PRP Records

Probable Primes Top 10000

(295025 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 ?
937525206!+p(4114)100001Henri Lifchitz09/2005
937625206!-p(5447)100001Henri Lifchitz10/2005
937725206!-p(12402)100001Henri Lifchitz04/2006
937825206!-p(16290)100001Henri Lifchitz09/2006
937925206!-p(19647)100001Henri Lifchitz02/2007
93802^332194+11473100001Henri Lifchitz03/2007
937010^100000+342909100001Milton L. Brown12/2007
937110^100000+346579100001Robert Price04/2012
937210^100000+829767100001Robert Price05/2012
937310^100000+871899100001Robert Price05/2012
937410^100000+1475997100001Robert Price07/2012
936310^100000+1751769100001Robert Price08/2012
936410^100000+2155489100001Robert Price10/2012
936510^100000+2483527100001Robert Price12/2012
936610^100000+2503087100001Robert Price12/2012
936710^100000+2686179100001Robert Price12/2012
936810^100000+2688933100001Robert Price12/2012
936910^100000+3667159100001Robert Price08/2013
934310^100000+15136771100001Robert Price09/2019
934410^100000+15219873100001Robert Price10/2019
934510^100000+15274039100001Robert Price10/2019
934610^100000+15394069100001Robert Price10/2019
934710^100000+15547119100001Robert Price10/2019
934810^100000+15932923100001Robert Price11/2019
934910^100000+16345467100001Robert Price12/2019
935010^100000+16672143100001Robert Price01/2020
935110^100000+16731939100001Robert Price02/2020
935210^100000+16907049100001Robert Price03/2020
935310^100000+17652523100001Robert Price05/2020
935410^100000+18047167100001Robert Price05/2020
935510^100000+18471819100001Robert Price06/2020
935610^100000+18494793100001Robert Price07/2020
935710^100000+18762609100001Robert Price07/2020
935810^100000+19204141100001Robert Price08/2020
935910^100000+19349793100001Robert Price08/2020
936010^100000+19495699100001Robert Price09/2020
936110^100000+19668927100001Robert Price09/2020
936210^100000+19704313100001Robert Price09/2020
931210^100000+19956229100001Robert Price09/2020
931310^100000+3*(10^37093-1)/9*10^31454+1100001Makoto Morimoto09/2020
931410^100000+4*(10^36149-1)/9*10^31926+1100001Makoto Morimoto09/2020
931510^100000+6*(10^41029-1)/9*10^29486+1100001Makoto Morimoto09/2020
931610^100000+7*(10^55505-1)/9*10^22248+1100001Makoto Morimoto09/2020
931710^100000+20234607100001Robert Price10/2020
931810^100000+20752303100001Robert Price11/2020
931910^100000+20774041100001Robert Price11/2020
932010^100000+20854741100001Robert Price11/2020
932110^100000+20908917100001Robert Price11/2020
932210^100000+20994793100001Robert Price11/2020
932310^100000+21354249100001Robert Price12/2020
932410^100000+21455559100001Robert Price12/2020
932510^100000+21538873100001Robert Price12/2020
932610^100000+21830901100001Robert Price01/2021
932710^100000+21842629100001Robert Price01/2021
932810^100000+21930861100001Robert Price01/2021
932910^100000+22092943100001Robert Price03/2021
933010^100000+22278417100001Robert Price03/2021
933110^100000+22388581100001Robert Price03/2021
933210^100000+22390933100001Robert Price03/2021
933310^100000+22436169100001Robert Price03/2021
933410^100000+22714557100001Robert Price04/2021
933510^100000+22847671100001Robert Price04/2021
933610^100000+23178567100001Robert Price05/2021
933710^100000+23332003100001Robert Price05/2021
933810^100000+23414571100001Robert Price05/2021
933910^100000+23529979100001Robert Price05/2021
934010^100000+23749243100001Robert Price06/2021
934110^100000+23821771100001Robert Price06/2021
934210^100000+24179307100001Robert Price07/2021
925110^100000+41853379100001Robert Price09/2023
925210^100000+41983459100001Robert Price09/2023
925310^100000+42043387100001Robert Price09/2023
925410^100000+42048453100001Robert Price09/2023
925510^100000+42336543100001Robert Price09/2023
925610^100000+42394797100001Robert Price09/2023
925710^100000+42880261100001Robert Price09/2023
925810^100000+42906303100001Robert Price09/2023
925910^100000+43061901100001Robert Price09/2023
926010^100000+43089789100001Robert Price09/2023
926110^100000+43418013100001Robert Price09/2023
926210^100000+43813831100001Robert Price09/2023
926310^100000+43950739100001Robert Price09/2023
926410^100000+44108359100001Robert Price09/2023
926510^100000+44183733100001Robert Price09/2023
926610^100000+45126303100001Robert Price09/2023
926710^100000+45218437100001Robert Price09/2023
926810^100000+45241837100001Robert Price09/2023
926910^100000+45665701100001Robert Price09/2023
927010^100000+60000000+8592669100001Robert Price10/2023
927110^100000+60000000+9092577100001Robert Price10/2023
927210^100000+60000000+9210001100001Robert Price10/2023
927310^100000+60000000+9402451100001Robert Price10/2023
927410^100000+60000000+9794877100001Robert Price10/2023
927510^100000+60000000+9951523100001Robert Price10/2023
927610^100000+72282091100001Robert Price11/2023
927710^100000+72440769100001Robert Price11/2023
927810^100000+73067163100001Robert Price11/2023
927910^100000+73186987100001Robert Price11/2023
928010^100000+73364199100001Robert Price11/2023
928110^100000+73582809100001Robert Price11/2023
928210^100000+73780641100001Robert Price11/2023
928310^100000+73803067100001Robert Price11/2023
928410^100000+74038329100001Robert Price11/2023
928510^100000+74050969100001Robert Price11/2023
928610^100000+74166241100001Robert Price11/2023
928710^100000+74812939100001Robert Price11/2023
928810^100000+75141423100001Robert Price11/2023
928910^100000+75209967100001Robert Price11/2023
929010^100000+75324327100001Robert Price11/2023
929110^100000+75681951100001Robert Price11/2023
929210^100000+75756217100001Robert Price11/2023
929310^100000+75904543100001Robert Price11/2023
929410^100000+76129519100001Robert Price11/2023
929510^100000+77011297100001Robert Price11/2023
929610^100000+77133961100001Robert Price11/2023
929710^100000+77281647100001Robert Price11/2023
929810^100000+77316129100001Robert Price11/2023
929910^100000+77431989100001Robert Price11/2023
930010^100000+77826001100001Robert Price11/2023
930110^100000+77912487100001Robert Price11/2023
930210^100000+77981233100001Robert Price11/2023
930310^100000+78381711100001Robert Price11/2023
930410^100000+78539001100001Robert Price11/2023
930510^100000+78766053100001Robert Price11/2023
930610^100000+79189899100001Robert Price11/2023
930710^100000+78957711100001Robert Price11/2023
930810^100000+79685547100001Robert Price11/2023
930910^100000+79726413100001Robert Price11/2023
931010^100000+79726737100001Robert Price11/2023
931110^100000+79826767100001Robert Price11/2023
938110^99999+309403100000Daniel Heuer01/2004
938210^100000-260199100000Patrick De Geest01/2010
93832^332192+10192681100000Sujan Das06/2022
93841610172603059^8192+1610172602878^8192100000Youcef Lemsafer01/2023
938610^99999-5951199999Patrick De Geest07/2009
938510^99998+23543799999Patrick De Geest02/2020
938710^99998-28658799998Patrick De Geest02/2020
938810^99997+7229799998Patrick De Geest02/2020
938910^99997-40262799997Patrick De Geest02/2020
939010^99996+27985399997Patrick De Geest02/2020
939110^99997-50000000199997Robert Price12/2020
939210^99996-9496199996Patrick De Geest02/2020
939310^99995+5463399996Patrick De Geest02/2020
939410^99995-10142999995Patrick De Geest02/2020
939510^99994+11727199995Patrick De Geest02/2020
939610^99994-45228999994Patrick De Geest02/2020
939710^99993+37131199994Patrick De Geest02/2020
939810^99993-18649199993Patrick De Geest02/2020
939910^99992+1743199993Patrick De Geest02/2020
940010^99992-2860799992Patrick De Geest02/2020
940110^99991+12539199992Patrick De Geest02/2020
940210^99991-20457399991Patrick De Geest02/2020
940310^99990+1389999991Patrick De Geest02/2020
940410^99990-811199990Patrick De Geest02/2020
94052^332141-11307399985Enzo Doria07/2014
9406(1610172603037^8192+1610172602919^8192)/1711094812747366699983Youcef Lemsafer01/2023
94076*10^99979-7999980Robert Price03/2022
9409(3^209561+2)/72810125599978Lelio R Paula09/2013
940823827^15702+15702^2382799978Hans Havermann04/2018
94102^332085+186589799968Enzo Doria03/2016
9411(9787*2^332070-1)/93640236999959Lelio R Paula05/2015
94122^332023+19199949Lelio R Paula02/2011
9413(6271^26321-1)/627099946Serge Batalov06/2022
94147*10^99944+2799945Robert Price11/2020
94153188^28523-28523^318899931Norbert Schneider06/2023
94162^331938+7114999924Enzo Doria04/2016
94172^331932-7879599922Lelio R Paula09/2016
94182^331921+77199919Lelio R Paula01/2013
94197947^25618-25618^794799916Norbert Schneider08/2023
9420(3^209419-2)/513275599912Lelio R Paula09/2013
94212^331860-11498999900Enzo Doria05/2015
942223*31^66974+297099884Eric Chen04/2024
94232^331746-1165599866Lelio R Paula09/2016
942411^95891-2899861Lelio R Paula08/2016
9425(2^331694-5)/1199849Lelio R Paula10/2013
9426(3^209246+7)/6499834Lelio R Paula09/2013
942725062^9617+9617^2506299823Hans Havermann04/2018
942815^84866-5299811Lelio R Paula08/2016
942913^89600+3099810Lelio R Paula08/2016
94302^331527+10028024506599800Paul Bourdelais10/2021
943122950^22309+22309^2295099798Hans Havermann03/2018
94325^142772-3899794Lelio R Paula08/2016
9433(7482^25759-1)/748199787Serge Batalov06/2022
9434(23*2^331459+1)/47599778Lelio R Paula11/2013
94352^331416-331416+199767Robert Price10/2014
94362^331256-5799718Lelio R Paula12/2012
943728192^3443+3443^2819299714Hans Havermann03/2018
94382^331185+73799697Lelio R Paula01/2013
9439(4*10^99693+149)/999693Robert Price03/2017
94402^331154+188052799688Enzo Doria10/2016
9442(19^77951+1)/2099679Paul Bourdelais03/2010
944124354^12385+12385^2435499679Hans Havermann03/2018
94432^331110+187045999675Enzo Doria05/2016
94445*2^331075+799665Lelio R Paula08/2014
944525776^7351+7351^2577699659Hans Havermann02/2018
9446(16*10^99656-31)/399657Robert Price03/2016
9447(6059^26347-1)/605899652Serge Batalov06/2022
9448(15544^23773-1)/1554399642Serge Batalov06/2022
94502^330968+34599632Lelio R Paula09/2016
9449(2^330969+690)/299632Stefano Morozzi09/2020
94522*5^142528-799624Lelio R Paula11/2014
94512^330942+7732999624Enzo Doria05/2016
945314^86914-9999615Lelio R Paula08/2016
9454(19*2^330902+1)/7799611Lelio R Paula11/2013
945522971^21692+21692^2297199610Hans Havermann03/2018
94562^330845+7168799595Enzo Doria04/2016
9457(26667^22501-1)/2666699585Serge Batalov06/2022
9458(23*2^330770+1)/399573Lelio R Paula11/2013
945924494^11613+11613^2449499567Hans Havermann03/2018
94602^330735+841599562Lelio R Paula09/2016
94612^330720+7407199557Enzo Doria04/2016
9462(10405^24781-1)/1040499548Serge Batalov06/2022
946431^66738-299531Lelio R Paula09/2013
9463(9002^25171-1)/900199531Serge Batalov06/2022
9465(5023^26893-1)/502299527Serge Batalov06/2022
94667*3^208567+499513Lelio R Paula08/2014
9467(15881^23689-1)/1588099511Serge Batalov06/2022
9468(13*10^99508+47)/399509Robert Price01/2017
94692^330553+77999507Lelio R Paula01/2013
947015^84606-9499505Lelio R Paula08/2016
9471(10^99497+173)/399497Robert Price05/2021
94729*10^99493-4399494Robert Price09/2021
94736^127858+4799493Lelio R Paula08/2016
94745^142337+4899490Lelio R Paula08/2016
94757^117724-2099489Lelio R Paula08/2016
9476(559^36209-1)/55899479Serge Batalov06/2022
9477(13470^24091-1)/1346999477Serge Batalov06/2022
9478(29*10^99474-17)/399475Erik Branger09/2014
9479(185*10^99466-11)/399468Robert Price10/2020
9480(2^330410+2038)/299464Stefano Morozzi09/2020
9481(9*2^330407-1)/799463Lelio R Paula03/2014
9482(516*32^66077-175)/3199458Eric Chen04/2023
9483(2863^28771-1)/286299453Serge Batalov06/2022
9484(2^330373+2114)/299452Stefano Morozzi09/2020
9485(68*10^99441+7)/399443Robert Price03/2016
948610^99434+15557199435Patrick De Geest04/2020
948710^99434-12345678999434Robert Price02/2020
948810^99434-19123799434Patrick De Geest04/2020
948946^59791-45^5979199418Jean-Louis Charton01/2013
949023839^14802+14802^2383999417Hans Havermann02/2018
9491(2*10^99408+529)/999408Robert Price01/2017
9492(2^330216+3510)/299405Stefano Morozzi09/2020
949353^57646-299398Lelio R Paula09/2013
94942^330165+187002599390Enzo Doria05/2016
94957*10^99383+9799384Robert Price09/2021
94962^330142-15599383Lelio R Paula12/2012
94972^330088-11525999367Enzo Doria06/2015
949824216^12671+12671^2421699354Hans Havermann01/2018
9499Phi(200548,10)/320876999354Makoto Kamada04/2019
9500(746*10^99303+1)/999305Robert Price02/2017


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Created by  Henri Lifchitz & Renaud Lifchitz : October, 26 2000, last modification: April, 18 2024 10:19 (Time in France)

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