PRP Records

Probable Primes Top 10000

(180278 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) !!!


Submit your PRPs


See the Top discoverers
See the Latest PRPs
Search by form



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 ?
302625206!+p(4114)100001Henri Lifchitz09/2005
302725206!-p(5447)100001Henri Lifchitz10/2005
302825206!-p(12402)100001Henri Lifchitz04/2006
302925206!-p(16290)100001Henri Lifchitz09/2006
303025206!-p(19647)100001Henri Lifchitz02/2007
30312^332194+11473100001Henri Lifchitz03/2007
302510^100000+342909100001Milton L. Brown12/2007
302110^100000+346579100001Robert Price04/2012
302210^100000+829767100001Robert Price05/2012
302310^100000+871899100001Robert Price05/2012
302410^100000+1475997100001Robert Price07/2012
300810^100000+1751769100001Robert Price08/2012
300910^100000+2155489100001Robert Price10/2012
301010^100000+2483527100001Robert Price12/2012
301110^100000+2503087100001Robert Price12/2012
301210^100000+2686179100001Robert Price12/2012
301310^100000+2688933100001Robert Price12/2012
301410^100000+3667159100001Robert Price08/2013
301510^100000+3938473100001Robert Price05/2015
301610^100000+3979761100001Robert Price05/2015
301710^100000+4293973100001Robert Price09/2015
301810^100000+4858267100001Robert Price12/2015
301910^100000+5113299100001Robert Price02/2016
302010^100000+5169411100001Robert Price02/2016
300110^100000+5717979100001Robert Price05/2016
300210^100000+6080631100001Robert Price07/2016
300310^100000+6308469100001Robert Price07/2016
300410^100000+6512023100001Robert Price08/2016
300510^100000+6596557100001Robert Price08/2016
300610^100000+7115409100001Robert Price10/2016
300710^100000+7235803100001Robert Price10/2016
303210^100000+7867333100001Robert Price12/2016
303310^100000+8743093100001Robert Price02/2017
303410^100000+8955391100001Robert Price03/2017
303510^100000+9180019100001Robert Price03/2017
303610^100000+9225987100001Robert Price04/2017
303710^100000+9265587100001Robert Price04/2017
303810^100000+9287049100001Robert Price04/2017
303910^100000+9425053100001Robert Price05/2017
304010^100000+9450769100001Robert Price05/2017
304110^100000+9528747100001Robert Smith05/2017
304210^100000+9548071100001Robert Price06/2017
304410^99999+309403100000Daniel Heuer01/2004
304310^100000-260199100000Patrick De Geest01/2010
304510^99999-5951199999Patrick De Geest07/2009
30462^332141-11307399985Enzo Doria07/2014
3047(3^209561+2)/72810125599978Lelio R Paula09/2013
30482^332085+186589799968Enzo Doria03/2016
3049(9787*2^332070-1)/93640236999959Lelio R Paula05/2015
30502^332023+19199949Lelio R Paula02/2011
30512^331938+7114999924Enzo Doria04/2016
30522^331932-7879599922Lelio R Paula09/2016
30532^331921+77199919Lelio R Paula01/2013
3054(3^209419-2)/513275599912Lelio R Paula09/2013
30552^331860-11498999900Enzo Doria05/2015
30562^331746-1165599866Lelio R Paula09/2016
305711^95891-2899861Lelio R Paula08/2016
3058(2^331694-5)/1199849Lelio R Paula10/2013
3059(3^209246+7)/6499834Lelio R Paula09/2013
306015^84866-5299811Lelio R Paula08/2016
306113^89600+3099810Lelio R Paula08/2016
30625^142772-3899794Lelio R Paula08/2016
3063(23*2^331459+1)/47599778Lelio R Paula11/2013
30642^331416-331416+199767Robert Price10/2014
30652^331256-5799718Lelio R Paula12/2012
30662^331185+73799697Lelio R Paula01/2013
3067(4*10^99693+149)/999693Robert Price03/2017
30682^331154+188052799688Enzo Doria10/2016
3069(19^77951+1)/2099679Paul Bourdelais03/2010
30702^331110+187045999675Enzo Doria05/2016
30715*2^331075+799665Lelio R Paula08/2014
3072(16*10^99656-31)/399657Robert Price03/2016
30732^330968+34599632Lelio R Paula09/2016
30752*5^142528-799624Lelio R Paula11/2014
30742^330942+7732999624Enzo Doria05/2016
307614^86914-9999615Lelio R Paula08/2016
3077(19*2^330902+1)/7799611Lelio R Paula11/2013
30782^330845+7168799595Enzo Doria04/2016
3079(23*2^330770+1)/399573Lelio R Paula11/2013
30802^330735+841599562Lelio R Paula09/2016
30812^330720+7407199557Enzo Doria04/2016
308231^66738-299531Lelio R Paula09/2013
30837*3^208567+499513Lelio R Paula08/2014
3084(13*10^99508+47)/399509Robert Price01/2017
30852^330553+77999507Lelio R Paula01/2013
308615^84606-9499505Lelio R Paula08/2016
30876^127858+4799493Lelio R Paula08/2016
30885^142337+4899490Lelio R Paula08/2016
30897^117724-2099489Lelio R Paula08/2016
3090(29*10^99474-17)/399475Erik Branger09/2014
3091(9*2^330407-1)/799463Lelio R Paula03/2014
3092(68*10^99441+7)/399443Robert Price03/2016
309346^59791-45^5979199418Jean-Louis Charton01/2013
3094(2*10^99408+529)/999408Robert Price01/2017
309553^57646-299398Lelio R Paula09/2013
30962^330165+187002599390Enzo Doria05/2016
30972^330142-15599383Lelio R Paula12/2012
30982^330088-11525999367Enzo Doria06/2015
3099(746*10^99303+1)/999305Robert Price02/2017
31003^208107+4099293Lelio R Paula08/2016
3101(5*2^329833-1)/36999288Lelio R Paula02/2014
31028*3^208093+599287Lelio R Paula08/2014
31035^142043+5699284Lelio R Paula08/2016
310422*10^99275+799277Robert Price04/2016
31052^329778+187618999274Enzo Doria07/2016
3106(10^99239-13)/399239Robert Price02/2017
31073^207987+6299236Lelio R Paula08/2016
31082^329638+4999231Lelio R Paula12/2012
31097^117413-1899226Lelio R Paula08/2016
31102^329586-45890399216Enzo Doria04/2015
31112^329553+10199206Lelio R Paula12/2012
31122^329551-11289799205Enzo Doria06/2014
3113(3^207925+7)/5099204Lelio R Paula09/2013
31146^127458-1799399182Enzo Doria03/2013
3115(46*10^99143-1)/999144Robert Price12/2014
311618^78968-306599127Enzo Doria03/2013
31172^329259+18999117Lelio R Paula12/2012
31188*10^99113+3999114Robert Price01/2017
31196^127364+7799109Lelio R Paula08/2016
31206^127285+1399047Lelio R Paula08/2016
31212^329007+7328399041Enzo Doria04/2016
31225*3^207543-899024Lelio R Paula08/2014
31232^328885+14999005Lelio R Paula12/2012
3124(2^328879-9)/11999001Lelio R Paula10/2013
31255^141618+5498987Lelio R Paula08/2016
31268*10^98982+5198983Robert Price05/2017
3127(21*2^328809-1)/770998979Lelio R Paula03/2014
31282^328794-279760198977Enzo Doria04/2016
31296^127176+598963Lelio R Paula11/2014
31302^328700-10970998949Enzo Doria04/2014
313146711!2-2^4671198916Robert Price09/2015
31329*7^117037+498909Lelio R Paula11/2014
3133(10^98890+149)/398890Serge Batalov12/2014
313422775^21978+21978^2277598889Hans Havermann08/2017
31352^328497-21693398888Enzo Doria05/2014
31362^328487+3276998885Lelio R Paula08/2016
31373^207250-11235898884Enzo Doria06/2014
313813^88754-9098867Lelio R Paula08/2016
31392^328406+70998861Lelio R Paula02/2013
3140(17*2^328413-1)/1617398860Lelio R Paula03/2014
31417^116976+7698857Lelio R Paula08/2016
31422^328335+115598839Lelio R Paula08/2016
3144(3*2^328311+1)/598832Lelio R Paula11/2013
3143287^40210+40210^28798832Norbert Schneider11/2014
3145(2^328284+9)/132598821Lelio R Paula10/2013
3146(21*2^328258+1)/212598814Lelio R Paula11/2013
314765^54491+4898788Lelio R Paula04/2016
31483^207042+9898785Lelio R Paula08/2016
31493^206977-11275698754Enzo Doria07/2014
31507^116846-5098747Lelio R Paula08/2016
31512^327967-2863598728Lelio R Paula08/2016
31526^126850-4798709Lelio R Paula08/2016
31538*6^126830-798694Lelio R Paula11/2014
315411^94770-27098693Enzo Doria08/2012
31552^327832+4398688Lelio R Paula12/2012
31562^327795+76198677Lelio R Paula02/2013
315710^98669+14741198670Patrick De Geest11/2016
315910^98669-9^(98669-1)98669Robert Price05/2016
315810^98669-10524998669Patrick De Geest11/2016
31602^327671-10980198639Enzo Doria04/2014
31615^141090-1498618Lelio R Paula08/2016
316220^75799+4798617Lelio R Paula08/2016
31632^327515-101798592Lelio R Paula08/2016
31646^126692+9768198586Mike Oakes04/2011
31652^327467-74198578Lelio R Paula08/2016
3166(2^327329+9)/1998535Lelio R Paula10/2013
31677^116577-6698519Lelio R Paula08/2016
3168(3*2^327250+1)/798512Lelio R Paula11/2013
3169(19*2^327192+1)/27598494Lelio R Paula11/2013
31702^327162-6694598486Lelio R Paula08/2016
31714*10^98472-398473Erik Branger11/2013
3172(6883*2^327047-1)/7798453Lelio R Paula05/2015
3173(71*10^98446+1)/998447Serge Batalov11/2010
317413^88363+9498432Lelio R Paula08/2016
317548^58543-47^5854398425Jean-Louis Charton11/2005
31766^126481+4198422Lelio R Paula08/2016
317778*10^98413-798415Robert Price05/2017
31787^116416+4698383Lelio R Paula08/2016
31797^116407-2498376Lelio R Paula07/2016
31812^326782-186067198372Enzo Doria03/2016
318017^79948+5898372Lelio R Paula08/2016
31823^206143-9898356Lelio R Paula08/2016
31838*5^140705+798350Lelio R Paula11/2014
31842^326585+1198312Lelio R Paula12/2012
31852^326582-45916198311Enzo Doria05/2015
3186(2^326548+9)/598301Lelio R Paula10/2013
31872^326538+7165998298Enzo Doria04/2016
318815^83575-5898292Lelio R Paula08/2016
318910^98288+398289Robert Price03/2011
319010^98288-11701798288Patrick De Geest11/2011
31912^326421-279757398263Enzo Doria04/2016
31922^326401+1609598257Lelio R Paula07/2016
31937^116240-116240^798235Norbert Schneider05/2017
319417^79826-7898222Lelio R Paula08/2016
31952^326268-80998217Yves Minet04/2011
319615^83496-7698199Lelio R Paula08/2016
3197(10223*2^326179+1)/612598190Lelio R Paula07/2014
31989*5^140471-498186Lelio R Paula11/2014
31992^326069-238398157Yves Minet10/2013
32002^325973+118598128Lelio R Paula07/2016
3201(25*2^325949-1)/1798121Lelio R Paula02/2014
32022^325945-184726998120Enzo Doria07/2015
32032^325866+1598096Lelio R Paula12/2012
32042^325765+197430598066Enzo Doria06/2016
32052^325733-5869598056Lelio R Paula07/2016
32062^325717-364598051Lelio R Paula07/2016
3207(23*2^325583-1)/2198011Lelio R Paula02/2014
3208(7*10^98007-13)/398008Robert Price06/2016
32092^325512-45995997989Enzo Doria05/2015
3210(3^205354-8)/1797978Lelio R Paula09/2013
32112^325433+7681797966Enzo Doria05/2016
32122^325390-10906197953Enzo Doria04/2014
321313^87921+2497940Lelio R Paula08/2016
3214961^32831-960^3283197926Jean-Louis Charton02/2011
32152^325215+1290997900Lelio R Paula07/2016
32167*10^97874-6997875Robert Price01/2017
3218(17^79537+5^79537)/2297865Robert Price06/2013
321715^83212+2297865Lelio R Paula08/2016
32192^325087-10905797861Enzo Doria04/2014
32202^325074+187065797858Enzo Doria05/2016
32222^325066-211197855Yves Minet08/2013
3221CopelandErdos(97855)97855Eric W. Weisstein10/2015
322318^77944-8997841Lelio R Paula07/2016
32246^125720-1766397830Enzo Doria02/2013
32252^324972-206997827Yves Minet05/2013
32262^324944-278831997818Enzo Doria03/2016
32284*10^97799-997800Erik Branger11/2013
32272^324882+57729457597800Lelio R Paula09/2016
32292^324863-186792197794Enzo Doria04/2016
32306^125662-1847397785Enzo Doria03/2013
323112^90604+1197779Lelio R Paula07/2016
32325^139830+2497737Lelio R Paula04/2016
32332^324612+115597718Lelio R Paula07/2016
323419^76404-4497702Lelio R Paula07/2016
32352^324505-298397686Yves Minet04/2011
3236(31*2^324496-1)/4597683Lelio R Paula02/2014
32376^125488-1784397649Enzo Doria02/2013
32387^115515-297622Lelio R Paula09/2013
32396^125418-597595Lelio R Paula11/2014
32402^324076+115597557Lelio R Paula07/2016
3241(2^324074+9)/1397555Lelio R Paula10/2013
3242(55459*2^323993+1)/2197536Lelio R Paula07/2014
324313^87557-12^8755797534Jean-Louis Charton12/2008
32442^323946+7393997518Enzo Doria04/2016
32452^323937+186694797515Enzo Doria03/2016
32466^125290-1853397495Enzo Doria03/2013
32472^323845+10197488Lelio R Paula12/2012
324818^77662+6597487Lelio R Paula07/2016
32492^323772+7677197466Enzo Doria05/2016
32502^323765-11221397463Enzo Doria06/2014


Find by discoverer :


Created by  Henri Lifchitz & Renaud Lifchitz : October, 26 2000, last modification: August, 20 2017 08:36 (Time in France)

Go back
Valid XHTML 1.0!    Valid CSS!