PRP Records

Probable Primes Top 10000

(288515 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(21323^18181-1)/2132278699Serge Batalov08/2020
97526^101128-1643378693Enzo Doria02/2013
975320^60482+9978689Lelio R Paula03/2015
97542^261348-11063378674Enzo Doria05/2014
9755191^34487+278666Lelio R Paula05/2013
97562^261305-11013978661Enzo Doria04/2014
9757(682*10^78656-7)/978658Robert Price08/2021
9758(82*10^78635-1)/978636Robert Price12/2014
975910^78632+8178633Robert Price03/2011
976010^78632-40269378632Patrick De Geest07/2013
97613*10^78631+1778632Robert Price03/2017
97622^261174-391178622Yves Minet04/2017
97632^261167+7484378620Enzo Doria04/2016
976418810^15119+15119^1881078617Hans Havermann04/2020
9765L(376121)+F(376122)78605Henri Lifchitz01/2007
976614^68580-2978602Lelio R Paula02/2015
9767(4270^21649-1)/426978592Serge Batalov08/2020
976820603^6522+6522^2060378588Hans Havermann03/2020
9769(2^261056+646)/278586Stefano Morozzi01/2020
9770(73*10^78576-1)/978577Robert Price01/2015
9771(2^261020+2158)/278575Stefano Morozzi01/2020
9772(17*2^261026-1)/4045178574Lelio R Paula02/2014
9773(2415^23227-1)/241478572Serge Batalov08/2020
97752^261001-19578570Lelio R Paula05/2012
977418532^17365+17365^1853278570Hans Havermann02/2020
97765*2^260950+978555Lelio R Paula06/2014
97772^260931-760578549Lelio R Paula07/2013
977819863^9002+9002^1986378546Hans Havermann02/2020
977915^66778-3278538Lelio R Paula02/2015
9780(11*2^260896-1)/24578537Lelio R Paula02/2014
978130^53166+2978533Norbert Schneider03/2017
9782lucasU(2403,1,23229)-lucasU(2403,1,23228)78529Mike Oakes05/2009
978318729^15592+15592^1872978529Hans Havermann04/2020
97847*3^164574-278523Lelio R Paula06/2014
978518518^17385+17385^1851878520Hans Havermann03/2020
97862^260830-11213378518Enzo Doria06/2014
978713^70486+4278518Lelio R Paula03/2015
978811^75386-708078507Enzo Doria01/2013
9790(86^40583-1)/8578506Paul Bourdelais08/2017
9789(2^260790+1914)/278506Stefano Morozzi01/2020
97915*10^78504+1178505Robert Price08/2019
97922^260711-5869578482Lelio R Paula07/2013
9793(2^260695+2258)/278477Stefano Morozzi01/2020
97942^260678-11106578472Enzo Doria05/2014
979521560^4359+4359^2156078466Hans Havermann02/2020
979618^62501-9778456Lelio R Paula02/2015
979753^45498-278452Lelio R Paula08/2013
9798(8890^19867-1)/888978449Serge Batalov08/2020
9799(2^260549+642)/278433Stefano Morozzi01/2020
9800(2^260527+3906)/278427Stefano Morozzi01/2020
98012^260513-11112178423Enzo Doria05/2014
980237845!2-6478412Robert Price06/2015
98032^260469-11069578409Enzo Doria05/2014
9804(11*10^78408-113)/378409Robert Price01/2017
98052^260447+841578403Lelio R Paula07/2013
98065*10^78395-6978396Robert Price02/2021
980737837!2-6478394Robert Price06/2015
98082^260410-11154643578392Paul Bourdelais10/2021
9810(19*2^260379-1)/5378382Lelio R Paula02/2014
98112^260377-11323378382Enzo Doria07/2014
9809(2^260378+3750)/278382Stefano Morozzi01/2020
98139^82138+6^82138-2^8213878380Mike Oakes08/2010
981269^42624+278380Lelio R Paula05/2013
98142^260369-185971378379Enzo Doria03/2016
981518634^16067+16067^1863478374Hans Havermann02/2020
981614*10^78362+108978364Jens K. Andersen11/2007
9817(2^260317+3542)/278363Stefano Morozzi01/2020
9818(1942^23827-1)/194178346Serge Batalov08/2020
98195^112070-5478334Lelio R Paula02/2015
982020120^7821+7821^2012078333Hans Havermann03/2020
9821(10^(2*39165+1)+54*10^39165-1)/978331Robert Price04/2017
9822(2^260195+3546)/278327Stefano Morozzi01/2020
98232^260182-11345378323Enzo Doria07/2014
9824f(16405)78319Robert Price09/2017
982518547^16678+16678^1854778309Hans Havermann02/2020
9826(78557*2^260084+1)/51978296Lelio R Paula06/2014
982810^78288+9^(78288+1)78289Robert Price08/2016
982710^78288+3910978289Patrick De Geest12/2016
982910^78288-21629978288Patrick De Geest12/2016
9830(2^260059+2430)/278286Stefano Morozzi01/2020
9831(2^260056+1662)/278285Stefano Morozzi01/2020
9832(376*70^42427-1)/378285Eric Chen10/2020
98335^111997+3678283Lelio R Paula02/2015
9834(2^260017+1602)/278273Stefano Morozzi01/2020
9835(2^260017+2162)/278273Stefano Morozzi01/2020
983623969^1842+1842^2396978266Hans Havermann05/2020
983719297^11370+11370^1929778265Hans Havermann05/2020
9838(21^59183+1)/2278252Paul Bourdelais03/2010
983919090^12561+12561^1909078251Hans Havermann04/2020
9840(88*10^78242-7)/978243Robert Price11/2014
98412*6^100547+778242Lelio R Paula10/2014
9842(2^259913+3470)/278242Stefano Morozzi01/2020
9843(2^259885+3726)/278233Stefano Morozzi01/2020
98442^259860-11108978226Enzo Doria05/2014
984518226^18359+18359^1822678223Norbert Schneider02/2020
9846(2^259833+3342)/278218Stefano Morozzi01/2020
984737^49875-278215Lelio R Paula09/2013
9848(13*10^78213+401)/978214Robert Price10/2017
98497*5^111893-478211Lelio R Paula10/2014
9850(11*2^259809-1)/143778209Lelio R Paula02/2014
98517^92511-678181Theodore Burton11/2005
9852(3^163859-4)/25378179Lelio R Paula10/2012
9853(2^259689+1346)/278174Stefano Morozzi01/2020
9854(27*2^259666-1)/62569178163Lelio R Paula02/2014
9855(2^259642+3202)/278160Stefano Morozzi01/2020
9856(2^259624+442)/278155Stefano Morozzi01/2020
98573*10^78146+1778147Robert Price03/2017
9858(2^259594+1558)/278146Stefano Morozzi01/2020
9859(576^28307+1)/57778137Richard Fischer01/2018
98602^259503+7433378119Enzo Doria04/2016
9861(2^259503+2438)/278118Stefano Morozzi01/2020
9862(31*2^259504-1)/1336578116Lelio R Paula02/2014
9864(58547^16384+1)/278111Lelio R Paula11/2011
98636^100379+1378111Lelio R Paula03/2015
98652^259469-10990978108Enzo Doria04/2014
986615^66413-2678108Lelio R Paula02/2015
986718550^16229+16229^1855078101Hans Havermann05/2020
98687^92410-926678096Mike Oakes02/2010
98692^259398+7579978087Enzo Doria04/2016
98702^259394+187618978086Enzo Doria07/2016
9871PIPrime(78073)78073Eric W. Weisstein07/2006
98725*2^259344-778072Lelio R Paula06/2014
9873(2^259347+990)/278071Stefano Morozzi01/2020
987421702^3955+3955^2170278066Hans Havermann04/2020
987514^68097-8778048Lelio R Paula02/2015
98762^259233-47557378037Paul Bourdelais03/2013
9877181^34554-278012Lelio R Paula10/2017
98783^163500-2878010Robert Price12/2013
9879(206*10^78005+7)/378007Robert Price07/2020
9880(65*10^77992+691)/977993Robert Price08/2016
9881(2^259035+3930)/277978Stefano Morozzi01/2020
98822^259013-11259177971Enzo Doria06/2014
98837*10^77969-1177970Robert Price10/2017
9884(2^259011+2430)/277970Stefano Morozzi01/2020
98856^100193-100193^677966Norbert Schneider04/2017
9886(2^258974+2638)/277959Stefano Morozzi01/2020
988724214^1657+1657^2421477953Hans Havermann03/2020
9888(2^258945+674)/277950Stefano Morozzi01/2020
9889(2^258939+2450)/277949Stefano Morozzi01/2020
989018090^18307+18307^1809077941Norbert Schneider02/2020
9891(11259^19237-1)/1125877935Serge Batalov08/2020
98922^258863-11023577926Enzo Doria05/2014
98932^258852+160577923Lelio R Paula06/2013
989410^77919+23802777920Patrick De Geest04/2020
989510^77919-12345678977919Robert Price02/2020
989610^77919-2543377919Patrick De Geest04/2020
9897(11*10^77909+49)/377910Robert Price05/2016
98982*7^92187-977908Lelio R Paula10/2014
98992^258763-11015577896Enzo Doria04/2014
9900(2^258738+1062)/277888Stefano Morozzi01/2020
99012^258694-11038777875Enzo Doria05/2014
990211^74773-9477869Lelio R Paula02/2015
99036^100067+12577868Lelio R Paula03/2015
990415^66205+877864Lelio R Paula07/2014
9905(2^258637+17)/1860500377851Stefano Morozzi03/2020
99065^111373-1813677847Enzo Doria05/2014
9907(2^258566+1974)/277836Stefano Morozzi01/2020
99082^258524-10987777824Enzo Doria04/2014
990922828^2565+2565^2282877823Hans Havermann04/2020
9910(2^258515+3914)/277821Stefano Morozzi01/2020
99116^100002-1664377817Enzo Doria02/2013
9912(13*10^77811+347)/977812Robert Price10/2017
991311*10^77807+377809Robert Price07/2021
991419376^10365+10365^1937677806Hans Havermann04/2020
9915(29*10^77803+31)/377804Robert Price04/2021
991665^42916+2877803Lelio R Paula01/2016
9917(2^258405+3302)/277788Stefano Morozzi01/2020
9918(89*10^77781-17)/977782Robert Price11/2015
99192^258382-11040577781Enzo Doria05/2014
99205^111278-1499677780Enzo Doria02/2013
9921(2^258378+2314)/277780Stefano Morozzi01/2020
992214^67862+6177779Lelio R Paula02/2015
992310^77777+4848377778Patrick De Geest11/2010
992410^77777-18324377777Patrick De Geest11/2010
99257*((10^77777-1)/9)-81432*277777Matt Stath10/2020
9926(27*2^258352+1)/4377772Lelio R Paula08/2012
9927(22329^17881-1)/2232877758Serge Batalov08/2020
9928(2^258294+2454)/277754Stefano Morozzi01/2020
9929337^30756-1000277740Enzo Doria07/2012
993010^77726+9977727Robert Price03/2011
993110^77726-8594777726Patrick De Geest06/2013
993289^39870-277723Lelio R Paula08/2013
99337^91966-3277721Lelio R Paula02/2015
993435^50327+277709Lelio R Paula05/2013
993624^56298+2377704Norbert Schneider12/2016
9935(2^258128+3502)/277704Stefano Morozzi01/2020
9937(2^258105+78557)/1977697Lelio R Paula10/2012
9938(2^258102+2842)/277697Stefano Morozzi01/2020
99392^258079+17977690Lelio R Paula03/2012
99402^258062-11311177685Enzo Doria07/2014
9941(21752^17911-1)/2175177685Serge Batalov08/2020
9942(2^258022+2422)/277673Stefano Morozzi01/2020
994310^77669+12345678977670Robert Price10/2019
994410^77669+5912777670Patrick De Geest12/2019
994510^77669-10910377669Patrick De Geest12/2019
9946(2^258002+3822)/277667Stefano Morozzi01/2020
994780^40807-7977660Norbert Schneider03/2015
994870385!4-477658Robert Price11/2019
9949(10^77637+359)/977637Serge Batalov12/2014
9950(10^77650+7)/29/89489773/10814863977633Alfred Reich06/2021
99512^257862-16577625Lelio R Paula03/2012
9952(25*2^257853+1)/377623Lelio R Paula07/2012
9953(2^257832+1362)/277615Stefano Morozzi01/2020
9954(2^257869+1)/(3*18645362967379)77613Henri Lifchitz04/2005
99556^99728+7177604Lelio R Paula01/2015
99562^257778-11276777599Enzo Doria06/2014
9957(31*2^257771+1)/53777596Lelio R Paula07/2012
9958(2^257762+2214)/277594Stefano Morozzi01/2020
99592^257729-7377585Lelio R Paula03/2012
9960(2^257728+1890)/277584Stefano Morozzi01/2020
99612^257689-6377573Lelio R Paula03/2012
9962(47*10^77572+493)/977573Robert Price11/2017
996391*10^77563-977565Robert Price06/2021
9964(78557*2^257665+1)/610872577564Lelio R Paula06/2014
9965(5570^20707-1)/556977562Serge Batalov08/2020
99662^257650+11154643577561Paul Bourdelais10/2021
9967(3^162563+8)/288577559Lelio R Paula10/2012
99682^257636-11023577557Enzo Doria05/2014
9969(23*10^77556+97)/377557Robert Price02/2017
9970(2^257639+2630)/277557Stefano Morozzi01/2020
9971(2^257625+3354)/277553Stefano Morozzi01/2020
99722^257621-11007177552Enzo Doria04/2014
997319580^9129+9129^1958077546Hans Havermann03/2020
99742^257567-6487577536Lelio R Paula06/2013
9975(18098^18211-1)/1809777532Serge Batalov08/2020
9976(2^257429+2394)/277494Stefano Morozzi01/2020
9977(2^257373+1206)/277477Stefano Morozzi01/2020
99782*7^91674+977474Lelio R Paula10/2014
9979(2^257248+2442)/277440Stefano Morozzi01/2020
9980(17*10^77427-47)/377428Robert Price05/2017
998110^77418+84168377419Patrick De Geest06/2013
998210^77418-3377418Robert Price05/2011
998319^60539-3677415Lelio R Paula03/2015
9984(9562^19447-1)/956177406Serge Batalov08/2020
998537401!!-102477397Robert Price11/2015
9986(2^257095+1410)/277394Stefano Morozzi01/2020
998711^74313-1875077390Enzo Doria12/2012
99882^257044-11288377378Enzo Doria06/2014
99898*10^77377+5177378Robert Price05/2017
9990Phi(258121,2)/71977375Jeppe Stig Nielsen09/2020
99912*7^91553+977372Lelio R Paula10/2014
9992713^27118+27118^71377371Norbert Schneider12/2016
9993(22711^17761-1)/2271077367Serge Batalov08/2020
999418652^14043+14043^1865277359Hans Havermann03/2020
9995(11391^19069-1)/1139077351Serge Batalov08/2020
99966*10^77346-2977347Robert Price08/2020
99972^256920-11115577341Enzo Doria05/2014
99982^256896-655577334Lelio R Paula06/2013
9999(52*10^77322-7)/977323Robert Price12/2014
100002^256849-11293977320Enzo Doria06/2014


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Created by  Henri Lifchitz & Renaud Lifchitz : October, 26 2000, last modification: December, 01 2021 22:29 (Time in France)

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