PRP Records

Probable Primes Top 10000

(259919 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 ?
9751(2^212131-3)/48563856Lelio R Paula04/2012
97522^212112-45999563853Enzo Doria06/2015
975315^54290+5863850Lelio R Paula05/2013
97543*2^212097-763849Lelio R Paula04/2014
975555^36683-5463842Norbert Schneider08/2014
9756(509203*2^212056-1)/363841Lelio R Paula04/2015
9757(3^133805-7)/17263839Lelio R Paula04/2012
9758(2^212053+2414)/263835Stefano Morozzi12/2019
97592^212049+14963834Lelio R Paula08/2011
97605^91318-1863829Lelio R Paula04/2013
976118468^2857+2857^1846863824Hans Havermann03/2017
9762(2^212024-5)/111163823Lelio R Paula04/2012
97632^211961+1291563807Lelio R Paula02/2013
976413046^15503-15503^1304663803Norbert Schneider09/2019
9766(3^133707-7)/578063791Lelio R Paula04/2012
9765(44*10^63790-161)/963791Robert Price11/2017
9767(2^211902+2490)/263789Stefano Morozzi12/2019
9768747^22198+22198^74763782Norbert Schneider07/2016
976911820^15659-15659^1182063774Norbert Schneider01/2020
97712^211800-1716963759Enzo Doria05/2013
9770(85*10^63757-1)/363759Robert Price07/2017
977285089!6-863757Robert Price08/2018
9773(14*10^63747-11)/363748Erik Branger09/2014
977491*19^49848+663746Curtis Bright05/2015
977518855^2402+2402^1885563741Hans Havermann03/2017
9776(142*10^63734-7)/963736Robert Price02/2017
97772^211699-11163728Lelio R Paula08/2011
977811^61192-555063725Enzo Doria01/2013
9779(11*10^63718+7)/963719Serge Batalov06/2011
97806^81872-1363709Lelio R Paula04/2013
97813^133522+9863707Lelio R Paula05/2013
97832^211607-6163701Lelio R Paula08/2011
97825^91135+863701Lelio R Paula04/2013
978411^61157-27063689Enzo Doria07/2012
978510^63685+114514191963686Marisa Kirisame03/2015
978610^63685+10383763686Patrick De Geest03/2016
978710^63685-13079763685Patrick De Geest03/2016
97882^211547+1155*21154763682Henri Lifchitz02/2005
97892^211543+4563681Lelio R Paula08/2011
97902^211534+4363679Lelio R Paula08/2011
979111^61140-6063671Enzo Doria07/2012
97922^211491-11232163666Enzo Doria06/2014
9793(2^211459+2130)/263656Stefano Morozzi12/2019
979519085^2164+2164^1908563654Hans Havermann03/2017
9794(2^211454+3474)/263654Stefano Morozzi12/2019
9796(2^211451+2910)/263653Stefano Morozzi12/2019
9797(2^211430-5)/85963644Lelio R Paula04/2012
97982^211401-9163639Lelio R Paula08/2011
9799(2^211403+1050)/263639Stefano Morozzi12/2019
9800(6883*2^211378-1)/6963634Lelio R Paula04/2015
9801(F(152232)^3-F(152231)^3)/F(152230)63629Wayne Halsdorf03/2012
9802(29*2^211384-1)/5012262163627Lelio R Paula01/2014
9803(2^211344+3946)/263621Stefano Morozzi12/2019
98042^211333+1501563618Lelio R Paula01/2013
9805(2^211321+842)/263614Stefano Morozzi12/2019
980633^41889-3263610Norbert Schneider03/2014
9807(2^211275+3354)/263600Stefano Morozzi12/2019
980813^57093+1863599Lelio R Paula05/2013
9809(2^211267+3006)/263598Stefano Morozzi12/2019
9810(5*2^211219-1)/963583Lelio R Paula01/2014
9811(107*10^63576-17)/963578Robert Price02/2017
981223^46687-102063575Enzo Doria08/2012
9813(67607*2^211188+1)/523431963573Lelio R Paula06/2014
9814(3^133243+7)/1072663570Lelio R Paula04/2012
9815(7*2^211181+1)/274563570Lelio R Paula06/2012
9816(20^48859-1)/1963566Paul Bourdelais03/2010
98172*3^133227+563566Lelio R Paula04/2014
9818(2^211160+3822)/263566Stefano Morozzi12/2019
98192^211155+11363564Lelio R Paula08/2011
98202^211134+34563558Lelio R Paula09/2011
98212^211121+1638563554Lelio R Paula09/2011
982216996^5483+5483^1699663549Hans Havermann02/2017
9823(2^211083+2958)/263543Stefano Morozzi12/2019
9824(2^211079+9)/36428363536Lelio R Paula03/2012
9825(2^211043+3806)/263530Stefano Morozzi12/2019
98263*10^63522+1363523Robert Price08/2017
982715852^10157+10157^1585263516Hans Havermann02/2017
9828(2^210996+3150)/263516Stefano Morozzi12/2019
9829(2^210962+2854)/263506Stefano Morozzi12/2019
98302^210948-1587363502Enzo Doria04/2013
98317^75136+663498Lelio R Paula04/2013
98322^210928+1291563496Lelio R Paula02/2013
98337*10^63493+3963494Robert Price07/2016
98352^210909+13563490Lelio R Paula08/2011
9834(2^210909+422)/263490Stefano Morozzi12/2019
983611457^15638-15638^1145763476Norbert Schneider01/2020
9839(3*2^210832+1)/763467Lelio R Paula07/2012
98388*7^75098-363467Lelio R Paula09/2014
9837(2^210832+2458)/263467Stefano Morozzi12/2019
984017683^3882+3882^1768363466Hans Havermann03/2017
9842Pell-LucasQ(165799)/263464Eric W. Weisstein11/2006
98412^210820-1690563464Enzo Doria05/2013
98435^90795-3663463Lelio R Paula04/2013
984484731!6-4863463Robert Price08/2018
98452^210816-1319763462Enzo Doria10/2012
98462^210750+13363443Lelio R Paula08/2011
9847(2^210743+1106)/263440Stefano Morozzi12/2019
9848291^25742+25742^29163426Norbert Schneider09/2014
9849(2^210641+1742)/263409Stefano Morozzi12/2019
9850(3^132908+8)/27985963408Lelio R Paula04/2012
98516^81480-13963404Lelio R Paula04/2013
98522^210576-17363390Lelio R Paula08/2011
985318^50497+5563388Lelio R Paula05/2013
98542^210545+1163381Lelio R Paula08/2011
98552^210543+6363380Lelio R Paula08/2011
9856155^28929-15463365Norbert Schneider12/2018
985883^33016+8263361Norbert Schneider04/2015
9857(2^210480+1690)/263361Stefano Morozzi12/2019
98592^210464+9876533163356Jason Earls12/2008
98607*10^63351+963352Dmitry Domanov11/2010
986158483!4+463351Robert Price09/2019
9862p(13534)#/2+51263348Robert Price05/2017
98631741^19546+19546^174163345Serge Batalov05/2014
986410^63336+1981963337Patrick De Geest12/2013
986510^63336-12288363336Patrick De Geest12/2013
9866(19^49523-2^49523)/1763327Robert Price09/2013
9867(2^210378+47)/9551693163323Lelio R Paula03/2012
986831191!2+25663316Robert Price01/2015
986916458^7031+7031^1645863315Hans Havermann01/2017
9870(lucasV(1,2,420636)-2)/(7*31^2*210319)63303Mike Oakes03/2017
9871156^28864+15563303Norbert Schneider12/2018
9872(2^210269+3542)/263297Stefano Morozzi12/2019
9873(2^210283+7)/169114563296Lelio R Paula03/2012
9874(2^210256+1842)/263294Stefano Morozzi12/2019
98762^210217+129963282Lelio R Paula09/2011
9875(2^210218+2598)/263282Stefano Morozzi12/2019
9877(2^210221-3)/26963281Lelio R Paula04/2012
9878Phi(193404,10)/386809/812296963268Maksym Voznyy10/2011
9879(2^210153+2402)/263263Stefano Morozzi12/2019
988096^31913-9563261Norbert Schneider04/2016
98813^132572+28063253Lelio R Paula04/2013
98823^132570-2^(132570-1)63252Robert Price01/2016
988311^60734-492063248Enzo Doria01/2013
9884(2^210075+2070)/263239Stefano Morozzi12/2019
98862^210061+2163235Donovan Johnson06/2006
988518^50375+9563235Lelio R Paula05/2013
988785^32773-263233Lelio R Paula08/2013
9888(-lucasV(1,2,420115)-2)/(3*5^3)63232Mike Oakes02/2017
9889(2^210054-1017)/67163230Lelio R Paula04/2012
98903*2^210022+563224Lelio R Paula04/2014
989115^53756+3263222Lelio R Paula05/2013
989217^51380+2263221Lelio R Paula05/2013
9893(lucasV(1,2,420045)+2)/25763221Mike Oakes02/2017
989443^38700+4263216Norbert Schneider06/2014
98955^90431-9663209Lelio R Paula04/2013
9896(172*10^63202-1)/963204Serge Batalov12/2014
9897(43*10^63200+83)/963201Robert Price08/2017
9898(2^209928+1146)/263195Stefano Morozzi12/2019
98992^209914-1600563191Enzo Doria04/2013
9900(2^209913+3642)/263190Stefano Morozzi12/2019
99013*6^81190-563179Lelio R Paula09/2014
990211424^15569-15569^1142463177Norbert Schneider11/2019
99032^209820+425763163Lelio R Paula10/2011
990499^31648+263158Lelio R Paula05/2013
990516976^5253+5253^1697663158Hans Havermann01/2017
99062^209790+6763154Lelio R Paula08/2011
9907145878#-p(145878)63152Henri Lifchitz12/2018
9908(2^209771+2486)/263148Stefano Morozzi12/2019
99092^209759+9019563144Lelio R Paula02/2013
9910145823#+21150763142Arkadiusz Wesolowski03/2013
99112^209707+51363129Lelio R Paula10/2011
9912(3^132314-8)/1763129Lelio R Paula04/2012
9913(2*10^63117+7)/963117Erik Branger03/2011
99149*2^209654-763114Lelio R Paula04/2014
991584304!6-963112Robert Price08/2018
991611^60598-1463107Lelio R Paula05/2013
991715103^15078+15078^1510363106Hans Havermann01/2017
991815346^12941+12941^1534663103Hans Havermann01/2017
99203^132253+7663101Lelio R Paula04/2013
9919(56*10^63100+403)/963101Robert Price10/2017
992117549^3936+3936^1754963090Hans Havermann01/2017
9923(55459*2^209553+1)/42363084Lelio R Paula06/2014
9922(2^209560+1602)/263084Stefano Morozzi12/2019
9924(331^25033-1)/33063077Eric Chen09/2017
992620^48480+3163074Lelio R Paula06/2013
9925(26*10^63073-23)/363074Robert Price08/2016
99272^209499+7625363066Enzo Doria04/2016
9928(2^209462+1618)/263055Stefano Morozzi12/2019
992911^60546-1134063053Enzo Doria12/2012
99302^209426+5788963044Yves Minet02/2010
9931(2^209419+2486)/263042Stefano Morozzi12/2019
9932(22699*2^209405+1)/2163041Lelio R Paula06/2014
99335^90189+5463040Lelio R Paula04/2013
9934(22*10^63034-73)/363035Robert Price09/2017
9935(314021^11467+1)/31402263029Faysal YAtim05/2008
9936(2^209306+450)/263008Stefano Morozzi12/2019
9937V(301486)63007Henri Lifchitz05/2003
9938(2^209302+3258)/263006Stefano Morozzi12/2019
9939(31*2^209298+1)/9563005Lelio R Paula08/2012
9940(2^209289+3290)/263002Stefano Morozzi12/2019
9941(27*2^209245+1)/562990Lelio R Paula08/2012
99426^80946-5^(80946-1)62989Robert Price05/2016
9943467^23596+23596^46762986Norbert Schneider08/2016
9944(7*2^209212-1)/362980Lelio R Paula01/2014
9945(27*2^209206-1)/1162978Lelio R Paula01/2014
99461456^19909+19909^145662976Serge Batalov05/2014
9947(5^90107-1)/(4*2162569)62976Gord Palameta07/2019
9948(3^131964-5)/18521239662955Lelio R Paula04/2012
994935^40772-146662955Enzo Doria03/2013
99505^90064-1370662953Enzo Doria02/2013
9951(2^209070+2658)/262937Stefano Morozzi12/2019
9952(22*10^62926+257)/962927Robert Price11/2017
9953(13*10^62914+401)/962915Robert Price10/2017
99542^208993+10762914Lelio R Paula08/2011
99552^208993+7762914Lelio R Paula08/2011
9956189^27636-262913Lelio R Paula10/2017
9957(2^208948-7)/26162898Lelio R Paula03/2012
995815804^9545+9545^1580462897Hans Havermann06/2019
9959(151*10^62879-1)/362881Robert Price04/2017
996015^53464-8262879Lelio R Paula05/2013
996111018^15555-15555^1101862875Norbert Schneider11/2019
99622^208843-11292162869Enzo Doria06/2014
9963(2^208841+2274)/262868Stefano Morozzi12/2019
996414005^15162-15162^1400562866Norbert Schneider03/2020
9965(2^208794+3594)/262853Stefano Morozzi12/2019
99662^208779+8162849Henri Lifchitz01/2007
9967159^28548+15862846Norbert Schneider12/2018
9968(21181*2^208780+1)/899383884162844Lelio R Paula06/2014
9969(73*10^62824+17)/962825Robert Price10/2015
99703^131670-8262823Lelio R Paula04/2013
997119^49128-9062823Lelio R Paula05/2013
9972(2^208684+2190)/262820Stefano Morozzi12/2019
9973(2^208684+3942)/262820Stefano Morozzi12/2019
997417687^3562+3562^1768762819Hans Havermann06/2019
997511^60314-441062811Enzo Doria01/2013
9976(17*2^208614-1)/5362799Lelio R Paula01/2014
99772^208594+9362794Donovan Johnson06/2008
9978(-lucasV(1,2,417184)+2)/(3*104297)62788Mike Oakes02/2017
9979(2^208544+3466)/262778Stefano Morozzi12/2019
9980(2^208534+7)/905962772Lelio R Paula03/2012
9981(2^208505+2570)/262766Stefano Morozzi12/2019
998214168^15119-15119^1416862764Norbert Schneider02/2020
9984(13^56333+1)/1462751Paul Bourdelais03/2010
998310^62750+5762751Robert Price01/2011
998510^62750-26742962750Patrick De Geest01/2013
99862^208427-6962743Lelio R Paula08/2011
99872^208421-11177562741Enzo Doria05/2014
9988(2^208406+3802)/262737Stefano Morozzi12/2019
99892^208404-11207962736Enzo Doria06/2014
9990(2^208381+2930)/262729Stefano Morozzi12/2019
999115242^13041+13041^1524262726Hans Havermann06/2019
99922^208343-222162718Yves Minet08/2013
99932^208335+51362716Lelio R Paula10/2011
9994(2^208328+47)/362713Lelio R Paula03/2012
999511^60220-204062713Enzo Doria12/2012
99962^208292+8162703Henri Lifchitz10/2005
9997(2^208293+162)/262703Stefano Morozzi12/2019
999815013^15012-1501262698Henri Lifchitz10/2014
99992^208271-11274762696Enzo Doria06/2014
1000011^60202-438062694Enzo Doria01/2013


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Created by  Henri Lifchitz & Renaud Lifchitz : October, 26 2000, last modification: March, 29 2020 17:41 (Time in France)

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