PRP Records

Probable Primes Top 10000

(280932 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 ?
9001(2^261724+383949)/5/41/43/8378781Tony Prest / Never Odd Or Even04/2014
9002(2^261724+626567)/3/331/63178781Tony Prest / Never Odd Or Even05/2014
9003(2^261724+32987)/3/3/19/223/103178780Tony Prest / Never Odd Or Even04/2014
9004(2^261724+5813)/3/599139778780Tony Prest / Never Odd Or Even04/2014
9005(2^261724+13481)/3/11/239/208778780Tony Prest / Never Odd Or Even04/2014
9006(2^261724+103399)/5/13/37/1060778780Tony Prest / Never Odd Or Even04/2014
9007(2^261724+18477)/367/6511178780Tony Prest / Never Odd Or Even04/2014
9008(2^261724+121285)/167/227/121778780Tony Prest / Never Odd Or Even04/2014
9009(2^261724+262037)/3/3/11/23/1851778780Tony Prest / Never Odd Or Even04/2014
9010(2^261724+586157)/3/7/457/125978780Tony Prest / Never Odd Or Even05/2014
9011(2^261724+315287)/3/4582254178779Tony Prest / Never Odd Or Even04/2014
9012(2^261724+605675)/3/3/3/103/20748178779Tony Prest / Never Odd Or Even05/2014
9013(2^261724+60031)/13/31/702487778778Tony Prest / Never Odd Or Even04/2014
9014(2^261724+121879)/5/78943321778778Tony Prest / Never Odd Or Even04/2014
9015(2^261724+290135)/3/3/8467/905978778Tony Prest / Never Odd Or Even04/2014
9016(2^261724+79857)/59/3847/16533178777Tony Prest / Never Odd Or Even04/2014
9017(2^261724+22883)/3/17/23/2351/1007978777Tony Prest / Never Odd Or Even04/2014
9018(2^261724+154799)/3/5/365565371978777Tony Prest / Never Odd Or Even04/2014
9019(2^261724+391001)/3/11/17/41/43/2407178777Tony Prest / Never Odd Or Even04/2014
9020(2^261724+622383)/34843/55071778777Tony Prest / Never Odd Or Even05/2014
9021(2^261724+302829)/5/37/37/3707814778776Tony Prest / Never Odd Or Even04/2014
9022(2^261724+315837)/43/217613624378776Tony Prest / Never Odd Or Even04/2014
9023(2^261724+582373)/53/307/311/3211778776Tony Prest / Never Odd Or Even05/2014
9024(2^261724+295283)/3/3/3/29/43/1781227378775Tony Prest / Never Odd Or Even04/2014
9025(2^261724+27491)/3/22787/10597844978774Tony Prest / Never Odd Or Even04/2014
9026(2^261724+392751)/193813/28782668978774Tony Prest / Never Odd Or Even04/2014
9027(2^261724+328501)/7/1091/3149561051978773Tony Prest / Never Odd Or Even04/2014
9028(2^261724+111267)/19/4637/1514056042778772Tony Prest / Never Odd Or Even04/2014
9029(2^261724+572133)/127/131/7378775233378772Tony Prest / Never Odd Or Even05/2014
9030(2^261724+608733)/59/7079/18451/90915178771Tony Prest / Never Odd Or Even05/2014
9031(2^261724+255449)/3/3/5/7/1759/10177/3315886978770Tony Prest / Never Odd Or Even04/2014
9032(2^261724+99509)/3/5/5/6507271/674965928978769Tony Prest / Never Odd Or Even04/2014
9033(2^261724+52501)/563/53939/2794283139178769Tony Prest / Never Odd Or Even04/2014
9034(2^261724+117089)/3/5/37/149/967/2027/416374178769Tony Prest / Never Odd Or Even04/2014
9035(2^261724+372571)/1487/9209/21559/226324978769Tony Prest / Never Odd Or Even04/2014
9036(2^261724+184549)/5/8699/44053/140932299778769Tony Prest / Never Odd Or Even04/2014
9037(2^261724+363351)/937/159683/5952320022778768Tony Prest / Never Odd Or Even04/2014
9038(2^261724+326501)/3/43/193/263/19403/25350140378768Tony Prest / Never Odd Or Even04/2014
9039(2^261724+629477)/3/17/17/137/263/1993/16187/5734778768Tony Prest / Never Odd Or Even05/2014
9040(2^261724+94871)/3/3/13/6734017/167342524578778766Tony Prest / Never Odd Or Even04/2014
9041(2^261724+25981)/577/1181/3643/51778633474378766Tony Prest / Never Odd Or Even04/2014
9043(23*2^261642+1)/9378762Lelio R Paula10/2012
9042(2^261724+351227)/3/3/3/3/71/13997/9595373/819397800778762Tony Prest / Never Odd Or Even04/2014
9044(2^261724+22571)/3/7243/7321/18046081/4573074121178761Tony Prest / Never Odd Or Even04/2014
9045(2^261724+56495)/3/3/3/7/7/13/9041/512818459/2370858911978760Tony Prest / Never Odd Or Even04/2014
904671293!4-478759Robert Price11/2019
9047(2^261630+3582)/278759Stefano Morozzi01/2020
9048(2^261724+604119)/5/7/7/41/14107/19681/211777/90145981/103602083412778750Tony Prest / Never Odd Or Even05/2014
9049(2^261536+846)/278730Stefano Morozzi01/2020
90502^261507-228778722Yves Minet04/2009
90518*10^78717+3978718Robert Price01/2017
9052(78557*2^261440+1)/378706Lelio R Paula06/2014
9053(290^31963-1)/28978704Serge Batalov08/2020
9054(21323^18181-1)/2132278699Serge Batalov08/2020
90556^101128-1643378693Enzo Doria02/2013
905620^60482+9978689Lelio R Paula03/2015
90572^261348-11063378674Enzo Doria05/2014
9058191^34487+278666Lelio R Paula05/2013
90592^261305-11013978661Enzo Doria04/2014
9060(82*10^78635-1)/978636Robert Price12/2014
906110^78632+8178633Robert Price03/2011
906210^78632-40269378632Patrick De Geest07/2013
90633*10^78631+1778632Robert Price03/2017
90642^261174-391178622Yves Minet04/2017
90652^261167+7484378620Enzo Doria04/2016
906618810^15119+15119^1881078617Hans Havermann04/2020
9067L(376121)+F(376122)78605Henri Lifchitz01/2007
906814^68580-2978602Lelio R Paula02/2015
9069(4270^21649-1)/426978592Serge Batalov08/2020
907020603^6522+6522^2060378588Hans Havermann03/2020
9071(2^261056+646)/278586Stefano Morozzi01/2020
9072(73*10^78576-1)/978577Robert Price01/2015
9073(2^261020+2158)/278575Stefano Morozzi01/2020
9074(17*2^261026-1)/4045178574Lelio R Paula02/2014
9075(2415^23227-1)/241478572Serge Batalov08/2020
90772^261001-19578570Lelio R Paula05/2012
907618532^17365+17365^1853278570Hans Havermann02/2020
90785*2^260950+978555Lelio R Paula06/2014
90792^260931-760578549Lelio R Paula07/2013
908019863^9002+9002^1986378546Hans Havermann02/2020
908115^66778-3278538Lelio R Paula02/2015
9082(11*2^260896-1)/24578537Lelio R Paula02/2014
908330^53166+2978533Norbert Schneider03/2017
9085lucasU(2403,1,23229)-lucasU(2403,1,23228)78529Mike Oakes05/2009
908418729^15592+15592^1872978529Hans Havermann04/2020
90867*3^164574-278523Lelio R Paula06/2014
908718518^17385+17385^1851878520Hans Havermann03/2020
90882^260830-11213378518Enzo Doria06/2014
908913^70486+4278518Lelio R Paula03/2015
909011^75386-708078507Enzo Doria01/2013
9092(86^40583-1)/8578506Paul Bourdelais08/2017
9091(2^260790+1914)/278506Stefano Morozzi01/2020
90935*10^78504+1178505Robert Price08/2019
90942^260711-5869578482Lelio R Paula07/2013
9095(2^260695+2258)/278477Stefano Morozzi01/2020
90962^260678-11106578472Enzo Doria05/2014
909721560^4359+4359^2156078466Hans Havermann02/2020
909818^62501-9778456Lelio R Paula02/2015
909953^45498-278452Lelio R Paula08/2013
9100(8890^19867-1)/888978449Serge Batalov08/2020
9101(2^260549+642)/278433Stefano Morozzi01/2020
9102(2^260527+3906)/278427Stefano Morozzi01/2020
91032^260513-11112178423Enzo Doria05/2014
910437845!2-6478412Robert Price06/2015
91052^260469-11069578409Enzo Doria05/2014
9106(11*10^78408-113)/378409Robert Price01/2017
91072^260447+841578403Lelio R Paula07/2013
91085*10^78395-6978396Robert Price02/2021
910937837!2-6478394Robert Price06/2015
9110(19*2^260379-1)/5378382Lelio R Paula02/2014
91112^260377-11323378382Enzo Doria07/2014
9112(2^260378+3750)/278382Stefano Morozzi01/2020
91149^82138+6^82138-2^8213878380Mike Oakes08/2010
911369^42624+278380Lelio R Paula05/2013
91152^260369-185971378379Enzo Doria03/2016
911618634^16067+16067^1863478374Hans Havermann02/2020
911714*10^78362+108978364Jens K. Andersen11/2007
9118(2^260317+3542)/278363Stefano Morozzi01/2020
9119(1942^23827-1)/194178346Serge Batalov08/2020
91205^112070-5478334Lelio R Paula02/2015
912120120^7821+7821^2012078333Hans Havermann03/2020
9122(10^(2*39165+1)+54*10^39165-1)/978331Robert Price04/2017
9123(2^260195+3546)/278327Stefano Morozzi01/2020
91242^260182-11345378323Enzo Doria07/2014
9125f(16405)78319Robert Price09/2017
912618547^16678+16678^1854778309Hans Havermann02/2020
9127(78557*2^260084+1)/51978296Lelio R Paula06/2014
912810^78288+9^(78288+1)78289Robert Price08/2016
912910^78288+3910978289Patrick De Geest12/2016
913010^78288-21629978288Patrick De Geest12/2016
9131(2^260059+2430)/278286Stefano Morozzi01/2020
9132(2^260056+1662)/278285Stefano Morozzi01/2020
9133(376*70^42427-1)/378285Eric Chen10/2020
91345^111997+3678283Lelio R Paula02/2015
9135(2^260017+1602)/278273Stefano Morozzi01/2020
9136(2^260017+2162)/278273Stefano Morozzi01/2020
913723969^1842+1842^2396978266Hans Havermann05/2020
913819297^11370+11370^1929778265Hans Havermann05/2020
9139(21^59183+1)/2278252Paul Bourdelais03/2010
914019090^12561+12561^1909078251Hans Havermann04/2020
9141(88*10^78242-7)/978243Robert Price11/2014
91422*6^100547+778242Lelio R Paula10/2014
9143(2^259913+3470)/278242Stefano Morozzi01/2020
9144(2^259885+3726)/278233Stefano Morozzi01/2020
91452^259860-11108978226Enzo Doria05/2014
914618226^18359+18359^1822678223Norbert Schneider02/2020
9147(2^259833+3342)/278218Stefano Morozzi01/2020
914837^49875-278215Lelio R Paula09/2013
9149(13*10^78213+401)/978214Robert Price10/2017
91507*5^111893-478211Lelio R Paula10/2014
9151(11*2^259809-1)/143778209Lelio R Paula02/2014
91527^92511-678181Theodore Burton11/2005
9153(3^163859-4)/25378179Lelio R Paula10/2012
9154(2^259689+1346)/278174Stefano Morozzi01/2020
9155(27*2^259666-1)/62569178163Lelio R Paula02/2014
9156(2^259642+3202)/278160Stefano Morozzi01/2020
9157(2^259624+442)/278155Stefano Morozzi01/2020
91583*10^78146+1778147Robert Price03/2017
9159(2^259594+1558)/278146Stefano Morozzi01/2020
9160(576^28307+1)/57778137Richard Fischer01/2018
91612^259503+7433378119Enzo Doria04/2016
9162(2^259503+2438)/278118Stefano Morozzi01/2020
9163(31*2^259504-1)/1336578116Lelio R Paula02/2014
9165(58547^16384+1)/278111Lelio R Paula11/2011
91646^100379+1378111Lelio R Paula03/2015
91662^259469-10990978108Enzo Doria04/2014
916715^66413-2678108Lelio R Paula02/2015
916818550^16229+16229^1855078101Hans Havermann05/2020
91697^92410-926678096Mike Oakes02/2010
91702^259398+7579978087Enzo Doria04/2016
91712^259394+187618978086Enzo Doria07/2016
9172PIPrime(78073)78073Eric W. Weisstein07/2006
91735*2^259344-778072Lelio R Paula06/2014
9174(2^259347+990)/278071Stefano Morozzi01/2020
917521702^3955+3955^2170278066Hans Havermann04/2020
917614^68097-8778048Lelio R Paula02/2015
91772^259233-47557378037Paul Bourdelais03/2013
9178181^34554-278012Lelio R Paula10/2017
91793^163500-2878010Robert Price12/2013
9180(206*10^78005+7)/378007Robert Price07/2020
9181(65*10^77992+691)/977993Robert Price08/2016
9182(2^259035+3930)/277978Stefano Morozzi01/2020
91832^259013-11259177971Enzo Doria06/2014
91857*10^77969-1177970Robert Price10/2017
9184(2^259011+2430)/277970Stefano Morozzi01/2020
91866^100193-100193^677966Norbert Schneider04/2017
9187(2^258974+2638)/277959Stefano Morozzi01/2020
918824214^1657+1657^2421477953Hans Havermann03/2020
9189(2^258945+674)/277950Stefano Morozzi01/2020
9190(2^258939+2450)/277949Stefano Morozzi01/2020
919118090^18307+18307^1809077941Norbert Schneider02/2020
9192(11259^19237-1)/1125877935Serge Batalov08/2020
91932^258863-11023577926Enzo Doria05/2014
91942^258852+160577923Lelio R Paula06/2013
919510^77919+23802777920Patrick De Geest04/2020
919610^77919-12345678977919Robert Price02/2020
919710^77919-2543377919Patrick De Geest04/2020
9198(11*10^77909+49)/377910Robert Price05/2016
91992*7^92187-977908Lelio R Paula10/2014
92002^258763-11015577896Enzo Doria04/2014
9201(2^258738+1062)/277888Stefano Morozzi01/2020
92022^258694-11038777875Enzo Doria05/2014
920311^74773-9477869Lelio R Paula02/2015
92046^100067+12577868Lelio R Paula03/2015
920515^66205+877864Lelio R Paula07/2014
9206(2^258637+17)/1860500377851Stefano Morozzi03/2020
92075^111373-1813677847Enzo Doria05/2014
9208(2^258566+1974)/277836Stefano Morozzi01/2020
92092^258524-10987777824Enzo Doria04/2014
921022828^2565+2565^2282877823Hans Havermann04/2020
9211(2^258515+3914)/277821Stefano Morozzi01/2020
92126^100002-1664377817Enzo Doria02/2013
9213(13*10^77811+347)/977812Robert Price10/2017
921419376^10365+10365^1937677806Hans Havermann04/2020
9215(29*10^77803+31)/377804Robert Price04/2021
921665^42916+2877803Lelio R Paula01/2016
9217(2^258405+3302)/277788Stefano Morozzi01/2020
9218(89*10^77781-17)/977782Robert Price11/2015
92192^258382-11040577781Enzo Doria05/2014
92215^111278-1499677780Enzo Doria02/2013
9220(2^258378+2314)/277780Stefano Morozzi01/2020
922214^67862+6177779Lelio R Paula02/2015
922310^77777+4848377778Patrick De Geest11/2010
922410^77777-18324377777Patrick De Geest11/2010
92257*((10^77777-1)/9)-81432*277777Matt Stath10/2020
9226(27*2^258352+1)/4377772Lelio R Paula08/2012
9227(22329^17881-1)/2232877758Serge Batalov08/2020
9228(2^258294+2454)/277754Stefano Morozzi01/2020
9229337^30756-1000277740Enzo Doria07/2012
923010^77726+9977727Robert Price03/2011
923110^77726-8594777726Patrick De Geest06/2013
923289^39870-277723Lelio R Paula08/2013
92337^91966-3277721Lelio R Paula02/2015
923435^50327+277709Lelio R Paula05/2013
923624^56298+2377704Norbert Schneider12/2016
9235(2^258128+3502)/277704Stefano Morozzi01/2020
9238(2^258105+78557)/1977697Lelio R Paula10/2012
9237(2^258102+2842)/277697Stefano Morozzi01/2020
92392^258079+17977690Lelio R Paula03/2012
92412^258062-11311177685Enzo Doria07/2014
9240(21752^17911-1)/2175177685Serge Batalov08/2020
9242(2^258022+2422)/277673Stefano Morozzi01/2020
924310^77669+12345678977670Robert Price10/2019
924410^77669+5912777670Patrick De Geest12/2019
924510^77669-10910377669Patrick De Geest12/2019
9246(2^258002+3822)/277667Stefano Morozzi01/2020
924780^40807-7977660Norbert Schneider03/2015
924870385!4-477658Robert Price11/2019
9249(10^77637+359)/977637Serge Batalov12/2014
92502^257862-16577625Lelio R Paula03/2012


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Created by  Henri Lifchitz & Renaud Lifchitz : October, 26 2000, last modification: April, 13 2021 12:02 (Time in France)

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