PRP Records

Probable Primes Top 10000

(291910 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 ?
814425206!+p(4114)100001Henri Lifchitz09/2005
814525206!-p(5447)100001Henri Lifchitz10/2005
814625206!-p(12402)100001Henri Lifchitz04/2006
814725206!-p(16290)100001Henri Lifchitz09/2006
814825206!-p(19647)100001Henri Lifchitz02/2007
81492^332194+11473100001Henri Lifchitz03/2007
813910^100000+342909100001Milton L. Brown12/2007
814010^100000+346579100001Robert Price04/2012
814110^100000+829767100001Robert Price05/2012
814210^100000+871899100001Robert Price05/2012
814310^100000+1475997100001Robert Price07/2012
813210^100000+1751769100001Robert Price08/2012
813310^100000+2155489100001Robert Price10/2012
813410^100000+2483527100001Robert Price12/2012
813510^100000+2503087100001Robert Price12/2012
813610^100000+2686179100001Robert Price12/2012
813710^100000+2688933100001Robert Price12/2012
813810^100000+3667159100001Robert Price08/2013
800110^100000+9225987100001Robert Price04/2017
800210^100000+9265587100001Robert Price04/2017
800310^100000+9287049100001Robert Price04/2017
800410^100000+9425053100001Robert Price05/2017
800510^100000+9450769100001Robert Price05/2017
800610^100000+9528747100001Robert Smith05/2017
800710^100000+9548071100001Robert Price06/2017
800810^100000+10064287100001Robert Price08/2017
800910^100000+10229569100001Robert Price10/2017
801010^100000+11992051100001Robert Price09/2018
80112^332196-1-2*29696100001Matt Stath11/2018
801210^100000+12363957100001Robert Price11/2018
80132^332196+1+2*17152100001Matt Stath12/2018
801410^100000+12778033100001Robert Price02/2019
801510^100000+13581679100001Robert Price05/2019
801610^100000+13613199100001Robert Price05/2019
801710^100000+13752327100001Robert Price05/2019
801810^100000+14139243100001Robert Price06/2019
801910^100000+14151057100001Robert Price06/2019
802010^100000+14218923100001Robert Price06/2019
802110^100000+15136771100001Robert Price09/2019
802210^100000+15219873100001Robert Price10/2019
802310^100000+15274039100001Robert Price10/2019
802410^100000+15394069100001Robert Price10/2019
802510^100000+15547119100001Robert Price10/2019
802610^100000+15932923100001Robert Price11/2019
802710^100000+16345467100001Robert Price12/2019
802810^100000+16672143100001Robert Price01/2020
802910^100000+16731939100001Robert Price02/2020
803010^100000+16907049100001Robert Price03/2020
803110^100000+17652523100001Robert Price05/2020
803210^100000+18047167100001Robert Price05/2020
803310^100000+18471819100001Robert Price06/2020
803410^100000+18494793100001Robert Price07/2020
803510^100000+18762609100001Robert Price07/2020
803610^100000+19204141100001Robert Price08/2020
803710^100000+19349793100001Robert Price08/2020
803810^100000+19495699100001Robert Price09/2020
803910^100000+19668927100001Robert Price09/2020
804010^100000+19704313100001Robert Price09/2020
810110^100000+19956229100001Robert Price09/2020
810210^100000+3*(10^37093-1)/9*10^31454+1100001Makoto Morimoto09/2020
810310^100000+4*(10^36149-1)/9*10^31926+1100001Makoto Morimoto09/2020
810410^100000+6*(10^41029-1)/9*10^29486+1100001Makoto Morimoto09/2020
810510^100000+7*(10^55505-1)/9*10^22248+1100001Makoto Morimoto09/2020
810610^100000+20234607100001Robert Price10/2020
810710^100000+20752303100001Robert Price11/2020
810810^100000+20774041100001Robert Price11/2020
810910^100000+20854741100001Robert Price11/2020
811010^100000+20908917100001Robert Price11/2020
811110^100000+20994793100001Robert Price11/2020
811210^100000+21354249100001Robert Price12/2020
811310^100000+21455559100001Robert Price12/2020
811410^100000+21538873100001Robert Price12/2020
811510^100000+21830901100001Robert Price01/2021
811610^100000+21842629100001Robert Price01/2021
811710^100000+21930861100001Robert Price01/2021
811810^100000+22092943100001Robert Price03/2021
811910^100000+22278417100001Robert Price03/2021
812010^100000+22388581100001Robert Price03/2021
812110^100000+22390933100001Robert Price03/2021
812210^100000+22436169100001Robert Price03/2021
812310^100000+22714557100001Robert Price04/2021
812410^100000+22847671100001Robert Price04/2021
812510^100000+23178567100001Robert Price05/2021
812610^100000+23332003100001Robert Price05/2021
812710^100000+23414571100001Robert Price05/2021
812810^100000+23529979100001Robert Price05/2021
812910^100000+23749243100001Robert Price06/2021
813010^100000+23821771100001Robert Price06/2021
813110^100000+24179307100001Robert Price07/2021
804110^100000+24543147100001Robert Price08/2021
804210^100000+24781659100001Robert Price08/2021
804310^100000+24906153100001Robert Price08/2021
804410^100000+25682679100001Robert Price10/2021
804510^100000+25905301100001Robert Price10/2021
804610^100000+25923967100001Robert Price10/2021
804710^100000+26061691100001Robert Price10/2021
804810^100000+26173351100001Robert Price11/2021
804910^100000+26673487100001Robert Price11/2021
805010^100000+26849359100001Robert Price12/2021
805110^100000+26893887100001Robert Price12/2021
805210^100000+26954551100001Robert Price12/2021
805310^100000+27024543100001Robert Price12/2021
805410^100000+27060877100001Robert Price12/2021
805510^100000+27617577100001Robert Price03/2022
805610^100000+27869671100001Robert Price03/2022
805710^100000+27956481100001Robert Price03/2022
805810^100000+28078261100001Robert Price03/2022
805910^100000+28150203100001Robert Price03/2022
806010^100000+28626021100001Robert Price05/2022
806110^100000+28649299100001Robert Price05/2022
806210^100000+29409799100001Robert Price06/2022
806310^100000+29415577100001Robert Price06/2022
806410^100000+29424201100001Robert Price06/2022
806510^100000+29610153100001Robert Price07/2022
806610^100000+30166789100001Robert Price07/2022
806710^100000+30338259100001Robert Price07/2022
806810^100000+30540031100001Robert Price07/2022
806910^100000+30635157100001Robert Price07/2022
807010^100000+30762711100001Robert Price07/2022
807110^100000+30862057100001Robert Price07/2022
807210^100000+30998953100001Robert Price07/2022
807310^100000+31405203100001Robert Price07/2022
807410^100000+40159119100001Robert Price07/2022
807510^100000+40181863100001Robert Price07/2022
807610^100000+40277131100001Robert Price07/2022
807710^100000+40326061100001Robert Price07/2022
807810^100000+40417411100001Robert Price07/2022
807910^100000+50049909100001Robert Price07/2022
808010^100000+50510163100001Robert Price07/2022
808110^100000+50591583100001Robert Price07/2022
808210^100000+50850357100001Robert Price07/2022
808310^100000+50974641100001Robert Price07/2022
808410^100000+51046671100001Robert Price07/2022
808510^100000+51459657100001Robert Price07/2022
808610^100000+70081471100001Robert Price07/2022
808710^100000+70159557100001Robert Price07/2022
808810^100000+70262479100001Robert Price07/2022
808910^100000+70417521100001Robert Price07/2022
809010^100000+70476531100001Robert Price07/2022
809110^100000+70534627100001Robert Price07/2022
809210^100000+70873077100001Robert Price07/2022
809310^100000+71114643100001Robert Price07/2022
809410^100000+71272539100001Robert Price07/2022
809510^100000+80025337100001Robert Price07/2022
809610^100000+71580817100001Robert Price07/2022
809710^100000+80270349100001Robert Price07/2022
809810^100000+29831551100001Robert Price07/2022
809910^100000+29955417100001Robert Price08/2022
8100479072067*10^99992+1+2*1779100001Matt Stath12/2022
815010^99999+309403100000Daniel Heuer01/2004
815110^100000-260199100000Patrick De Geest01/2010
81522^332192+10192681100000Sujan Das06/2022
81531610172603059^8192+1610172602878^8192100000Youcef Lemsafer01/2023
815510^99999-5951199999Patrick De Geest07/2009
815410^99998+23543799999Patrick De Geest02/2020
815610^99998-28658799998Patrick De Geest02/2020
815710^99997+7229799998Patrick De Geest02/2020
815810^99997-40262799997Patrick De Geest02/2020
815910^99996+27985399997Patrick De Geest02/2020
816010^99997-50000000199997Robert Price12/2020
816110^99996-9496199996Patrick De Geest02/2020
816210^99995+5463399996Patrick De Geest02/2020
816310^99995-10142999995Patrick De Geest02/2020
816410^99994+11727199995Patrick De Geest02/2020
816510^99994-45228999994Patrick De Geest02/2020
816610^99993+37131199994Patrick De Geest02/2020
816710^99993-18649199993Patrick De Geest02/2020
816810^99992+1743199993Patrick De Geest02/2020
816910^99992-2860799992Patrick De Geest02/2020
817010^99991+12539199992Patrick De Geest02/2020
817110^99991-20457399991Patrick De Geest02/2020
817210^99990+1389999991Patrick De Geest02/2020
817310^99990-811199990Patrick De Geest02/2020
81742^332141-11307399985Enzo Doria07/2014
8175(1610172603037^8192+1610172602919^8192)/1711094812747366699983Youcef Lemsafer01/2023
81766*10^99979-7999980Robert Price03/2022
8178(3^209561+2)/72810125599978Lelio R Paula09/2013
817723827^15702+15702^2382799978Hans Havermann04/2018
81792^332085+186589799968Enzo Doria03/2016
8180(9787*2^332070-1)/93640236999959Lelio R Paula05/2015
81812^332023+19199949Lelio R Paula02/2011
8182(6271^26321-1)/627099946Serge Batalov06/2022
81837*10^99944+2799945Robert Price11/2020
81842^331938+7114999924Enzo Doria04/2016
81852^331932-7879599922Lelio R Paula09/2016
81862^331921+77199919Lelio R Paula01/2013
8187(3^209419-2)/513275599912Lelio R Paula09/2013
81882^331860-11498999900Enzo Doria05/2015
81892^331746-1165599866Lelio R Paula09/2016
819011^95891-2899861Lelio R Paula08/2016
8191(2^331694-5)/1199849Lelio R Paula10/2013
8192(3^209246+7)/6499834Lelio R Paula09/2013
819325062^9617+9617^2506299823Hans Havermann04/2018
819415^84866-5299811Lelio R Paula08/2016
819513^89600+3099810Lelio R Paula08/2016
81962^331527+10028024506599800Paul Bourdelais10/2021
819722950^22309+22309^2295099798Hans Havermann03/2018
81985^142772-3899794Lelio R Paula08/2016
8199(7482^25759-1)/748199787Serge Batalov06/2022
8200(23*2^331459+1)/47599778Lelio R Paula11/2013
82012^331416-331416+199767Robert Price10/2014
82022^331256-5799718Lelio R Paula12/2012
820328192^3443+3443^2819299714Hans Havermann03/2018
82042^331185+73799697Lelio R Paula01/2013
8205(4*10^99693+149)/999693Robert Price03/2017
82062^331154+188052799688Enzo Doria10/2016
8208(19^77951+1)/2099679Paul Bourdelais03/2010
820724354^12385+12385^2435499679Hans Havermann03/2018
82092^331110+187045999675Enzo Doria05/2016
82105*2^331075+799665Lelio R Paula08/2014
821125776^7351+7351^2577699659Hans Havermann02/2018
8212(16*10^99656-31)/399657Robert Price03/2016
8213(6059^26347-1)/605899652Serge Batalov06/2022
8214(15544^23773-1)/1554399642Serge Batalov06/2022
82162^330968+34599632Lelio R Paula09/2016
8215(2^330969+690)/299632Stefano Morozzi09/2020
82182*5^142528-799624Lelio R Paula11/2014
82172^330942+7732999624Enzo Doria05/2016
821914^86914-9999615Lelio R Paula08/2016
8220(19*2^330902+1)/7799611Lelio R Paula11/2013
822122971^21692+21692^2297199610Hans Havermann03/2018
82222^330845+7168799595Enzo Doria04/2016
8223(26667^22501-1)/2666699585Serge Batalov06/2022
8224(23*2^330770+1)/399573Lelio R Paula11/2013
822524494^11613+11613^2449499567Hans Havermann03/2018
82262^330735+841599562Lelio R Paula09/2016
82272^330720+7407199557Enzo Doria04/2016
8228(10405^24781-1)/1040499548Serge Batalov06/2022
823031^66738-299531Lelio R Paula09/2013
8229(9002^25171-1)/900199531Serge Batalov06/2022
8231(5023^26893-1)/502299527Serge Batalov06/2022
82327*3^208567+499513Lelio R Paula08/2014
8233(15881^23689-1)/1588099511Serge Batalov06/2022
8234(13*10^99508+47)/399509Robert Price01/2017
82352^330553+77999507Lelio R Paula01/2013
823615^84606-9499505Lelio R Paula08/2016
8237(10^99497+173)/399497Robert Price05/2021
82389*10^99493-4399494Robert Price09/2021
82396^127858+4799493Lelio R Paula08/2016
82405^142337+4899490Lelio R Paula08/2016
82417^117724-2099489Lelio R Paula08/2016
8242(559^36209-1)/55899479Serge Batalov06/2022
8243(13470^24091-1)/1346999477Serge Batalov06/2022
8244(29*10^99474-17)/399475Erik Branger09/2014
8245(185*10^99466-11)/399468Robert Price10/2020
8246(2^330410+2038)/299464Stefano Morozzi09/2020
8247(9*2^330407-1)/799463Lelio R Paula03/2014
8248(2863^28771-1)/286299453Serge Batalov06/2022
8249(2^330373+2114)/299452Stefano Morozzi09/2020
8250(68*10^99441+7)/399443Robert Price03/2016


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Created by  Henri Lifchitz & Renaud Lifchitz : October, 26 2000, last modification: February, 02 2023 13:22 (Time in France)

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