89408*6^126830-798694Lelio R Paula11/2014
894111^94770-27098693Enzo Doria08/2012
8942(2^327846+3250)/298692Stefano Morozzi01/2021
89432^327832+4398688Lelio R Paula12/2012
89442^327795+76198677Lelio R Paula02/2013
8945(2^327796+1522)/298677Stefano Morozzi09/2020
894610^98669+14741198670Patrick De Geest11/2016
894810^98669-9^(98669-1)98669Robert Price05/2016
894710^98669-10524998669Patrick De Geest11/2016
8949(7911^25309-1)/791098657Serge Batalov06/2022
89502^327671-10980198639Enzo Doria04/2014
895124398^11037+11037^2439898638Hans Havermann10/2019
89525^141090-1498618Lelio R Paula08/2016
895320^75799+4798617Lelio R Paula08/2016
8954(5452^26393-1)/545198616Serge Batalov06/2022
895528101^3226+3226^2810198597Hans Havermann07/2020
89562^327515-101798592Lelio R Paula08/2016
89576^126692+9768198586Mike Oakes04/2011
89582^327467-74198578Lelio R Paula08/2016
8959(2947^28411-1)/294698566Serge Batalov06/2022
896022713^21800+21800^2271398540Hans Havermann05/2020
8961(2^327329+9)/1998535Lelio R Paula10/2013
89627^116577-6698519Lelio R Paula08/2016
8963(3*2^327250+1)/798512Lelio R Paula11/2013
896423220^17479+17479^2322098512Hans Havermann03/2020
8965(2^327240+3798)/298509Stefano Morozzi02/2021
8966(28514^22111-1)/2851398502Serge Batalov06/2022
8967(19*2^327192+1)/27598494Lelio R Paula11/2013
89682^327162-6694598486Lelio R Paula08/2016
896930139^1852+1852^3013998484Hans Havermann02/2020
897023182^17703+17703^2318298479Hans Havermann01/2020
89714*10^98472-398473Erik Branger11/2013
897226167^5794+5794^2616798466Hans Havermann01/2020
8973(6883*2^327047-1)/7798453Lelio R Paula05/2015
8974(71*10^98446+1)/998447Serge Batalov11/2010
8975(2009^29803-1)/200898436Serge Batalov06/2022
897613^88363+9498432Lelio R Paula08/2016
897748^58543-47^5854398425Jean-Louis Charton11/2005
89786^126481+4198422Lelio R Paula08/2016
897978*10^98413-798415Robert Price05/2017
898022634^22263+22263^2263498404Hans Havermann07/2020
8981(47*10^98386+241)/998387Robert Price06/2022
89827^116416+4698383Lelio R Paula08/2016
89837^116407-2498376Lelio R Paula07/2016
8984439^37228+37228^43998374Norbert Schneider08/2018
89852^326782-186067198372Enzo Doria03/2016
898617^79948+5898372Lelio R Paula08/2016
898722499^22602-22602^2249998368Norbert Schneider08/2020
89883^206143-9898356Lelio R Paula08/2016
89898*5^140705+798350Lelio R Paula11/2014
8990(2^326632+1662)/298326Stefano Morozzi09/2020
8991(638^35053-1)/63798315Serge Batalov06/2022
89922^326585+1198312Lelio R Paula12/2012
89932^326582-45916198311Enzo Doria05/2015
8994(1266^31687-1)/126598304Serge Batalov06/2022
8996(2^326548+9)/598301Lelio R Paula10/2013
8995(2^326549+18)/1098301Stefano Morozzi03/2020
89972^326538+7165998298Enzo Doria04/2016
8998(2^326520+2082)/298293Stefano Morozzi09/2020
8999(2^326521+1002)/298293Stefano Morozzi09/2020
900015^83575-5898292Lelio R Paula08/2016


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Created by  Henri Lifchitz & Renaud Lifchitz : October, 26 2000, last modification: September, 29 2023 15:19 (Time in France)

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