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 ?
8251(2^276165+2046)/283134Stefano Morozzi01/2020
8252(2^276105+1274)/283116Stefano Morozzi01/2020
82532^276066-11160383105Enzo Doria05/2014
825419438^18837+18837^1943883098Hans Havermann07/2020
8255(431^31543-1)/43083097Serge Batalov08/2020
8256(2^276028-3)*6-783094Gilbert Mozzo09/2016
8257(26*10^83067+79)/383068Robert Price09/2020
82582^275926-469183063Yves Minet05/2019
8259(2^275919+1386)/283060Stefano Morozzi01/2020
8260(2^275897+9)/115383051Lelio R Paula12/2012
82612^275879-10980783048Enzo Doria04/2014
8263F(397379)83047Henri Lifchitz08/2003
8262U(397379)83047Serge Batalov03/2015
82643^174040-1483039Robert Price08/2013
8265(86*10^83038-221)/983039Robert Price06/2017
826621632^6897+6897^2163283038Hans Havermann05/2020
82672^275841-688383037Lelio R Paula07/2011
826819610^17127+17127^1961083023Hans Havermann06/2020
82693^174002-14083021Lelio R Paula12/2015
82706^106681+7783014Lelio R Paula12/2015
8271187^36539-283011Lelio R Paula10/2017
82721036^27529+27529^103683010Norbert Schneider03/2020
827311^79701-315083001Enzo Doria12/2012
8274(2^275721+1554)/283000Stefano Morozzi01/2020
8275(2^275704+1858)/282995Stefano Morozzi01/2020
8276(2^275696+1726)/282993Stefano Morozzi01/2020
8277(55459*2^275657+1)/2182985Lelio R Paula06/2014
8278(7*10^82960-457)/982960Robert Price09/2017
82792^275535-685582945Lelio R Paula08/2013
82803^173828-1482938Robert Price08/2013
82812^275512-10967782938Enzo Doria04/2014
8282(2^275450+1698)/282919Stefano Morozzi01/2020
82832^275446-11004582918Enzo Doria04/2014
8284(2^275473+47)/2952609744782916Lelio R Paula12/2012
82853*10^82914-8382915Robert Price02/2021
82863^173755-1482903Robert Price08/2013
8287(182*10^82898+43)/982900Robert Price11/2017
82882^275363-11230982893Enzo Doria06/2014
828961^46427-6082888Norbert Schneider10/2014
82903*10^82880-7^8288082881Mike Oakes02/2010
82912^275290+9019582871Lelio R Paula07/2013
8292(35*10^82870-71)/982871Robert Price05/2015
82932^275270-185962182865Enzo Doria03/2016
82942^275259+8182862Henri Lifchitz01/2007
829521436^7335+7335^2143682859Hans Havermann05/2020
8296(2^275247+1590)/282858Stefano Morozzi01/2020
829722515^4784+4784^2251582851Hans Havermann05/2020
82986*10^82842-3182843Robert Price07/2020
8299(10013^20707-1)/1001282836Serge Batalov08/2020
8300(113703^16384+1)/282834Richard Fischer04/2018
8301(2^275146+954)/282827Stefano Morozzi01/2020
83027^98003+98003^7+182823Robert Price05/2014
8303(2^275101+3566)/282814Stefano Morozzi01/2020
8304(2^275050+3150)/282798Stefano Morozzi01/2020
8305(2^275044+2482)/282797Stefano Morozzi01/2020
830610^82790+12604382791Patrick De Geest07/2013
830710^82790-4782790Robert Price05/2011
830820762^9711+9711^2076282784Hans Havermann05/2020
83092^274985-11266382779Enzo Doria06/2014
83102^274935+1501582764Lelio R Paula07/2013
8311(17*2^274922+1)/382761Lelio R Paula12/2012
8312[(55^5)^9511-(22434^2)^9511]/1982759Richard Fischer11/2019
8313(43*10^82752-61)/982753Robert Price06/2015
8314(3*2^274862+1)/102782740Lelio R Paula12/2012
8315(2^274851+3126)/282739Stefano Morozzi01/2020
8316(31*2^274848-1)/406582736Lelio R Paula02/2014
8317(4^137405+23)/382726Robert Price02/2017
8318(2^274798+414)/282723Stefano Morozzi01/2020
83192^274791-11049182721Enzo Doria05/2014
8320(11*2^274776-1)/9582715Lelio R Paula02/2014
8321(47*10^82706-119)/982707Robert Price09/2017
83222^274704-11139582695Enzo Doria05/2014
83232^274686-391182689Yves Minet04/2017
8324(1629^25741-1)/162882675Serge Batalov08/2020
832521474^7075+7075^2147482670Hans Havermann06/2020
8326(2^274663-1017)/4887131829227982669Lelio R Paula12/2012
8327(3^173263-5)/1449882664Lelio R Paula12/2012
832820488^10815+10815^2048882650Hans Havermann07/2020
8329(2^274554+894)/282649Stefano Morozzi01/2020
83312^274511-6487582637Lelio R Paula08/2013
8330(2^274512+1222)/282637Stefano Morozzi01/2020
833212^76572-8382636Lelio R Paula11/2015
83333^173191-2^17319182634Mike Oakes02/2004
8334(2^274500+2970)/282633Stefano Morozzi01/2020
833520507^10698+10698^2050782629Hans Havermann07/2020
8336(2^274429+3726)/282612Stefano Morozzi01/2020
833714^72072-1582604Lelio R Paula11/2015
8338(2^274374+2950)/282595Stefano Morozzi01/2020
8339(55459*2^274339+1)/382589Lelio R Paula06/2014
83402^274351+12382588Lelio R Paula06/2012
8341(1017*2^274339-1)/351582584Lelio R Paula04/2015
834221208^7833+7833^2120882583Hans Havermann07/2020
8343(2^274248+750)/282557Stefano Morozzi01/2020
8344(2^274240+822)/282555Stefano Morozzi01/2020
83456^106086+11382551Lelio R Paula12/2015
8346(17*10^82540-377)/982541Robert Price11/2017
8347(3470^23311-1)/346982526Serge Batalov08/2020
83482^274093-5869582511Lelio R Paula07/2013
83497*10^82509-4782510Robert Price02/2017
83502^274081-655582507Lelio R Paula07/2013
83522^274074-274074+182505Robert Price10/2014
835314^71985+4782505Lelio R Paula11/2015
83515*10^82504+2182505Robert Price01/2017
8354(2^274062+498)/282501Stefano Morozzi01/2020
83556^106014-13982495Lelio R Paula12/2015
8356(2^274046+47)/75382494Lelio R Paula12/2012
83572^274008-183809982485Enzo Doria05/2015
83582^273981-11002982477Enzo Doria04/2014
835919^64490-3082467Lelio R Paula12/2015
8360(2^273864+3150)/282441Stefano Morozzi01/2020
836121328^7333+7333^2132882439Hans Havermann07/2020
836220829^9070+9070^2082982434Hans Havermann07/2020
83652^273785+1171582418Lelio R Paula07/2013
83648*10^82417+5182418Robert Price05/2017
8363(2^273786+2242)/282418Stefano Morozzi01/2020
836611^79133-1082409Theodore Burton11/2005
8367(2^273752+1882)/282408Stefano Morozzi01/2020
836891^42063+9082404Norbert Schneider01/2016
83702^273662-6382381Lelio R Paula06/2012
83692^273661+25582381Lelio R Paula07/2013
8371(62*10^82377-17)/982378Robert Price09/2015
83722^273608+52428782365Paul Underwood08/2018
83738*10^82360-5182361Robert Price10/2017
8374(79*10^82347-1)/382349Robert Price11/2017
8375(11*10^82323+91)/382323Robert Price02/2017
8376(189977#+19081)/(19081*17260483)82317Makoto Morimoto10/2017
8377(189977#+196924)/(2*7*13*541*28874441)82316Makoto Morimoto10/2017
837815^69984+3282308Lelio R Paula11/2015
83799*6^105746+782288Lelio R Paula10/2014
838089^42211-8882286Norbert Schneider01/2016
8381gcd(V(1476435),5*F(295287)*(F(295287)+1)+1)82281Serge Batalov04/2015
838220596^9883+9883^2059682279Hans Havermann06/2020
8383(19*10^82270-43)/382271Robert Price10/2017
83842^273282-11024182267Enzo Doria05/2014
8385(2^273277+3746)/282265Stefano Morozzi01/2020
8386(13^73849+4^73849)/1782263Robert Price05/2013
838810^82254+9^(82254+1)82255Robert Price08/2016
838710^82254+45777382255Patrick De Geest12/2016
838910^82254-9960982254Patrick De Geest12/2016
8390(754*10^82250-7)/982252Robert Price11/2017
839118^65524+1382251Lelio R Paula11/2015
83922^273206-10782244Lelio R Paula06/2012
83932^273193-45914582240Enzo Doria05/2015
83952^273126+3693782220Yves Minet06/2010
839439505!2+12882220Robert Price03/2015
8396(2^273090+2214)/282208Stefano Morozzi01/2020
83972^273053-11211182198Enzo Doria06/2014
8398(2^273052+3138)/282197Stefano Morozzi01/2020
83992^273016+118582187Lelio R Paula07/2013
8400(2^273008+3)/782183Lelio R Paula12/2012
8401(2^272992+2230)/282179Stefano Morozzi01/2020
84035^117554-1538682167Enzo Doria02/2013
840221158^7647+7647^2115882167Hans Havermann06/2020
840420194^11715+11715^2019482165Hans Havermann06/2020
8405(38*10^82161+403)/982162Robert Price11/2017
84062^272907-11143982154Enzo Doria05/2014
8407(67607*2^272901+1)/5079011582149Lelio R Paula06/2014
84082^272875-6982144Lelio R Paula06/2012
8409(3997^22807-1)/399682142Serge Batalov08/2020
84107^97197+482141Robert Price01/2014
8411(4*6^105554+1)/582137Serge Batalov10/2014
84122^272826-443382129Yves Minet03/2019
84136^105531-10982120Lelio R Paula12/2015
84142^272766-6582111Lelio R Paula06/2012
841519^64205-7882103Lelio R Paula12/2015
84162^272702+186997982092Enzo Doria05/2016
8417(29*2^272687-1)/982088Lelio R Paula02/2014
8418(5*10^82085-119)/382086Robert Price04/2016
8419(2^272665+1334)/282081Stefano Morozzi01/2020
84202^272660-11004982079Enzo Doria04/2014
84216^105474+6782075Lelio R Paula12/2015
84222^272637+8287582072Lelio R Paula07/2013
8423(6330^21589-1)/632982065Serge Batalov08/2020
84242^272587-3182057Lelio R Paula06/2012
8425(1969^24907-1)/196882047Serge Batalov08/2020
8426(41*10^82044-59)/982045Robert Price10/2017
84278*5^117368+982038Lelio R Paula10/2014
8428(101525^16384+1)/13107482023Lelio R Paula11/2011
84294*5^117343-782020Lelio R Paula10/2014
8430(2^272381+506)/281995Stefano Morozzi01/2020
8431(265*10^81990+17)/381992Robert Price05/2016
84323^171843+1081990Robert Price10/2013
8433(2^272361+3762)/281989Stefano Morozzi01/2020
8434(7*10^81985+107)/381986Robert Price02/2017
8435(3*2^272356+1)/17716381983Lelio R Paula12/2012
84362^272296-11114981970Enzo Doria05/2014
8437(2^272293+2810)/281969Stefano Morozzi01/2020
8438(2^272278+2118)/281964Stefano Morozzi01/2020
8439(9*2^272243-1)/781954Lelio R Paula02/2014
84402^272177-11122381934Enzo Doria05/2014
8441(2^272127+3878)/281919Stefano Morozzi01/2020
8443(151009^15817+1)/15101081912Faysal YAtim06/2017
8442(2^272104+1950)/281912Stefano Morozzi01/2020
844423160^3437+3437^2316081898Hans Havermann05/2020
8445(16*10^81896-19)/381897Robert Price03/2016
8446(16*10^81872-73)/381873Robert Price07/2020
8447(2^271922+78557)/6381855Lelio R Paula12/2012
8448(10^81848+77)/381848Robert Price01/2017
8449(24737*2^271883+1)/375781846Lelio R Paula06/2014
8450(2^271885+1670)/281846Stefano Morozzi01/2020
845118813^19144-19144^1881381831Norbert Schneider02/2020
8452(14*10^81818-89)/381819Robert Price05/2020
845319492^15731+15731^1949281804Hans Havermann07/2020
845420420^10137+10137^2042081801Hans Havermann06/2020
8455(2^271734+3942)/281800Stefano Morozzi01/2020
8456(15429^19531-1)/1542881799Serge Batalov08/2020
845710^81778+3981779Robert Price03/2011
845810^81778-17199981778Patrick De Geest07/2013
8459(2^271652+2886)/281776Stefano Morozzi01/2020
8460(14*10^81767-11)/381768Erik Branger09/2014
8461(2^271546+610)/281744Stefano Morozzi01/2020
84622^271541+186841781742Enzo Doria04/2016
8463(2^271549-1)/23874968248781734Jens K. Andersen02/2009
846419339^16836+16836^1933981732Hans Havermann06/2020
84652^271484-16781725Lelio R Paula06/2012
8467(8*10^81709-611)/981709Robert Price11/2017
8466(2^271431+1790)/281709Stefano Morozzi01/2020
846819648^14399+14399^1964881703Hans Havermann05/2020
84692^271382+1290981695Lelio R Paula07/2013
847049^48334+4881694Norbert Schneider07/2014
84717^96668+4881694Lelio R Paula10/2015
847211^78435-141081682Enzo Doria12/2012
847319575^14882+14882^1957581680Hans Havermann04/2020
84745*10^81653+981654Dmitry Domanov11/2010
8475(2^271224+1230)/281647Stefano Morozzi01/2020
8476(2^271211-1)/61396149515981631Jens K. Andersen02/2009
8477(2^271168+1806)/281630Stefano Morozzi01/2020
84783^171068+5281621Lelio R Paula12/2015
84792^271115-11040781614Enzo Doria05/2014
84802^271111-11063581613Enzo Doria05/2014
84812^271098-11181609Lelio R Paula06/2012
8482(77*10^81606+13)/981607Robert Price10/2015
84832^271064-279020981599Enzo Doria03/2016
8484(13*2^271053-1)/309581593Lelio R Paula02/2014
84852^271040-5781592Lelio R Paula06/2012
8486(14*10^81585+73)/381586Robert Price04/2016
8487127^38779+12681584Norbert Schneider02/2015
848818^64966-4381551Lelio R Paula11/2015
848919406^15909+15909^1940681538Hans Havermann06/2020
8490(17*10^81535-161)/981536Robert Price02/2021
8491(2^270843+1074)/281532Stefano Morozzi01/2020
8492(2^270840+47)/59181529Lelio R Paula12/2012
849320^62654+8781515Lelio R Paula01/2016
849420120^11241+11241^2012081503Hans Havermann05/2020
8495(19*10^81488+191)/381489Robert Price01/2017
84968*10^81487+2181488Robert Price02/2017
8497(73*10^81485+107)/981486Robert Price08/2016
8498536^29847+29847^53681458Norbert Schneider03/2017
84998*7^96378+981450Lelio R Paula10/2014
8500(2^270560+3862)/281447Stefano Morozzi01/2020


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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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