PRP Records

Probable Primes Top 10000

(293016 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 ?
835525206!+p(4114)100001Henri Lifchitz09/2005
835625206!-p(5447)100001Henri Lifchitz10/2005
835725206!-p(12402)100001Henri Lifchitz04/2006
835825206!-p(16290)100001Henri Lifchitz09/2006
835925206!-p(19647)100001Henri Lifchitz02/2007
83602^332194+11473100001Henri Lifchitz03/2007
835010^100000+342909100001Milton L. Brown12/2007
835110^100000+346579100001Robert Price04/2012
835210^100000+829767100001Robert Price05/2012
835310^100000+871899100001Robert Price05/2012
835410^100000+1475997100001Robert Price07/2012
834310^100000+1751769100001Robert Price08/2012
834410^100000+2155489100001Robert Price10/2012
834510^100000+2483527100001Robert Price12/2012
834610^100000+2503087100001Robert Price12/2012
834710^100000+2686179100001Robert Price12/2012
834810^100000+2688933100001Robert Price12/2012
834910^100000+3667159100001Robert Price08/2013
832310^100000+15136771100001Robert Price09/2019
832410^100000+15219873100001Robert Price10/2019
832510^100000+15274039100001Robert Price10/2019
832610^100000+15394069100001Robert Price10/2019
832710^100000+15547119100001Robert Price10/2019
832810^100000+15932923100001Robert Price11/2019
832910^100000+16345467100001Robert Price12/2019
833010^100000+16672143100001Robert Price01/2020
833110^100000+16731939100001Robert Price02/2020
833210^100000+16907049100001Robert Price03/2020
833310^100000+17652523100001Robert Price05/2020
833410^100000+18047167100001Robert Price05/2020
833510^100000+18471819100001Robert Price06/2020
833610^100000+18494793100001Robert Price07/2020
833710^100000+18762609100001Robert Price07/2020
833810^100000+19204141100001Robert Price08/2020
833910^100000+19349793100001Robert Price08/2020
834010^100000+19495699100001Robert Price09/2020
834110^100000+19668927100001Robert Price09/2020
834210^100000+19704313100001Robert Price09/2020
829210^100000+19956229100001Robert Price09/2020
829310^100000+3*(10^37093-1)/9*10^31454+1100001Makoto Morimoto09/2020
829410^100000+4*(10^36149-1)/9*10^31926+1100001Makoto Morimoto09/2020
829510^100000+6*(10^41029-1)/9*10^29486+1100001Makoto Morimoto09/2020
829610^100000+7*(10^55505-1)/9*10^22248+1100001Makoto Morimoto09/2020
829710^100000+20234607100001Robert Price10/2020
829810^100000+20752303100001Robert Price11/2020
829910^100000+20774041100001Robert Price11/2020
830010^100000+20854741100001Robert Price11/2020
830110^100000+20908917100001Robert Price11/2020
830210^100000+20994793100001Robert Price11/2020
830310^100000+21354249100001Robert Price12/2020
830410^100000+21455559100001Robert Price12/2020
830510^100000+21538873100001Robert Price12/2020
830610^100000+21830901100001Robert Price01/2021
830710^100000+21842629100001Robert Price01/2021
830810^100000+21930861100001Robert Price01/2021
830910^100000+22092943100001Robert Price03/2021
831010^100000+22278417100001Robert Price03/2021
831110^100000+22388581100001Robert Price03/2021
831210^100000+22390933100001Robert Price03/2021
831310^100000+22436169100001Robert Price03/2021
831410^100000+22714557100001Robert Price04/2021
831510^100000+22847671100001Robert Price04/2021
831610^100000+23178567100001Robert Price05/2021
831710^100000+23332003100001Robert Price05/2021
831810^100000+23414571100001Robert Price05/2021
831910^100000+23529979100001Robert Price05/2021
832010^100000+23749243100001Robert Price06/2021
832110^100000+23821771100001Robert Price06/2021
832210^100000+24179307100001Robert Price07/2021
825110^100000+30762711100001Robert Price07/2022
825210^100000+30862057100001Robert Price07/2022
825310^100000+30998953100001Robert Price07/2022
825410^100000+31405203100001Robert Price07/2022
825510^100000+40159119100001Robert Price07/2022
825610^100000+40181863100001Robert Price07/2022
825710^100000+40277131100001Robert Price07/2022
825810^100000+40326061100001Robert Price07/2022
825910^100000+40417411100001Robert Price07/2022
826010^100000+50049909100001Robert Price07/2022
826110^100000+50510163100001Robert Price07/2022
826210^100000+50591583100001Robert Price07/2022
826310^100000+50850357100001Robert Price07/2022
826410^100000+50974641100001Robert Price07/2022
826510^100000+51046671100001Robert Price07/2022
826610^100000+51459657100001Robert Price07/2022
826710^100000+70081471100001Robert Price07/2022
826810^100000+70159557100001Robert Price07/2022
826910^100000+70262479100001Robert Price07/2022
827010^100000+70417521100001Robert Price07/2022
827110^100000+70476531100001Robert Price07/2022
827210^100000+70534627100001Robert Price07/2022
827310^100000+70873077100001Robert Price07/2022
827410^100000+71114643100001Robert Price07/2022
827510^100000+71272539100001Robert Price07/2022
827610^100000+80025337100001Robert Price07/2022
827710^100000+71580817100001Robert Price07/2022
827810^100000+80270349100001Robert Price07/2022
827910^100000+29831551100001Robert Price07/2022
828010^100000+29955417100001Robert Price08/2022
8281479072067*10^99992+1+2*1779100001Matt Stath12/2022
828210^100000+90000000+851439100001Robert Price04/2023
828310^100000+90000000+1088017100001Robert Price04/2023
828410^100000+90000000+1288173100001Robert Price04/2023
828510^100000+90000000+1324549100001Robert Price04/2023
828610^100000+90000000+3643869100001Robert Price04/2023
828710^100000+110000000+60221100001Robert Price04/2023
828810^100000+110000000+373261100001Robert Price04/2023
828910^100000+110000000+497513100001Robert Price04/2023
829010^100000+120000000+33823100001Robert Price04/2023
829110^100000+120000000+419053100001Robert Price04/2023
836110^99999+309403100000Daniel Heuer01/2004
836210^100000-260199100000Patrick De Geest01/2010
83632^332192+10192681100000Sujan Das06/2022
83641610172603059^8192+1610172602878^8192100000Youcef Lemsafer01/2023
836610^99999-5951199999Patrick De Geest07/2009
836510^99998+23543799999Patrick De Geest02/2020
836710^99998-28658799998Patrick De Geest02/2020
836810^99997+7229799998Patrick De Geest02/2020
836910^99997-40262799997Patrick De Geest02/2020
837010^99996+27985399997Patrick De Geest02/2020
837110^99997-50000000199997Robert Price12/2020
837210^99996-9496199996Patrick De Geest02/2020
837310^99995+5463399996Patrick De Geest02/2020
837410^99995-10142999995Patrick De Geest02/2020
837510^99994+11727199995Patrick De Geest02/2020
837610^99994-45228999994Patrick De Geest02/2020
837710^99993+37131199994Patrick De Geest02/2020
837810^99993-18649199993Patrick De Geest02/2020
837910^99992+1743199993Patrick De Geest02/2020
838010^99992-2860799992Patrick De Geest02/2020
838110^99991+12539199992Patrick De Geest02/2020
838210^99991-20457399991Patrick De Geest02/2020
838310^99990+1389999991Patrick De Geest02/2020
838410^99990-811199990Patrick De Geest02/2020
83852^332141-11307399985Enzo Doria07/2014
8386(1610172603037^8192+1610172602919^8192)/1711094812747366699983Youcef Lemsafer01/2023
83876*10^99979-7999980Robert Price03/2022
8389(3^209561+2)/72810125599978Lelio R Paula09/2013
838823827^15702+15702^2382799978Hans Havermann04/2018
83902^332085+186589799968Enzo Doria03/2016
8391(9787*2^332070-1)/93640236999959Lelio R Paula05/2015
83922^332023+19199949Lelio R Paula02/2011
8393(6271^26321-1)/627099946Serge Batalov06/2022
83947*10^99944+2799945Robert Price11/2020
83952^331938+7114999924Enzo Doria04/2016
83962^331932-7879599922Lelio R Paula09/2016
83972^331921+77199919Lelio R Paula01/2013
8398(3^209419-2)/513275599912Lelio R Paula09/2013
83992^331860-11498999900Enzo Doria05/2015
84002^331746-1165599866Lelio R Paula09/2016
840111^95891-2899861Lelio R Paula08/2016
8402(2^331694-5)/1199849Lelio R Paula10/2013
8403(3^209246+7)/6499834Lelio R Paula09/2013
840425062^9617+9617^2506299823Hans Havermann04/2018
840515^84866-5299811Lelio R Paula08/2016
840613^89600+3099810Lelio R Paula08/2016
84072^331527+10028024506599800Paul Bourdelais10/2021
840822950^22309+22309^2295099798Hans Havermann03/2018
84095^142772-3899794Lelio R Paula08/2016
8410(7482^25759-1)/748199787Serge Batalov06/2022
8411(23*2^331459+1)/47599778Lelio R Paula11/2013
84122^331416-331416+199767Robert Price10/2014
84132^331256-5799718Lelio R Paula12/2012
841428192^3443+3443^2819299714Hans Havermann03/2018
84152^331185+73799697Lelio R Paula01/2013
8416(4*10^99693+149)/999693Robert Price03/2017
84172^331154+188052799688Enzo Doria10/2016
8419(19^77951+1)/2099679Paul Bourdelais03/2010
841824354^12385+12385^2435499679Hans Havermann03/2018
84202^331110+187045999675Enzo Doria05/2016
84215*2^331075+799665Lelio R Paula08/2014
842225776^7351+7351^2577699659Hans Havermann02/2018
8423(16*10^99656-31)/399657Robert Price03/2016
8424(6059^26347-1)/605899652Serge Batalov06/2022
8425(15544^23773-1)/1554399642Serge Batalov06/2022
84272^330968+34599632Lelio R Paula09/2016
8426(2^330969+690)/299632Stefano Morozzi09/2020
84292*5^142528-799624Lelio R Paula11/2014
84282^330942+7732999624Enzo Doria05/2016
843014^86914-9999615Lelio R Paula08/2016
8431(19*2^330902+1)/7799611Lelio R Paula11/2013
843222971^21692+21692^2297199610Hans Havermann03/2018
84332^330845+7168799595Enzo Doria04/2016
8434(26667^22501-1)/2666699585Serge Batalov06/2022
8435(23*2^330770+1)/399573Lelio R Paula11/2013
843624494^11613+11613^2449499567Hans Havermann03/2018
84372^330735+841599562Lelio R Paula09/2016
84382^330720+7407199557Enzo Doria04/2016
8439(10405^24781-1)/1040499548Serge Batalov06/2022
844131^66738-299531Lelio R Paula09/2013
8440(9002^25171-1)/900199531Serge Batalov06/2022
8442(5023^26893-1)/502299527Serge Batalov06/2022
84437*3^208567+499513Lelio R Paula08/2014
8444(15881^23689-1)/1588099511Serge Batalov06/2022
8445(13*10^99508+47)/399509Robert Price01/2017
84462^330553+77999507Lelio R Paula01/2013
844715^84606-9499505Lelio R Paula08/2016
8448(10^99497+173)/399497Robert Price05/2021
84499*10^99493-4399494Robert Price09/2021
84506^127858+4799493Lelio R Paula08/2016
84515^142337+4899490Lelio R Paula08/2016
84527^117724-2099489Lelio R Paula08/2016
8453(559^36209-1)/55899479Serge Batalov06/2022
8454(13470^24091-1)/1346999477Serge Batalov06/2022
8455(29*10^99474-17)/399475Erik Branger09/2014
8456(185*10^99466-11)/399468Robert Price10/2020
8457(2^330410+2038)/299464Stefano Morozzi09/2020
8458(9*2^330407-1)/799463Lelio R Paula03/2014
8459(516*32^66077-175)/3199458Eric Chen04/2023
8460(2863^28771-1)/286299453Serge Batalov06/2022
8461(2^330373+2114)/299452Stefano Morozzi09/2020
8462(68*10^99441+7)/399443Robert Price03/2016
846310^99434+15557199435Patrick De Geest04/2020
846410^99434-12345678999434Robert Price02/2020
846510^99434-19123799434Patrick De Geest04/2020
846646^59791-45^5979199418Jean-Louis Charton01/2013
846723839^14802+14802^2383999417Hans Havermann02/2018
8468(2*10^99408+529)/999408Robert Price01/2017
8469(2^330216+3510)/299405Stefano Morozzi09/2020
847053^57646-299398Lelio R Paula09/2013
84712^330165+187002599390Enzo Doria05/2016
84727*10^99383+9799384Robert Price09/2021
84732^330142-15599383Lelio R Paula12/2012
84742^330088-11525999367Enzo Doria06/2015
847524216^12671+12671^2421699354Hans Havermann01/2018
8476Phi(200548,10)/320876999354Makoto Kamada04/2019
8477(746*10^99303+1)/999305Robert Price02/2017
84783^208107+4099293Lelio R Paula08/2016
8479(3939^27617-1)/393899291Serge Batalov06/2022
8480(5*2^329833-1)/36999288Lelio R Paula02/2014
84818*3^208093+599287Lelio R Paula08/2014
84825^142043+5699284Lelio R Paula08/2016
8483(13*10^99282-157)/999283Robert Price05/2021
8484(10^99284+7)/53/6799281Alfred Reich06/2021
848522*10^99275+799277Robert Price04/2016
84862^329778+187618999274Enzo Doria07/2016
8487(6580^25997-1)/657999259Serge Batalov06/2022
8488(2249^29611-1)/224899253Serge Batalov06/2022
8489(10^99239-13)/399239Robert Price02/2017
8490(1199^32233-1)/119899237Serge Batalov06/2022
84923^207987+6299236Lelio R Paula08/2016
8491(62*10^99235+91)/999236Robert Price07/2021
84932^329638+4999231Lelio R Paula12/2012
84947^117413-1899226Lelio R Paula08/2016
84952^329586-45890399216Enzo Doria04/2015
8496(6290^26119-1)/628999214Serge Batalov06/2022
84982^329553+10199206Lelio R Paula12/2012
8497(21297^22921-1)/2129699206Serge Batalov06/2022
84992^329551-11289799205Enzo Doria06/2014
8500(3^207925+7)/5099204Lelio R Paula09/2013


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Created by  Henri Lifchitz & Renaud Lifchitz : October, 26 2000, last modification: June, 04 2023 08:38 (Time in France)

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