PRP Records

Probable Primes Top 10000

(183432 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 ?
30012^334294-113111100633Enzo Doria07/2014
30026^129308-17723100622Enzo Doria03/2013
30036^129305+95100619Lelio R Paula10/2016
30042^334244-1167100618Lelio R Paula09/2016
3005(21*2^334050+1)/935100558Lelio R Paula12/2013
3006(78557*2^334018+1)/4326021100548Lelio R Paula07/2014
3007(35*10^100542+1)/9100543Serge Batalov11/2010
300813^90251+24100535Lelio R Paula10/2016
30092^333963+789100533Lelio R Paula08/2011
30102^333919-1840087100520Enzo Doria06/2015
30112^333911+72623100518Enzo Doria04/2016
301218^80064-67100503Lelio R Paula10/2016
30135^143742-48100472Lelio R Paula10/2016
30142^333757-112123100471Enzo Doria06/2014
30152^333603-108861100425Enzo Doria03/2014
30169*7^118818-2100414Lelio R Paula11/2014
30172^333546-17097100408Enzo Doria05/2013
301817^81597+72100401Lelio R Paula10/2016
3019p(20559)#/2+8100384Robert Price01/2017
302011^96390-24100380Lelio R Paula10/2016
30214832563059*2^333333+30029100353Donovan Johnson01/2008
30222^333354+763100350Lelio R Paula08/2011
30232^333289-109483100330Enzo Doria04/2014
30242^333240-2790209100316Enzo Doria03/2016
3026(2^333227-2^166614+1)/510031111/2006
30252^333225+719100311Lelio R Paula08/2011
30272^333221-2785333100310Enzo Doria10/2015
302876^53332-75100308Norbert Schneider02/2015
30296^128892-17573100298Enzo Doria03/2013
30302^333105-113215100275Enzo Doria07/2014
3031(31*2^333102+1)/2375100272Lelio R Paula11/2013
303217^81476-74100253Lelio R Paula10/2016
303317^81417-16100180Theodore Burton11/2005
30342^332739-113215100165Enzo Doria07/2014
30352^332730-1865621100162Enzo Doria03/2016
303691^51127-2100160Lelio R Paula09/2013
303715^85159-32100155Lelio R Paula10/2016
30386^128661+97100118Lelio R Paula10/2016
303919^78285+40100108Lelio R Paula07/2016
30406^128640+5100102Lelio R Paula11/2014
30416^128565-127100044Lelio R Paula08/2016
30422^332309-133100035Lelio R Paula02/2011
30432^332307+731100035Lelio R Paula07/2011
30442^332301+12927100033Lelio R Paula04/2013
304512^92684-13100023Lelio R Paula07/2016
308225206!+p(4114)100001Henri Lifchitz09/2005
308325206!-p(5447)100001Henri Lifchitz10/2005
308425206!-p(12402)100001Henri Lifchitz04/2006
308525206!-p(16290)100001Henri Lifchitz09/2006
308625206!-p(19647)100001Henri Lifchitz02/2007
30872^332194+11473100001Henri Lifchitz03/2007
307410^100000+342909100001Milton L. Brown12/2007
305410^100000+346579100001Robert Price04/2012
305510^100000+829767100001Robert Price05/2012
305610^100000+871899100001Robert Price05/2012
305710^100000+1475997100001Robert Price07/2012
307510^100000+1751769100001Robert Price08/2012
307610^100000+2155489100001Robert Price10/2012
307710^100000+2483527100001Robert Price12/2012
307810^100000+2503087100001Robert Price12/2012
307910^100000+2686179100001Robert Price12/2012
308010^100000+2688933100001Robert Price12/2012
308110^100000+3667159100001Robert Price08/2013
305810^100000+3938473100001Robert Price05/2015
305910^100000+3979761100001Robert Price05/2015
306010^100000+4293973100001Robert Price09/2015
308810^100000+4858267100001Robert Price12/2015
308910^100000+5113299100001Robert Price02/2016
309010^100000+5169411100001Robert Price02/2016
304610^100000+5354043100001Robert Price05/2016
304710^100000+5717979100001Robert Price05/2016
304810^100000+6080631100001Robert Price07/2016
304910^100000+6308469100001Robert Price07/2016
305010^100000+6512023100001Robert Price08/2016
305110^100000+6596557100001Robert Price08/2016
305210^100000+7115409100001Robert Price10/2016
305310^100000+7235803100001Robert Price10/2016
306110^100000+7867333100001Robert Price12/2016
306210^100000+8743093100001Robert Price02/2017
306310^100000+8955391100001Robert Price03/2017
306410^100000+9180019100001Robert Price03/2017
306510^100000+9225987100001Robert Price04/2017
306610^100000+9265587100001Robert Price04/2017
306710^100000+9287049100001Robert Price04/2017
306810^100000+9425053100001Robert Price05/2017
306910^100000+9450769100001Robert Price05/2017
307010^100000+9528747100001Robert Smith05/2017
307110^100000+9548071100001Robert Price06/2017
307210^100000+10064287100001Robert Price08/2017
307310^100000+10229569100001Robert Price10/2017
309210^99999+309403100000Daniel Heuer01/2004
309110^100000-260199100000Patrick De Geest01/2010
309310^99999-5951199999Patrick De Geest07/2009
30942^332141-11307399985Enzo Doria07/2014
3095(3^209561+2)/72810125599978Lelio R Paula09/2013
30962^332085+186589799968Enzo Doria03/2016
3097(9787*2^332070-1)/93640236999959Lelio R Paula05/2015
30982^332023+19199949Lelio R Paula02/2011
30992^331938+7114999924Enzo Doria04/2016
31002^331932-7879599922Lelio R Paula09/2016
31012^331921+77199919Lelio R Paula01/2013
3102(3^209419-2)/513275599912Lelio R Paula09/2013
31032^331860-11498999900Enzo Doria05/2015
31042^331746-1165599866Lelio R Paula09/2016
310511^95891-2899861Lelio R Paula08/2016
3106(2^331694-5)/1199849Lelio R Paula10/2013
3107(3^209246+7)/6499834Lelio R Paula09/2013
310815^84866-5299811Lelio R Paula08/2016
310913^89600+3099810Lelio R Paula08/2016
31105^142772-3899794Lelio R Paula08/2016
3111(23*2^331459+1)/47599778Lelio R Paula11/2013
31122^331416-331416+199767Robert Price10/2014
31132^331256-5799718Lelio R Paula12/2012
31142^331185+73799697Lelio R Paula01/2013
3115(4*10^99693+149)/999693Robert Price03/2017
31162^331154+188052799688Enzo Doria10/2016
3117(19^77951+1)/2099679Paul Bourdelais03/2010
31182^331110+187045999675Enzo Doria05/2016
31195*2^331075+799665Lelio R Paula08/2014
3120(16*10^99656-31)/399657Robert Price03/2016
31212^330968+34599632Lelio R Paula09/2016
31232*5^142528-799624Lelio R Paula11/2014
31222^330942+7732999624Enzo Doria05/2016
312414^86914-9999615Lelio R Paula08/2016
3125(19*2^330902+1)/7799611Lelio R Paula11/2013
31262^330845+7168799595Enzo Doria04/2016
3127(23*2^330770+1)/399573Lelio R Paula11/2013
31282^330735+841599562Lelio R Paula09/2016
31292^330720+7407199557Enzo Doria04/2016
313031^66738-299531Lelio R Paula09/2013
31317*3^208567+499513Lelio R Paula08/2014
3132(13*10^99508+47)/399509Robert Price01/2017
31332^330553+77999507Lelio R Paula01/2013
313415^84606-9499505Lelio R Paula08/2016
31356^127858+4799493Lelio R Paula08/2016
31365^142337+4899490Lelio R Paula08/2016
31377^117724-2099489Lelio R Paula08/2016
3138(29*10^99474-17)/399475Erik Branger09/2014
3139(9*2^330407-1)/799463Lelio R Paula03/2014
3140(68*10^99441+7)/399443Robert Price03/2016
314146^59791-45^5979199418Jean-Louis Charton01/2013
3142(2*10^99408+529)/999408Robert Price01/2017
314353^57646-299398Lelio R Paula09/2013
31442^330165+187002599390Enzo Doria05/2016
31452^330142-15599383Lelio R Paula12/2012
31462^330088-11525999367Enzo Doria06/2015
3147(746*10^99303+1)/999305Robert Price02/2017
31483^208107+4099293Lelio R Paula08/2016
3149(5*2^329833-1)/36999288Lelio R Paula02/2014
31508*3^208093+599287Lelio R Paula08/2014
31515^142043+5699284Lelio R Paula08/2016
315222*10^99275+799277Robert Price04/2016
31532^329778+187618999274Enzo Doria07/2016
3154(10^99239-13)/399239Robert Price02/2017
31553^207987+6299236Lelio R Paula08/2016
31562^329638+4999231Lelio R Paula12/2012
31577^117413-1899226Lelio R Paula08/2016
31582^329586-45890399216Enzo Doria04/2015
31592^329553+10199206Lelio R Paula12/2012
31602^329551-11289799205Enzo Doria06/2014
3161(3^207925+7)/5099204Lelio R Paula09/2013
31626^127458-1799399182Enzo Doria03/2013
316327197^4428+4428^2719799166Hans Havermann10/2017
3164(46*10^99143-1)/999144Robert Price12/2014
316518^78968-306599127Enzo Doria03/2013
316625927^6654+6654^2592799122Hans Havermann10/2017
31672^329259+18999117Lelio R Paula12/2012
31688*10^99113+3999114Robert Price01/2017
31696^127364+7799109Lelio R Paula08/2016
31706^127285+1399047Lelio R Paula08/2016
31712^329007+7328399041Enzo Doria04/2016
31725*3^207543-899024Lelio R Paula08/2014
31732^328885+14999005Lelio R Paula12/2012
317423392^17075+17075^2339299004Hans Havermann09/2017
3175(2^328879-9)/11999001Lelio R Paula10/2013
31765^141618+5498987Lelio R Paula08/2016
31778*10^98982+5198983Robert Price05/2017
3178(21*2^328809-1)/770998979Lelio R Paula03/2014
31792^328794-279760198977Enzo Doria04/2016
31806^127176+598963Lelio R Paula11/2014
318124262^11989+11989^2426298960Hans Havermann09/2017
31822^328700-10970998949Enzo Doria04/2014
318346711!2-2^4671198916Robert Price09/2015
31849*7^117037+498909Lelio R Paula11/2014
3185(10^98890+149)/398890Serge Batalov12/2014
318622775^21978+21978^2277598889Hans Havermann08/2017
31872^328497-21693398888Enzo Doria05/2014
31882^328487+3276998885Lelio R Paula08/2016
31893^207250-11235898884Enzo Doria06/2014
319013^88754-9098867Lelio R Paula08/2016
31912^328406+70998861Lelio R Paula02/2013
3192(17*2^328413-1)/1617398860Lelio R Paula03/2014
31937^116976+7698857Lelio R Paula08/2016
31942^328335+115598839Lelio R Paula08/2016
3196(3*2^328311+1)/598832Lelio R Paula11/2013
3195287^40210+40210^28798832Norbert Schneider11/2014
3197(2^328284+9)/132598821Lelio R Paula10/2013
3198(21*2^328258+1)/212598814Lelio R Paula11/2013
319965^54491+4898788Lelio R Paula04/2016
32003^207042+9898785Lelio R Paula08/2016
32013^206977-11275698754Enzo Doria07/2014
32027^116846-5098747Lelio R Paula08/2016
32032^327967-2863598728Lelio R Paula08/2016
32046^126850-4798709Lelio R Paula08/2016
32058*6^126830-798694Lelio R Paula11/2014
320611^94770-27098693Enzo Doria08/2012
32072^327832+4398688Lelio R Paula12/2012
32082^327795+76198677Lelio R Paula02/2013
320910^98669+14741198670Patrick De Geest11/2016
321110^98669-9^(98669-1)98669Robert Price05/2016
321010^98669-10524998669Patrick De Geest11/2016
32122^327671-10980198639Enzo Doria04/2014
32135^141090-1498618Lelio R Paula08/2016
321420^75799+4798617Lelio R Paula08/2016
32152^327515-101798592Lelio R Paula08/2016
32166^126692+9768198586Mike Oakes04/2011
32172^327467-74198578Lelio R Paula08/2016
3218(2^327329+9)/1998535Lelio R Paula10/2013
32197^116577-6698519Lelio R Paula08/2016
3220(3*2^327250+1)/798512Lelio R Paula11/2013
3221(19*2^327192+1)/27598494Lelio R Paula11/2013
32222^327162-6694598486Lelio R Paula08/2016
32234*10^98472-398473Erik Branger11/2013
3224(6883*2^327047-1)/7798453Lelio R Paula05/2015
3225(71*10^98446+1)/998447Serge Batalov11/2010
322613^88363+9498432Lelio R Paula08/2016
322748^58543-47^5854398425Jean-Louis Charton11/2005
32286^126481+4198422Lelio R Paula08/2016
322978*10^98413-798415Robert Price05/2017
32307^116416+4698383Lelio R Paula08/2016
32317^116407-2498376Lelio R Paula07/2016
32332^326782-186067198372Enzo Doria03/2016
323217^79948+5898372Lelio R Paula08/2016
32343^206143-9898356Lelio R Paula08/2016
32358*5^140705+798350Lelio R Paula11/2014
32362^326585+1198312Lelio R Paula12/2012
32372^326582-45916198311Enzo Doria05/2015
3238(2^326548+9)/598301Lelio R Paula10/2013
32392^326538+7165998298Enzo Doria04/2016
324015^83575-5898292Lelio R Paula08/2016
324110^98288+398289Robert Price03/2011
324210^98288-11701798288Patrick De Geest11/2011
32432^326421-279757398263Enzo Doria04/2016
32442^326401+1609598257Lelio R Paula07/2016
32457^116240-116240^798235Norbert Schneider05/2017
324617^79826-7898222Lelio R Paula08/2016
32472^326268-80998217Yves Minet04/2011
3248(418*10^98199+23)/998201Robert Price08/2017
324915^83496-7698199Lelio R Paula08/2016
3250(10223*2^326179+1)/612598190Lelio R Paula07/2014


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Created by  Henri Lifchitz & Renaud Lifchitz : October, 26 2000, last modification: October, 17 2017 09:44 (Time in France)

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