PRP Records

Probable Primes Top 10000

(224660 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 ?
3501(9787*2^332070-1)/93640236999959Lelio R Paula05/2015
35022^332023+19199949Lelio R Paula02/2011
35032^331938+7114999924Enzo Doria04/2016
35042^331932-7879599922Lelio R Paula09/2016
35052^331921+77199919Lelio R Paula01/2013
3506(3^209419-2)/513275599912Lelio R Paula09/2013
35072^331860-11498999900Enzo Doria05/2015
35082^331746-1165599866Lelio R Paula09/2016
350911^95891-2899861Lelio R Paula08/2016
3510(2^331694-5)/1199849Lelio R Paula10/2013
3511(3^209246+7)/6499834Lelio R Paula09/2013
351225062^9617+9617^2506299823Hans Havermann04/2018
351315^84866-5299811Lelio R Paula08/2016
351413^89600+3099810Lelio R Paula08/2016
351522950^22309+22309^2295099798Hans Havermann03/2018
35165^142772-3899794Lelio R Paula08/2016
3517(23*2^331459+1)/47599778Lelio R Paula11/2013
35182^331416-331416+199767Robert Price10/2014
35192^331256-5799718Lelio R Paula12/2012
352028192^3443+3443^2819299714Hans Havermann03/2018
35212^331185+73799697Lelio R Paula01/2013
3522(4*10^99693+149)/999693Robert Price03/2017
35232^331154+188052799688Enzo Doria10/2016
3524(19^77951+1)/2099679Paul Bourdelais03/2010
352524354^12385+12385^2435499679Hans Havermann03/2018
35262^331110+187045999675Enzo Doria05/2016
35275*2^331075+799665Lelio R Paula08/2014
352825776^7351+7351^2577699659Hans Havermann02/2018
3529(16*10^99656-31)/399657Robert Price03/2016
35302^330968+34599632Lelio R Paula09/2016
35322*5^142528-799624Lelio R Paula11/2014
35312^330942+7732999624Enzo Doria05/2016
353314^86914-9999615Lelio R Paula08/2016
3534(19*2^330902+1)/7799611Lelio R Paula11/2013
353522971^21692+21692^2297199610Hans Havermann03/2018
35362^330845+7168799595Enzo Doria04/2016
3537(23*2^330770+1)/399573Lelio R Paula11/2013
353824494^11613+11613^2449499567Hans Havermann03/2018
35392^330735+841599562Lelio R Paula09/2016
35402^330720+7407199557Enzo Doria04/2016
354131^66738-299531Lelio R Paula09/2013
35427*3^208567+499513Lelio R Paula08/2014
3543(13*10^99508+47)/399509Robert Price01/2017
35442^330553+77999507Lelio R Paula01/2013
354515^84606-9499505Lelio R Paula08/2016
35466^127858+4799493Lelio R Paula08/2016
35475^142337+4899490Lelio R Paula08/2016
35487^117724-2099489Lelio R Paula08/2016
3549(29*10^99474-17)/399475Erik Branger09/2014
3550(9*2^330407-1)/799463Lelio R Paula03/2014
3551(68*10^99441+7)/399443Robert Price03/2016
355246^59791-45^5979199418Jean-Louis Charton01/2013
355323839^14802+14802^2383999417Hans Havermann02/2018
3554(2*10^99408+529)/999408Robert Price01/2017
355553^57646-299398Lelio R Paula09/2013
35562^330165+187002599390Enzo Doria05/2016
35572^330142-15599383Lelio R Paula12/2012
35582^330088-11525999367Enzo Doria06/2015
355924216^12671+12671^2421699354Hans Havermann01/2018
3560(746*10^99303+1)/999305Robert Price02/2017
35613^208107+4099293Lelio R Paula08/2016
3562(5*2^329833-1)/36999288Lelio R Paula02/2014
35638*3^208093+599287Lelio R Paula08/2014
35645^142043+5699284Lelio R Paula08/2016
356522*10^99275+799277Robert Price04/2016
35662^329778+187618999274Enzo Doria07/2016
3567(10^99239-13)/399239Robert Price02/2017
35683^207987+6299236Lelio R Paula08/2016
35692^329638+4999231Lelio R Paula12/2012
35707^117413-1899226Lelio R Paula08/2016
35712^329586-45890399216Enzo Doria04/2015
35722^329553+10199206Lelio R Paula12/2012
35732^329551-11289799205Enzo Doria06/2014
3574(3^207925+7)/5099204Lelio R Paula09/2013
35756^127458-1799399182Enzo Doria03/2013
357627197^4428+4428^2719799166Hans Havermann10/2017
3577(46*10^99143-1)/999144Robert Price12/2014
35787*10^99133+6999134Robert Price10/2017
357918^78968-306599127Enzo Doria03/2013
358025927^6654+6654^2592799122Hans Havermann10/2017
35812^329259+18999117Lelio R Paula12/2012
35828*10^99113+3999114Robert Price01/2017
35836^127364+7799109Lelio R Paula08/2016
35846^127285+1399047Lelio R Paula08/2016
3585(228581#+235862)/(2^3*11*71*151)99044Makoto Morimoto10/2017
35862^329007+7328399041Enzo Doria04/2016
35875*3^207543-899024Lelio R Paula08/2014
35882^328885+14999005Lelio R Paula12/2012
358923392^17075+17075^2339299004Hans Havermann09/2017
3590(2^328879-9)/11999001Lelio R Paula10/2013
35915^141618+5498987Lelio R Paula08/2016
35928*10^98982+5198983Robert Price05/2017
3593(21*2^328809-1)/770998979Lelio R Paula03/2014
35942^328794-279760198977Enzo Doria04/2016
35956^127176+598963Lelio R Paula11/2014
359624262^11989+11989^2426298960Hans Havermann09/2017
35972^328700-10970998949Enzo Doria04/2014
359846711!2-2^4671198916Robert Price09/2015
35999*7^117037+498909Lelio R Paula11/2014
3600(10^98890+149)/398890Serge Batalov12/2014
360122775^21978+21978^2277598889Hans Havermann08/2017
36022^328497-21693398888Enzo Doria05/2014
36032^328487+3276998885Lelio R Paula08/2016
36043^207250-11235898884Enzo Doria06/2014
360513^88754-9098867Lelio R Paula08/2016
36062^328406+70998861Lelio R Paula02/2013
3607(17*2^328413-1)/1617398860Lelio R Paula03/2014
36087^116976+7698857Lelio R Paula08/2016
36092^328335+115598839Lelio R Paula08/2016
3611(3*2^328311+1)/598832Lelio R Paula11/2013
3610287^40210+40210^28798832Norbert Schneider11/2014
3612(2^328284+9)/132598821Lelio R Paula10/2013
3613(21*2^328258+1)/212598814Lelio R Paula11/2013
361465^54491+4898788Lelio R Paula04/2016
36153^207042+9898785Lelio R Paula08/2016
36163^206977-11275698754Enzo Doria07/2014
36177^116846-5098747Lelio R Paula08/2016
36182^327967-2863598728Lelio R Paula08/2016
3619707^34642+34642^70798710Norbert Schneider12/2017
36206^126850-4798709Lelio R Paula08/2016
36218*6^126830-798694Lelio R Paula11/2014
362211^94770-27098693Enzo Doria08/2012
36232^327832+4398688Lelio R Paula12/2012
36242^327795+76198677Lelio R Paula02/2013
362510^98669+14741198670Patrick De Geest11/2016
362710^98669-9^(98669-1)98669Robert Price05/2016
362610^98669-10524998669Patrick De Geest11/2016
36282^327671-10980198639Enzo Doria04/2014
36295^141090-1498618Lelio R Paula08/2016
363020^75799+4798617Lelio R Paula08/2016
36312^327515-101798592Lelio R Paula08/2016
36326^126692+9768198586Mike Oakes04/2011
36332^327467-74198578Lelio R Paula08/2016
3634(2^327329+9)/1998535Lelio R Paula10/2013
36357^116577-6698519Lelio R Paula08/2016
3636(3*2^327250+1)/798512Lelio R Paula11/2013
3637(19*2^327192+1)/27598494Lelio R Paula11/2013
36382^327162-6694598486Lelio R Paula08/2016
36394*10^98472-398473Erik Branger11/2013
3640(6883*2^327047-1)/7798453Lelio R Paula05/2015
3641(71*10^98446+1)/998447Serge Batalov11/2010
364213^88363+9498432Lelio R Paula08/2016
364348^58543-47^5854398425Jean-Louis Charton11/2005
36446^126481+4198422Lelio R Paula08/2016
364578*10^98413-798415Robert Price05/2017
36467^116416+4698383Lelio R Paula08/2016
36477^116407-2498376Lelio R Paula07/2016
3648439^37228+37228^43998374Norbert Schneider08/2018
36492^326782-186067198372Enzo Doria03/2016
365017^79948+5898372Lelio R Paula08/2016
36513^206143-9898356Lelio R Paula08/2016
36528*5^140705+798350Lelio R Paula11/2014
36532^326585+1198312Lelio R Paula12/2012
36542^326582-45916198311Enzo Doria05/2015
3655(2^326548+9)/598301Lelio R Paula10/2013
36562^326538+7165998298Enzo Doria04/2016
365715^83575-5898292Lelio R Paula08/2016
365810^98288+398289Robert Price03/2011
365910^98288-11701798288Patrick De Geest11/2011
3660(44*10^98284-719)/998285Robert Price12/2017
36612^326421-279757398263Enzo Doria04/2016
36622^326401+1609598257Lelio R Paula07/2016
36637^116240-116240^798235Norbert Schneider05/2017
366417^79826-7898222Lelio R Paula08/2016
36652^326268-80998217Yves Minet04/2011
3666(418*10^98199+23)/998201Robert Price08/2017
366712*10^98198-798200Robert Price11/2017
366815^83496-7698199Lelio R Paula08/2016
3669(10223*2^326179+1)/612598190Lelio R Paula07/2014
36709*5^140471-498186Lelio R Paula11/2014
36712^326069-238398157Yves Minet10/2013
36722^325973+118598128Lelio R Paula07/2016
3673(25*2^325949-1)/1798121Lelio R Paula02/2014
36742^325945-184726998120Enzo Doria07/2015
36758*10^98111-6798112Robert Price10/2017
36762^325866+1598096Lelio R Paula12/2012
36772^325765+197430598066Enzo Doria06/2016
36782^325733-5869598056Lelio R Paula07/2016
36792^325717-364598051Lelio R Paula07/2016
3680(23*2^325583-1)/2198011Lelio R Paula02/2014
3681(7*10^98007-13)/398008Robert Price06/2016
36822^325512-45995997989Enzo Doria05/2015
3683(3^205354-8)/1797978Lelio R Paula09/2013
36842^325433+7681797966Enzo Doria05/2016
36855*10^97963+8197964Robert Price08/2017
36862^325390-10906197953Enzo Doria04/2014
368713^87921+2497940Lelio R Paula08/2016
3688961^32831-960^3283197926Jean-Louis Charton02/2011
36892^325215+1290997900Lelio R Paula07/2016
36907*10^97874-6997875Robert Price01/2017
3692(17^79537+5^79537)/2297865Robert Price06/2013
369115^83212+2297865Lelio R Paula08/2016
36932^325087-10905797861Enzo Doria04/2014
36942^325074+187065797858Enzo Doria05/2016
36952^325066-211197855Yves Minet08/2013
3696CopelandErdos(97855)97855Eric W. Weisstein10/2015
369718^77944-8997841Lelio R Paula07/2016
3698119^47136+11897833Norbert Schneider09/2018
36996^125720-1766397830Enzo Doria02/2013
37002^324972-206997827Yves Minet05/2013
37012^324944-278831997818Enzo Doria03/2016
37034*10^97799-997800Erik Branger11/2013
37022^324882+57729457597800Lelio R Paula09/2016
37042^324863-186792197794Enzo Doria04/2016
37056^125662-1847397785Enzo Doria03/2013
370612^90604+1197779Lelio R Paula07/2016
37075^139830+2497737Lelio R Paula04/2016
37082^324612+115597718Lelio R Paula07/2016
370919^76404-4497702Lelio R Paula07/2016
37102^324505-298397686Yves Minet04/2011
3711(31*2^324496-1)/4597683Lelio R Paula02/2014
37126^125488-1784397649Enzo Doria02/2013
37137^115515-297622Lelio R Paula09/2013
3714(89^50069-1)/8897603Paul Bourdelais08/2017
37156^125418-597595Lelio R Paula11/2014
37162^324076+115597557Lelio R Paula07/2016
3717(2^324074+9)/1397555Lelio R Paula10/2013
3718(55459*2^323993+1)/2197536Lelio R Paula07/2014
371913^87557-12^8755797534Jean-Louis Charton12/2008
37202^323946+7393997518Enzo Doria04/2016
37212^323937+186694797515Enzo Doria03/2016
37226^125290-1853397495Enzo Doria03/2013
37232^323845+10197488Lelio R Paula12/2012
372418^77662+6597487Lelio R Paula07/2016
37252^323772+7677197466Enzo Doria05/2016
37262^323765-11221397463Enzo Doria06/2014
37272^323720-655597450Lelio R Paula07/2016
37282^323694-186040197442Enzo Doria03/2016
372920^74886+397429Lelio R Paula06/2016
37313*10^97399+7397400Robert Price04/2016
37307^115252-5097400Lelio R Paula07/2016
3732224737#+39358197389Nicolas PALAU12/2016
3733(26*10^97353+31)/397354Robert Price07/2016
373461^54517-60^5451797331Jean-Louis Charton09/2005
3735(38*10^97329+187)/997330Robert Price11/2017
3736p(19982)#/2-102497293Robert Price09/2017
37376^125021-8597286Lelio R Paula08/2016
37382^323164-4735597283Lelio R Paula07/2016
3739(3^203902+4)/3605101515797276Lelio R Paula09/2013
37402^323054-655597249Lelio R Paula07/2016
37419*10^97247-2997248Robert Price05/2017
3742(31*10^97242+41)/997243Robert Price04/2015
3743GoldenRatioPrime[97241]97241Eric W. Weisstein06/2009
374412^90098-4197233Lelio R Paula07/2016
37452^322928-21692997212Enzo Doria05/2014
3746(7*2^322896-1)/5797201Lelio R Paula02/2014
3747(2^322897+5)/314610748997193Lelio R Paula10/2013
37482^322725+7576197150Enzo Doria04/2016
3749(13*2^322686+1)/11997138Lelio R Paula11/2013
3750(41*10^97085+373)/997086Robert Price04/2017


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Created by  Henri Lifchitz & Renaud Lifchitz : October, 26 2000, last modification: October, 15 2018 21:33 (Time in France)

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