PRP Records

Probable Primes Top 10000

(205869 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 (> 30000) Who ? When ?
5001(11*10^82323+91)/382323Robert Price02/2017
5002(189977#+19081)/(19081*17260483)82317Makoto Morimoto10/2017
5003(189977#+196924)/(2*7*13*541*28874441)82316Makoto Morimoto10/2017
500415^69984+3282308Lelio R Paula11/2015
50059*6^105746+782288Lelio R Paula10/2014
500689^42211-8882286Norbert Schneider01/2016
5007gcd(V(1476435),5*F(295287)*(F(295287)+1)+1)82281Serge Batalov04/2015
5008(19*10^82270-43)/382271Robert Price10/2017
50092^273282-11024182267Enzo Doria05/2014
5010(13^73849+4^73849)/1782263Robert Price05/2013
501210^82254+9^(82254+1)82255Robert Price08/2016
501110^82254+45777382255Patrick De Geest12/2016
501310^82254-9960982254Patrick De Geest12/2016
5014(754*10^82250-7)/982252Robert Price11/2017
501518^65524+1382251Lelio R Paula11/2015
50162^273206-10782244Lelio R Paula06/2012
50172^273193-45914582240Enzo Doria05/2015
50192^273126+3693782220Yves Minet06/2010
501839505!2+12882220Robert Price03/2015
50202^273053-11211182198Enzo Doria06/2014
50212^273016+118582187Lelio R Paula07/2013
5022(2^273008+3)/782183Lelio R Paula12/2012
50235^117554-1538682167Enzo Doria02/2013
5024(38*10^82161+403)/982162Robert Price11/2017
50252^272907-11143982154Enzo Doria05/2014
5026(67607*2^272901+1)/5079011582149Lelio R Paula06/2014
50272^272875-6982144Lelio R Paula06/2012
50287^97197+482141Robert Price01/2014
5029(4*6^105554+1)/582137Serge Batalov10/2014
50306^105531-10982120Lelio R Paula12/2015
50312^272766-6582111Lelio R Paula06/2012
503219^64205-7882103Lelio R Paula12/2015
50332^272702+186997982092Enzo Doria05/2016
5034(29*2^272687-1)/982088Lelio R Paula02/2014
5035(5*10^82085-119)/382086Robert Price04/2016
50362^272660-11004982079Enzo Doria04/2014
50376^105474+6782075Lelio R Paula12/2015
50382^272637+8287582072Lelio R Paula07/2013
50392^272587-3182057Lelio R Paula06/2012
5040(41*10^82044-59)/982045Robert Price10/2017
50418*5^117368+982038Lelio R Paula10/2014
5042(101525^16384+1)/13107482023Lelio R Paula11/2011
50434*5^117343-782020Lelio R Paula10/2014
5044(265*10^81990+17)/381992Robert Price05/2016
50453^171843+1081990Robert Price10/2013
5046(7*10^81985+107)/381986Robert Price02/2017
5047(3*2^272356+1)/17716381983Lelio R Paula12/2012
50482^272296-11114981970Enzo Doria05/2014
5049(9*2^272243-1)/781954Lelio R Paula02/2014
50502^272177-11122381934Enzo Doria05/2014
5051(151009^15817+1)/15101081912Faysal YAtim06/2017
5052(16*10^81896-19)/381897Robert Price03/2016
5053(2^271922+78557)/6381855Lelio R Paula12/2012
5054(10^81848+77)/381848Robert Price01/2017
5055(24737*2^271883+1)/375781846Lelio R Paula06/2014
505610^81778+3981779Robert Price03/2011
505710^81778-17199981778Patrick De Geest07/2013
5058(14*10^81767-11)/381768Erik Branger09/2014
50592^271541+186841781742Enzo Doria04/2016
5060(2^271549-1)/23874968248781734Jens K. Andersen02/2009
50612^271484-16781725Lelio R Paula06/2012
5062(8*10^81709-611)/981709Robert Price11/2017
50632^271382+1290981695Lelio R Paula07/2013
506449^48334+4881694Norbert Schneider07/2014
50657^96668+4881694Lelio R Paula10/2015
506611^78435-141081682Enzo Doria12/2012
50675*10^81653+981654Dmitry Domanov11/2010
5068(2^271211-1)/61396149515981631Jens K. Andersen02/2009
50693^171068+5281621Lelio R Paula12/2015
50702^271115-11040781614Enzo Doria05/2014
50712^271111-11063581613Enzo Doria05/2014
50722^271098-11181609Lelio R Paula06/2012
5073(77*10^81606+13)/981607Robert Price10/2015
50742^271064-279020981599Enzo Doria03/2016
5075(13*2^271053-1)/309581593Lelio R Paula02/2014
50762^271040-5781592Lelio R Paula06/2012
5077(14*10^81585+73)/381586Robert Price04/2016
5078127^38779+12681584Norbert Schneider02/2015
507918^64966-4381551Lelio R Paula11/2015
5080(2^270840+47)/59181529Lelio R Paula12/2012
508120^62654+8781515Lelio R Paula01/2016
5082(19*10^81488+191)/381489Robert Price01/2017
50838*10^81487+2181488Robert Price02/2017
5084(73*10^81485+107)/981486Robert Price08/2016
5085536^29847+29847^53681458Norbert Schneider03/2017
50868*7^96378+981450Lelio R Paula10/2014
50872^270546-11034581443Enzo Doria05/2014
508813^73105-6081435Lelio R Paula11/2015
508944^49524+4381391Norbert Schneider06/2014
5090(3*2^270368-1)/1381389Lelio R Paula02/2014
5091(10^81363+719)/981363Serge Batalov12/2014
5092(10^81353+449)/981353Serge Batalov12/2014
509314^70978-8981350Lelio R Paula11/2015
509411^78108-204081342Enzo Doria12/2012
50953^170400-5881302Lelio R Paula12/2015
5096(17*10^81300-131)/381301Robert Price12/2017
509710^81297+3699181298Patrick De Geest06/2013
509810^81297-5781297Robert Price05/2011
50992^270055-11304781295Enzo Doria07/2014
510018^64759-5581291Lelio R Paula11/2015
5101(2^269987+1)/381274H.&R. Lifchitz10/2000
5102(31^54493-1)/3081268Alexander Zhirkov10/2010
5103(2^270059-1)/540119/6481417/712497615775672596781265Dario Alpern09/2014
5104(2^269816+7)/42490181218Lelio R Paula12/2012
5105(23*10^81214+1)/381215Serge Batalov06/2009
5106(17*2^269720+1)/30381193Lelio R Paula07/2012
510756^46441-55^4644181188Robert Price10/2013
51082^269664+17781177Lelio R Paula06/2012
5109(13*2^269665-1)/18581177Lelio R Paula02/2014
51102^269539-11224981140Enzo Doria06/2014
5111((2*170026-3)*3^(170026-1)+1)/481128Robert Price01/2015
5112(2^269495-5)/981126Lelio R Paula12/2012
51132^269490-362381125Yves Minet10/2009
5114(55459*2^269444+1)/3581114Lelio R Paula06/2014
5115(2^269417+78557)/525781099Lelio R Paula12/2012
51164*5^116011-781089Lelio R Paula10/2014
51177*10^81058+7981059Robert Price02/2017
51182^269236-10990781049Enzo Doria04/2014
5119(8*10^81029-11)/381030Erik Branger03/2014
51203*10^81021+781022Erik Branger11/2013
51216^104115+10381018Lelio R Paula12/2015
51222^269120+186915181014Enzo Doria05/2016
51235^115901+1281012Lelio R Paula10/2015
5124(2^269083-9)/32036980997Lelio R Paula12/2012
512517^65810-2080976Lelio R Paula11/2015
512620^62236-2380971Lelio R Paula01/2016
51272^268974-11218180970Enzo Doria06/2014
5129L(387433)80969Renaud Lifchitz11/2003
5128V(387433)80969Serge Batalov03/2015
5130(2^268955-509203)/580963Lelio R Paula12/2012
5131(87398^16384+1)/6553780957Lelio R Paula11/2011
5132329^32160+32160^32980954Norbert Schneider11/2014
51332^268859-15980935Lelio R Paula05/2012
5134(2^268841-lucasV(1,2,268841)+1)/280929Mike Oakes11/2016
51352^268827+577580925Lelio R Paula07/2013
51362^268824-11025580925Enzo Doria05/2014
51372^268798-186832180917Enzo Doria04/2016
51382^268753-11462180903Enzo Doria05/2015
51392^268743+160580900Lelio R Paula07/2013
51406^103954-13980892Lelio R Paula12/2015
514110^80883+4980884Robert Price03/2011
514210^80883-8032780883Patrick De Geest07/2013
51436^103937+12180879Lelio R Paula12/2015
5144(26*10^80875-119)/380876Robert Price07/2016
5145(22699*2^268657+1)/635180875Lelio R Paula06/2014
51462^268581-86968810580851Lelio R Paula05/2016
5147(11*2^268521-1)/380834Lelio R Paula02/2014
51482^268516-24980832Yves Minet02/2012
51492^268500+1609580827Lelio R Paula07/2013
51503^169402+10080826Lelio R Paula12/2015
51519^84698+8^(84698-1)80823Robert Price03/2016
51522^268472-10973980819Enzo Doria04/2014
5153(9*2^268454+1)/3780813Lelio R Paula12/2012
5154(3*2^268502+1)/37790218843535364780811Lelio R Paula12/2012
5155134^37987-133^3798780803Jean-Louis Charton12/2005
515615^68702-7680800Lelio R Paula11/2015
51572^268408+780799Lelio R Paula05/2012
51582^268375+14180789Lelio R Paula05/2012
515912^74856-4780784Lelio R Paula11/2015
51606^103770-10780749Lelio R Paula12/2015
51613^169224-6280741Lelio R Paula12/2015
5162p(16866)#/2+6480741Robert Price03/2017
51635^115502-7280733Lelio R Paula10/2015
51642^268079-192780700Yves Minet10/2009
51652^268028+11780685Lelio R Paula05/2012
5166121^38738+12080683Norbert Schneider01/2015
5167(3^169097-8)/83580677Lelio R Paula12/2012
51682^267918+6780652Lelio R Paula05/2012
5169(89*10^80650-179)/980651Robert Price11/2017
5170(302*10^80638+13)/980640Robert Price01/2017
51713^169004+266080636Lelio R Paula12/2015
51722^267860-11285980634Enzo Doria06/2014
51732^267828-11070580625Enzo Doria05/2014
51742^267743+1270580599Lelio R Paula07/2013
5175(22*10^80595+23)/980596Robert Price03/2015
51762^267674-5180578Lelio R Paula05/2012
5177(86*10^80571-41)/980572Robert Price11/2015
51782^267612-196580560Lelio R Paula07/2013
51792^267553+409780542Lelio R Paula07/2013
51807^95276-880518Robert Price01/2014
5181(15185*2^267457-1)/4782980513Lelio R Paula04/2015
51826^103467+16380513Lelio R Paula12/2015
5183(7*10^80490+143)/380491Robert Price04/2016
518486^41597-85^4159780470Robert Price04/2015
518513^72237+3080468Lelio R Paula11/2015
518617^65389+1480458Lelio R Paula11/2015
5187423^30634+30634^42380456Norbert Schneider05/2017
51882^267232+10580445Lelio R Paula05/2012
518911^77237-307200080435Enzo Doria01/2013
51902^267116-45995980410Enzo Doria06/2015
519138715!2+880406Robert Price01/2015
5192(2^267017+1)/380380H.&R. Lifchitz09/2000
51932^266968-4580366Lelio R Paula05/2012
519420^61768-6380363Lelio R Paula01/2016
51952^266920-11296780351Enzo Doria06/2014
51968*10^80342+8780343Robert Price10/2017
519712^74428-1380322Lelio R Paula11/2015
51982^266680+2780279Lelio R Paula05/2012
51992^266630-13180264Lelio R Paula05/2012
52002^266598+7681980254Enzo Doria05/2016
52012^266587+188063380251Enzo Doria10/2016
52022^266541-11004980237Enzo Doria04/2014
520338635!2-880222Robert Price06/2015
52043^168111+168111^3-180210Robert Price04/2014
52052^266443+51380208Lelio R Paula07/2013
5206(26*10^80200+61)/380201Robert Price06/2017
52072^266412-10991380199Enzo Doria04/2014
5208(10223*2^266417+1)/4509180199Lelio R Paula06/2014
520913^71988+6680191Lelio R Paula11/2015
521011^77002-432080190Enzo Doria01/2013
521118^63879-1380186Lelio R Paula11/2015
52122^266368-11229580185Enzo Doria06/2014
5213(3^168050+5)/102145480175Lelio R Paula10/2012
5214(22*10^80167+41)/980168Robert Price02/2015
5215(34*10^80162-43)/980163Ray Chandler12/2010
5217(38*10^80150-11)/980151Robert Price05/2015
5216(598*10^80149-31)/980151Robert Price02/2017
521819^62678-8080150Lelio R Paula12/2015
521910^80139+3234380140Patrick De Geest02/2011
522010^80139-980139Alexander Gramolin01/2011
52213^167955-10680135Lelio R Paula12/2015
5222(197*10^80089-11)/380091Robert Price10/2017
52232^265998+7555980074Enzo Doria04/2016
52242^265969-10980180065Enzo Doria04/2014
52252^265888-11275780041Enzo Doria06/2014
52262^265809+170180017Lelio R Paula07/2013
5227gcd(V(957175),5*F(191435)*(F(191435)+1)+1)80014Serge Batalov04/2015
52283^167687-10480008Lelio R Paula02/2015
522911^76826-579080007Enzo Doria01/2013
523010^80000+8573180001Patrick De Geest10/2009
523110^80000-716980000Patrick De Geest09/2009
523210^79999+2239980000Patrick De Geest09/2009
523310^79999-7487379999Patrick De Geest09/2009
52343^167668+5879998Lelio R Paula02/2015
5235155^36506-279961Lelio R Paula10/2017
52362^265612+425779958Lelio R Paula07/2013
52375*3^167577+479956Lelio R Paula06/2014
5238(9179*2^265593-1)/979955Lelio R Paula04/2015
52396^102723-4379935Lelio R Paula04/2015
524011^76748-336079925Enzo Doria12/2012
5241(13*2^265498-1)/18711979919Lelio R Paula02/2014
52422^265399-10985579894Enzo Doria04/2014
5243(20^61403-1)/1979886Paul Bourdelais03/2010
524418^63635+5979880Lelio R Paula02/2015
5245(11*10^79867-107)/379868Robert Price11/2016
52463^167375+8079859Lelio R Paula02/2015
52475^114240-1448679851Enzo Doria02/2013
524849^47238+4879842Norbert Schneider07/2014
52492^265212-377979837Yves Minet04/2017
525091^40746+40746^9179824Norbert Schneider12/2014


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Created by  Henri Lifchitz & Renaud Lifchitz : October, 26 2000, last modification: April, 22 2018 09:48 (Time in France)

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