PRP Records

Probable Primes Top 10000

(288949 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 ?
9501(7*10^81985+107)/381986Robert Price02/2017
9502(3*2^272356+1)/17716381983Lelio R Paula12/2012
95032^272296-11114981970Enzo Doria05/2014
9504(2^272293+2810)/281969Stefano Morozzi01/2020
9505(2^272278+2118)/281964Stefano Morozzi01/2020
9506(9*2^272243-1)/781954Lelio R Paula02/2014
95072^272177-11122381934Enzo Doria05/2014
9508(2^272127+3878)/281919Stefano Morozzi01/2020
9510(151009^15817+1)/15101081912Faysal YAtim06/2017
9509(2^272104+1950)/281912Stefano Morozzi01/2020
951123160^3437+3437^2316081898Hans Havermann05/2020
9512(16*10^81896-19)/381897Robert Price03/2016
9513(16*10^81872-73)/381873Robert Price07/2020
9514(2^271922+78557)/6381855Lelio R Paula12/2012
9515(10^81848+77)/381848Robert Price01/2017
9516(24737*2^271883+1)/375781846Lelio R Paula06/2014
9517(2^271885+1670)/281846Stefano Morozzi01/2020
951818813^19144-19144^1881381831Norbert Schneider02/2020
9519(14*10^81818-89)/381819Robert Price05/2020
952019492^15731+15731^1949281804Hans Havermann07/2020
952120420^10137+10137^2042081801Hans Havermann06/2020
9522(2^271734+3942)/281800Stefano Morozzi01/2020
9523(15429^19531-1)/1542881799Serge Batalov08/2020
952410^81778+3981779Robert Price03/2011
952510^81778-17199981778Patrick De Geest07/2013
9526(2^271652+2886)/281776Stefano Morozzi01/2020
9527(14*10^81767-11)/381768Erik Branger09/2014
9528(2^271546+610)/281744Stefano Morozzi01/2020
95292^271541+186841781742Enzo Doria04/2016
9530(2^271549-1)/23874968248781734Jens K. Andersen02/2009
953119339^16836+16836^1933981732Hans Havermann06/2020
95322^271484-16781725Lelio R Paula06/2012
9534(8*10^81709-611)/981709Robert Price11/2017
9533(2^271431+1790)/281709Stefano Morozzi01/2020
953519648^14399+14399^1964881703Hans Havermann05/2020
95362^271382+1290981695Lelio R Paula07/2013
953749^48334+4881694Norbert Schneider07/2014
95387^96668+4881694Lelio R Paula10/2015
953911^78435-141081682Enzo Doria12/2012
954019575^14882+14882^1957581680Hans Havermann04/2020
95415*10^81653+981654Dmitry Domanov11/2010
9542(2^271224+1230)/281647Stefano Morozzi01/2020
9543(2^271211-1)/61396149515981631Jens K. Andersen02/2009
9544(2^271168+1806)/281630Stefano Morozzi01/2020
95453^171068+5281621Lelio R Paula12/2015
95462^271115-11040781614Enzo Doria05/2014
95472^271111-11063581613Enzo Doria05/2014
95482^271098-11181609Lelio R Paula06/2012
9549(77*10^81606+13)/981607Robert Price10/2015
95502^271064-279020981599Enzo Doria03/2016
9551(13*2^271053-1)/309581593Lelio R Paula02/2014
95522^271040-5781592Lelio R Paula06/2012
9553(14*10^81585+73)/381586Robert Price04/2016
9554127^38779+12681584Norbert Schneider02/2015
955518^64966-4381551Lelio R Paula11/2015
955619406^15909+15909^1940681538Hans Havermann06/2020
9557(17*10^81535-161)/981536Robert Price02/2021
9558(2^270843+1074)/281532Stefano Morozzi01/2020
9559(2^270840+47)/59181529Lelio R Paula12/2012
956020^62654+8781515Lelio R Paula01/2016
956120120^11241+11241^2012081503Hans Havermann05/2020
9562(19*10^81488+191)/381489Robert Price01/2017
95638*10^81487+2181488Robert Price02/2017
9564(73*10^81485+107)/981486Robert Price08/2016
9565536^29847+29847^53681458Norbert Schneider03/2017
95668*7^96378+981450Lelio R Paula10/2014
9567(2^270560+3862)/281447Stefano Morozzi01/2020
9568(5728^21673-1)/572781444Serge Batalov08/2020
95692^270546-11034581443Enzo Doria05/2014
957013^73105-6081435Lelio R Paula11/2015
9571(2^270502+1518)/281429Stefano Morozzi01/2020
9572(2^270479+2114)/281422Stefano Morozzi01/2020
9573(2^270384+1218)/281394Stefano Morozzi01/2020
957444^49524+4381391Norbert Schneider06/2014
9575(3*2^270368-1)/1381389Lelio R Paula02/2014
957696*10^81387-781389Robert Price03/2021
957719548^14563+14563^1954881384Hans Havermann05/2020
9578(2^270337+1130)/281380Stefano Morozzi01/2020
957927405^932+932^2740581377Hans Havermann05/2020
958019396^15683+15683^1939681375Hans Havermann05/2020
9582(10^81363+719)/981363Serge Batalov12/2014
9581(734^28393-1)/73381363Serge Batalov08/2020
9583(10^81353+449)/981353Serge Batalov12/2014
958414^70978-8981350Lelio R Paula11/2015
958511^78108-204081342Enzo Doria12/2012
95867*10^81327-5781328Robert Price06/2020
9587(7*10^81328-79)/981328Robert Price01/2021
958819102^18065+18065^1910281315Hans Havermann07/2020
95893^170400-5881302Lelio R Paula12/2015
9590(17*10^81300-131)/381301Robert Price12/2017
959110^81297+3699181298Patrick De Geest06/2013
959210^81297-5781297Robert Price05/2011
9593(2^270063+3206)/281297Stefano Morozzi01/2020
959419359^15826+15826^1935981296Hans Havermann06/2020
95952^270055-11304781295Enzo Doria07/2014
959618^64759-5581291Lelio R Paula11/2015
95973*10^81290-1781291Robert Price03/2021
9598(2^269987+1)/381274H.&R. Lifchitz10/2000
9599(31^54493-1)/3081268Alexander Zhirkov10/2010
9600(2^270059-1)/540119/6481417/712497615775672596781265Dario Alpern09/2014
9601(194^35521-1)/19381263Serge Batalov08/2020
960220722^8343+8343^2072281258Hans Havermann07/2020
9603(2^269922+3574)/281255Stefano Morozzi01/2020
960421310^6497+6497^2131081249Hans Havermann07/2020
9605(16392^19273-1)/1639181225Serge Batalov08/2020
96062^269819-459781224Yves Minet03/2019
9607(2^269816+7)/42490181218Lelio R Paula12/2012
960823470^2887+2887^2347081217Hans Havermann05/2020
9609(23*10^81214+1)/381215Serge Batalov06/2009
9610(2^269720+3778)/281194Stefano Morozzi01/2020
9611(17*2^269720+1)/30381193Lelio R Paula07/2012
961256^46441-55^4644181188Robert Price10/2013
96132^269664+17781177Lelio R Paula06/2012
9614(13*2^269665-1)/18581177Lelio R Paula02/2014
961521642^5615+5615^2164281144Hans Havermann07/2020
96162^269539-11224981140Enzo Doria06/2014
9617((2*170026-3)*3^(170026-1)+1)/481128Robert Price01/2015
9619(2^269495-5)/981126Lelio R Paula12/2012
96181239^26228+26228^123981126Norbert Schneider10/2019
96202^269490-362381125Yves Minet10/2009
9621(55459*2^269444+1)/3581114Lelio R Paula06/2014
962219554^14065+14065^1955481113Hans Havermann06/2020
9623(2^269417+78557)/525781099Lelio R Paula12/2012
96244*5^116011-781089Lelio R Paula10/2014
9625(2^269349+2366)/281082Stefano Morozzi01/2020
9626(2^269303+2946)/281068Stefano Morozzi01/2020
96276*10^81060+5381061Robert Price05/2020
96287*10^81058+7981059Robert Price02/2017
96292^269236-10990781049Enzo Doria04/2014
9630(2^269182+1870)/281032Stefano Morozzi01/2020
9631(2^269179+3006)/281031Stefano Morozzi01/2020
9632(8*10^81029-11)/381030Erik Branger03/2014
963319749^12668+12668^1974981025Hans Havermann05/2020
96343*10^81021+781022Erik Branger11/2013
96356^104115+10381018Lelio R Paula12/2015
96362^269120+186915181014Enzo Doria05/2016
96375^115901+1281012Lelio R Paula10/2015
9638(622*10^80999-1)/981001Robert Price11/2021
9639(2^269072+3610)/280999Stefano Morozzi01/2020
9640(2^269083-9)/32036980997Lelio R Paula12/2012
9641(5*10^80992-179)/380993Robert Price10/2020
96422*10^80981-4980982Robert Price09/2020
9643(2^269002+1614)/280978Stefano Morozzi01/2020
964417^65810-2080976Lelio R Paula11/2015
964520^62236-2380971Lelio R Paula01/2016
96462^268974-11218180970Enzo Doria06/2014
9648L(387433)80969Renaud Lifchitz11/2003
9647V(387433)80969Serge Batalov03/2015
964922732^3645+3645^2273280965Hans Havermann06/2020
9650(2^268957+602)/280964Stefano Morozzi01/2020
9651(2^268955-509203)/580963Lelio R Paula12/2012
965219485^14284+14284^1948580958Hans Havermann05/2020
9653(87398^16384+1)/6553780957Lelio R Paula11/2011
9654329^32160+32160^32980954Norbert Schneider11/2014
965519678^12973+12973^1967880937Hans Havermann02/2020
9656(2^268864+3558)/280936Stefano Morozzi01/2020
96572^268859-15980935Lelio R Paula05/2012
9658(2^268841-lucasV(1,2,268841)+1)/280929Mike Oakes11/2016
96602^268827+577580925Lelio R Paula07/2013
96592^268824-11025580925Enzo Doria05/2014
9661(2^268824+1902)/280924Stefano Morozzi01/2020
96622^268798-186832180917Enzo Doria04/2016
966320613^8420+8420^2061380913Hans Havermann03/2020
96642^268753-11462180903Enzo Doria05/2015
96652^268743+160580900Lelio R Paula07/2013
96666^103954-13980892Lelio R Paula12/2015
966710^80883+4980884Robert Price03/2011
966810^80883-8032780883Patrick De Geest07/2013
96696^103937+12180879Lelio R Paula12/2015
9670148^37266+14780877Norbert Schneider12/2018
9671(26*10^80875-119)/380876Robert Price07/2016
9672(22699*2^268657+1)/635180875Lelio R Paula06/2014
9673(2^268612+2530)/280860Stefano Morozzi01/2020
96742^268581-86968810580851Lelio R Paula05/2016
967510^80849-7000180849Robert Price12/2021
9676(11*2^268521-1)/380834Lelio R Paula02/2014
96772^268516-24980832Yves Minet02/2012
967822259^4278+4278^2225980828Hans Havermann03/2020
96792^268500+1609580827Lelio R Paula07/2013
96803^169402+10080826Lelio R Paula12/2015
9681(2^268495+566)/280825Stefano Morozzi01/2020
96829^84698+8^(84698-1)80823Robert Price03/2016
96832^268472-10973980819Enzo Doria04/2014
9684(9*2^268454+1)/3780813Lelio R Paula12/2012
9685(3*2^268502+1)/37790218843535364780811Lelio R Paula12/2012
9686(2^268441+3962)/280809Stefano Morozzi01/2020
9687134^37987-133^3798780803Jean-Louis Charton12/2005
968815^68702-7680800Lelio R Paula11/2015
96892^268408+780799Lelio R Paula05/2012
9690(16095^19207-1)/1609480794Serge Batalov08/2020
96912^268375+14180789Lelio R Paula05/2012
969212^74856-4780784Lelio R Paula11/2015
96932^268346+52428780781Paul Underwood08/2018
96949*10^80777-4180778Robert Price08/2020
9695(10868^20011-1)/1086780764Serge Batalov08/2020
96966^103770-10780749Lelio R Paula12/2015
9697(751^28081-1)/75080748Serge Batalov08/2020
96983^169224-6280741Lelio R Paula12/2015
9699p(16866)#/2+6480741Robert Price03/2017
97005^115502-7280733Lelio R Paula10/2015
9701(2^268154+2262)/280723Stefano Morozzi01/2020
9702(2^268156+1290)/280723Stefano Morozzi01/2020
97042^268079-192780700Yves Minet10/2009
9703(2^268078+2514)/280700Stefano Morozzi01/2020
9705(13*10^80685+71)/380686Robert Price06/2021
97062^268028+11780685Lelio R Paula05/2012
9707121^38738+12080683Norbert Schneider01/2015
9708(3^169097-8)/83580677Lelio R Paula12/2012
9709(2^267956+1810)/280663Stefano Morozzi01/2020
971019359^14666+14666^1935980656Hans Havermann12/2019
97112^267918+6780652Lelio R Paula05/2012
9712(89*10^80650-179)/980651Robert Price11/2017
9713(2^267914+2094)/280650Stefano Morozzi01/2020
9714(2^267894+2202)/280644Stefano Morozzi01/2020
9715(302*10^80638+13)/980640Robert Price01/2017
97163^169004+266080636Lelio R Paula12/2015
97172^267860-11285980634Enzo Doria06/2014
971896*10^80624-780626Robert Price03/2021
97192^267828-11070580625Enzo Doria05/2014
9720(2956^23227-1)/295580611Serge Batalov08/2020
9721(2^267752+2602)/280602Stefano Morozzi01/2020
97222^267743+1270580599Lelio R Paula07/2013
9723(22*10^80595+23)/980596Robert Price03/2015
9724(2^267712+2358)/280590Stefano Morozzi01/2020
9725(2^267685+854)/280581Stefano Morozzi01/2020
97262^267674-5180578Lelio R Paula05/2012
9727(86*10^80571-41)/980572Robert Price11/2015
9728(2^267637+2454)/280567Stefano Morozzi01/2020
972920452^8693+8693^2045280564Hans Havermann02/2020
97302^267612-196580560Lelio R Paula07/2013
97312^267553+409780542Lelio R Paula07/2013
97327^95276-880518Robert Price01/2014
9733(15185*2^267457-1)/4782980513Lelio R Paula04/2015
97346^103467+16380513Lelio R Paula12/2015
973520283^9314+9314^2028380506Hans Havermann02/2020
9736(2^267387+2294)/280492Stefano Morozzi01/2020
9737(7*10^80490+143)/380491Robert Price04/2016
973819887^11152+11152^1988780490Hans Havermann01/2020
9739(2^267348+3810)/280480Stefano Morozzi01/2020
974086^41597-85^4159780470Robert Price04/2015
974113^72237+3080468Lelio R Paula11/2015
974217^65389+1480458Lelio R Paula11/2015
9743423^30634+30634^42380456Norbert Schneider05/2017
9744(2^267257+470)/280453Stefano Morozzi01/2020
97452^267232+10580445Lelio R Paula05/2012
9747(298*10^80442+11)/380444Robert Price11/2020
9746(55*10^80443+629)/980444Robert Price01/2022
974822101^4360+4360^2210180437Hans Havermann02/2020
974911^77237-307200080435Enzo Doria01/2013
975020696^7689+7689^2069680422Hans Havermann01/2020


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Created by  Henri Lifchitz & Renaud Lifchitz : October, 26 2000, last modification: January, 19 2022 17:15 (Time in France)

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