PRP Records

Probable Primes Top 10000

(277034 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 ?
77511036^27529+27529^103683010Norbert Schneider03/2020
775211^79701-315083001Enzo Doria12/2012
7753(2^275721+1554)/283000Stefano Morozzi01/2020
7754(2^275704+1858)/282995Stefano Morozzi01/2020
7755(2^275696+1726)/282993Stefano Morozzi01/2020
7756(55459*2^275657+1)/2182985Lelio R Paula06/2014
7757(7*10^82960-457)/982960Robert Price09/2017
77582^275535-685582945Lelio R Paula08/2013
77593^173828-1482938Robert Price08/2013
77602^275512-10967782938Enzo Doria04/2014
7761(2^275450+1698)/282919Stefano Morozzi01/2020
77622^275446-11004582918Enzo Doria04/2014
7763(2^275473+47)/2952609744782916Lelio R Paula12/2012
77643^173755-1482903Robert Price08/2013
7765(182*10^82898+43)/982900Robert Price11/2017
77662^275363-11230982893Enzo Doria06/2014
776761^46427-6082888Norbert Schneider10/2014
77683*10^82880-7^8288082881Mike Oakes02/2010
77692^275290+9019582871Lelio R Paula07/2013
7770(35*10^82870-71)/982871Robert Price05/2015
77712^275270-185962182865Enzo Doria03/2016
77722^275259+8182862Henri Lifchitz01/2007
777321436^7335+7335^2143682859Hans Havermann05/2020
7774(2^275247+1590)/282858Stefano Morozzi01/2020
777522515^4784+4784^2251582851Hans Havermann05/2020
77766*10^82842-3182843Robert Price07/2020
7777(10013^20707-1)/1001282836Serge Batalov08/2020
7778(113703^16384+1)/282834Richard Fischer04/2018
7779(2^275146+954)/282827Stefano Morozzi01/2020
77807^98003+98003^7+182823Robert Price05/2014
7781(2^275101+3566)/282814Stefano Morozzi01/2020
7782(2^275050+3150)/282798Stefano Morozzi01/2020
7783(2^275044+2482)/282797Stefano Morozzi01/2020
778410^82790+12604382791Patrick De Geest07/2013
778510^82790-4782790Robert Price05/2011
778620762^9711+9711^2076282784Hans Havermann05/2020
77872^274985-11266382779Enzo Doria06/2014
77882^274935+1501582764Lelio R Paula07/2013
7789(17*2^274922+1)/382761Lelio R Paula12/2012
7790[(55^5)^9511-(22434^2)^9511]/1982759Richard Fischer11/2019
7791(43*10^82752-61)/982753Robert Price06/2015
7792(3*2^274862+1)/102782740Lelio R Paula12/2012
7793(2^274851+3126)/282739Stefano Morozzi01/2020
7794(31*2^274848-1)/406582736Lelio R Paula02/2014
7795(4^137405+23)/382726Robert Price02/2017
7796(2^274798+414)/282723Stefano Morozzi01/2020
77972^274791-11049182721Enzo Doria05/2014
7798(11*2^274776-1)/9582715Lelio R Paula02/2014
7799(47*10^82706-119)/982707Robert Price09/2017
78002^274704-11139582695Enzo Doria05/2014
78012^274686-391182689Yves Minet04/2017
7802(1629^25741-1)/162882675Serge Batalov08/2020
780321474^7075+7075^2147482670Hans Havermann06/2020
7804(2^274663-1017)/4887131829227982669Lelio R Paula12/2012
7805(3^173263-5)/1449882664Lelio R Paula12/2012
780620488^10815+10815^2048882650Hans Havermann07/2020
7807(2^274554+894)/282649Stefano Morozzi01/2020
78092^274511-6487582637Lelio R Paula08/2013
7808(2^274512+1222)/282637Stefano Morozzi01/2020
781012^76572-8382636Lelio R Paula11/2015
78113^173191-2^17319182634Mike Oakes02/2004
7812(2^274500+2970)/282633Stefano Morozzi01/2020
781320507^10698+10698^2050782629Hans Havermann07/2020
7814(2^274429+3726)/282612Stefano Morozzi01/2020
781514^72072-1582604Lelio R Paula11/2015
7816(2^274374+2950)/282595Stefano Morozzi01/2020
7817(55459*2^274339+1)/382589Lelio R Paula06/2014
78182^274351+12382588Lelio R Paula06/2012
7819(1017*2^274339-1)/351582584Lelio R Paula04/2015
782021208^7833+7833^2120882583Hans Havermann07/2020
7821(2^274248+750)/282557Stefano Morozzi01/2020
7822(2^274240+822)/282555Stefano Morozzi01/2020
78236^106086+11382551Lelio R Paula12/2015
7824(17*10^82540-377)/982541Robert Price11/2017
7825(3470^23311-1)/346982526Serge Batalov08/2020
78262^274093-5869582511Lelio R Paula07/2013
78277*10^82509-4782510Robert Price02/2017
78282^274081-655582507Lelio R Paula07/2013
78302^274074-274074+182505Robert Price10/2014
783114^71985+4782505Lelio R Paula11/2015
78295*10^82504+2182505Robert Price01/2017
7832(2^274062+498)/282501Stefano Morozzi01/2020
78336^106014-13982495Lelio R Paula12/2015
7834(2^274046+47)/75382494Lelio R Paula12/2012
78352^274008-183809982485Enzo Doria05/2015
78362^273981-11002982477Enzo Doria04/2014
783719^64490-3082467Lelio R Paula12/2015
7838(2^273864+3150)/282441Stefano Morozzi01/2020
783921328^7333+7333^2132882439Hans Havermann07/2020
784020829^9070+9070^2082982434Hans Havermann07/2020
78432^273785+1171582418Lelio R Paula07/2013
78428*10^82417+5182418Robert Price05/2017
7841(2^273786+2242)/282418Stefano Morozzi01/2020
784411^79133-1082409Theodore Burton11/2005
7845(2^273752+1882)/282408Stefano Morozzi01/2020
784691^42063+9082404Norbert Schneider01/2016
78482^273662-6382381Lelio R Paula06/2012
78472^273661+25582381Lelio R Paula07/2013
7849(62*10^82377-17)/982378Robert Price09/2015
78502^273608+52428782365Paul Underwood08/2018
78518*10^82360-5182361Robert Price10/2017
7852(79*10^82347-1)/382349Robert Price11/2017
7853(11*10^82323+91)/382323Robert Price02/2017
7854(189977#+19081)/(19081*17260483)82317Makoto Morimoto10/2017
7855(189977#+196924)/(2*7*13*541*28874441)82316Makoto Morimoto10/2017
785615^69984+3282308Lelio R Paula11/2015
78579*6^105746+782288Lelio R Paula10/2014
785889^42211-8882286Norbert Schneider01/2016
7859gcd(V(1476435),5*F(295287)*(F(295287)+1)+1)82281Serge Batalov04/2015
786020596^9883+9883^2059682279Hans Havermann06/2020
7861(19*10^82270-43)/382271Robert Price10/2017
78622^273282-11024182267Enzo Doria05/2014
7863(2^273277+3746)/282265Stefano Morozzi01/2020
7864(13^73849+4^73849)/1782263Robert Price05/2013
786510^82254+9^(82254+1)82255Robert Price08/2016
786610^82254+45777382255Patrick De Geest12/2016
786710^82254-9960982254Patrick De Geest12/2016
7868(754*10^82250-7)/982252Robert Price11/2017
786918^65524+1382251Lelio R Paula11/2015
78702^273206-10782244Lelio R Paula06/2012
78712^273193-45914582240Enzo Doria05/2015
78732^273126+3693782220Yves Minet06/2010
787239505!2+12882220Robert Price03/2015
7874(2^273090+2214)/282208Stefano Morozzi01/2020
78752^273053-11211182198Enzo Doria06/2014
7876(2^273052+3138)/282197Stefano Morozzi01/2020
78772^273016+118582187Lelio R Paula07/2013
7878(2^273008+3)/782183Lelio R Paula12/2012
7879(2^272992+2230)/282179Stefano Morozzi01/2020
78815^117554-1538682167Enzo Doria02/2013
788021158^7647+7647^2115882167Hans Havermann06/2020
788220194^11715+11715^2019482165Hans Havermann06/2020
7883(38*10^82161+403)/982162Robert Price11/2017
78842^272907-11143982154Enzo Doria05/2014
7885(67607*2^272901+1)/5079011582149Lelio R Paula06/2014
78862^272875-6982144Lelio R Paula06/2012
7887(3997^22807-1)/399682142Serge Batalov08/2020
78887^97197+482141Robert Price01/2014
7889(4*6^105554+1)/582137Serge Batalov10/2014
78902^272826-443382129Yves Minet03/2019
78916^105531-10982120Lelio R Paula12/2015
78922^272766-6582111Lelio R Paula06/2012
789319^64205-7882103Lelio R Paula12/2015
78942^272702+186997982092Enzo Doria05/2016
7895(29*2^272687-1)/982088Lelio R Paula02/2014
7896(5*10^82085-119)/382086Robert Price04/2016
7897(2^272665+1334)/282081Stefano Morozzi01/2020
78982^272660-11004982079Enzo Doria04/2014
78996^105474+6782075Lelio R Paula12/2015
79002^272637+8287582072Lelio R Paula07/2013
7901(6330^21589-1)/632982065Serge Batalov08/2020
79022^272587-3182057Lelio R Paula06/2012
7903(1969^24907-1)/196882047Serge Batalov08/2020
7904(41*10^82044-59)/982045Robert Price10/2017
79058*5^117368+982038Lelio R Paula10/2014
7906(101525^16384+1)/13107482023Lelio R Paula11/2011
79074*5^117343-782020Lelio R Paula10/2014
7908(2^272381+506)/281995Stefano Morozzi01/2020
7909(265*10^81990+17)/381992Robert Price05/2016
79103^171843+1081990Robert Price10/2013
7911(2^272361+3762)/281989Stefano Morozzi01/2020
7912(7*10^81985+107)/381986Robert Price02/2017
7913(3*2^272356+1)/17716381983Lelio R Paula12/2012
79142^272296-11114981970Enzo Doria05/2014
7915(2^272293+2810)/281969Stefano Morozzi01/2020
7916(2^272278+2118)/281964Stefano Morozzi01/2020
7917(9*2^272243-1)/781954Lelio R Paula02/2014
79182^272177-11122381934Enzo Doria05/2014
7919(2^272127+3878)/281919Stefano Morozzi01/2020
7921(151009^15817+1)/15101081912Faysal YAtim06/2017
7920(2^272104+1950)/281912Stefano Morozzi01/2020
792223160^3437+3437^2316081898Hans Havermann05/2020
7923(16*10^81896-19)/381897Robert Price03/2016
7924(16*10^81872-73)/381873Robert Price07/2020
7925(2^271922+78557)/6381855Lelio R Paula12/2012
7926(10^81848+77)/381848Robert Price01/2017
7927(24737*2^271883+1)/375781846Lelio R Paula06/2014
7928(2^271885+1670)/281846Stefano Morozzi01/2020
792918813^19144-19144^1881381831Norbert Schneider02/2020
7930(14*10^81818-89)/381819Robert Price05/2020
793119492^15731+15731^1949281804Hans Havermann07/2020
793220420^10137+10137^2042081801Hans Havermann06/2020
7933(2^271734+3942)/281800Stefano Morozzi01/2020
7934(15429^19531-1)/1542881799Serge Batalov08/2020
793510^81778+3981779Robert Price03/2011
793610^81778-17199981778Patrick De Geest07/2013
7937(2^271652+2886)/281776Stefano Morozzi01/2020
7938(14*10^81767-11)/381768Erik Branger09/2014
7939(2^271546+610)/281744Stefano Morozzi01/2020
79402^271541+186841781742Enzo Doria04/2016
7941(2^271549-1)/23874968248781734Jens K. Andersen02/2009
794219339^16836+16836^1933981732Hans Havermann06/2020
79432^271484-16781725Lelio R Paula06/2012
7945(8*10^81709-611)/981709Robert Price11/2017
7944(2^271431+1790)/281709Stefano Morozzi01/2020
794619648^14399+14399^1964881703Hans Havermann05/2020
79472^271382+1290981695Lelio R Paula07/2013
794849^48334+4881694Norbert Schneider07/2014
79497^96668+4881694Lelio R Paula10/2015
795011^78435-141081682Enzo Doria12/2012
795119575^14882+14882^1957581680Hans Havermann04/2020
79525*10^81653+981654Dmitry Domanov11/2010
7953(2^271224+1230)/281647Stefano Morozzi01/2020
7954(2^271211-1)/61396149515981631Jens K. Andersen02/2009
7955(2^271168+1806)/281630Stefano Morozzi01/2020
79563^171068+5281621Lelio R Paula12/2015
79572^271115-11040781614Enzo Doria05/2014
79582^271111-11063581613Enzo Doria05/2014
79592^271098-11181609Lelio R Paula06/2012
7960(77*10^81606+13)/981607Robert Price10/2015
79612^271064-279020981599Enzo Doria03/2016
7962(13*2^271053-1)/309581593Lelio R Paula02/2014
79632^271040-5781592Lelio R Paula06/2012
7964(14*10^81585+73)/381586Robert Price04/2016
7965127^38779+12681584Norbert Schneider02/2015
796618^64966-4381551Lelio R Paula11/2015
796719406^15909+15909^1940681538Hans Havermann06/2020
7968(2^270843+1074)/281532Stefano Morozzi01/2020
7969(2^270840+47)/59181529Lelio R Paula12/2012
797020^62654+8781515Lelio R Paula01/2016
797120120^11241+11241^2012081503Hans Havermann05/2020
7972(19*10^81488+191)/381489Robert Price01/2017
79738*10^81487+2181488Robert Price02/2017
7974(73*10^81485+107)/981486Robert Price08/2016
7975536^29847+29847^53681458Norbert Schneider03/2017
79768*7^96378+981450Lelio R Paula10/2014
7977(2^270560+3862)/281447Stefano Morozzi01/2020
7978(5728^21673-1)/572781444Serge Batalov08/2020
79792^270546-11034581443Enzo Doria05/2014
798013^73105-6081435Lelio R Paula11/2015
7981(2^270502+1518)/281429Stefano Morozzi01/2020
7982(2^270479+2114)/281422Stefano Morozzi01/2020
7983(2^270384+1218)/281394Stefano Morozzi01/2020
798444^49524+4381391Norbert Schneider06/2014
7985(3*2^270368-1)/1381389Lelio R Paula02/2014
798619548^14563+14563^1954881384Hans Havermann05/2020
7987(2^270337+1130)/281380Stefano Morozzi01/2020
798827405^932+932^2740581377Hans Havermann05/2020
798919396^15683+15683^1939681375Hans Havermann05/2020
7991(10^81363+719)/981363Serge Batalov12/2014
7990(734^28393-1)/73381363Serge Batalov08/2020
7992(10^81353+449)/981353Serge Batalov12/2014
799314^70978-8981350Lelio R Paula11/2015
799411^78108-204081342Enzo Doria12/2012
79957*10^81327-5781328Robert Price06/2020
7996(7*10^81328-79)/981328Robert Price01/2021
799719102^18065+18065^1910281315Hans Havermann07/2020
79983^170400-5881302Lelio R Paula12/2015
7999(17*10^81300-131)/381301Robert Price12/2017
800010^81297+3699181298Patrick De Geest06/2013


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Created by  Henri Lifchitz & Renaud Lifchitz : October, 26 2000, last modification: January, 18 2021 19:57 (Time in France)

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