PRP Records

Probable Primes Top 10000

(193407 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 ?
3001(31*2^336189-1)/19101204Lelio R Paula03/2014
3002(78557*2^336178+1)/1268757101199Lelio R Paula07/2014
30032^336150-20393101192Enzo Doria06/2013
30042^336112-1865249101180Enzo Doria03/2016
30052^336103-109015101178Enzo Doria04/2014
300613^90809-96101157Lelio R Paula10/2016
300719^79098-30101147Lelio R Paula10/2016
300819^79095+88101144Lelio R Paula10/2016
300915^85976+32101116Lelio R Paula10/2016
3010(3^211950+7)/28854513015920697088101107Lelio R Paula11/2013
3011(4^167933+17)/3101106Robert Price02/2017
30122^335858+153101104Lelio R Paula10/2009
30136^129918-35101096Lelio R Paula10/2016
30143^211885-70101095Lelio R Paula09/2016
3015(29*2^335835-1)/550599101093Lelio R Paula03/2014
30162^335818-20033101092Enzo Doria06/2013
30172^335813-110083101090Enzo Doria04/2014
30182^335804+2155101088Lelio R Paula09/2016
30192^335784-16145101082Enzo Doria04/2013
302011^97051+62101069Lelio R Paula10/2016
3021(2^335691-3)/26515101049Lelio R Paula12/2013
30222^335658-94395101044Lelio R Paula09/2016
30232^335586+169101022Lelio R Paula10/2009
3024(56^57787-1)/55101021Paul Bourdelais08/2017
302547599!2+1024100991Robert Price02/2015
30262^335468-18629100986Enzo Doria05/2013
30272^335454-20961100982Enzo Doria06/2013
302810^100978+61100979Lelio R Paula09/2016
302910^100978-156437100978Patrick De Geest11/2016
3030(15*2^335417+1)/481100970Lelio R Paula12/2013
30312^335403-1859167100967Enzo Doria03/2016
30329*2^335364-5100956Lelio R Paula08/2014
30332^335349+72287100951Enzo Doria04/2016
30342^335329+16095100945Lelio R Paula09/2016
3035232823#+233663100937Makoto Morimoto10/2017
30362^335237-20893100917Enzo Doria06/2013
30372^335222-19337100912Enzo Doria05/2013
30382^335222-109985100912Enzo Doria04/2014
30392^335182-17237100900Enzo Doria05/2013
30402^335043-16737100858Enzo Doria05/2013
3041(21181*2^335049+1)/1343811100858Lelio R Paula07/2014
30422^335038-20633100857Enzo Doria06/2013
30432^335031+1873373100855Enzo Doria06/2016
30443^211354-8816100842Enzo Doria05/2014
30452^334984-112757100841Enzo Doria06/2014
30462^334857+48527100803Lelio R Paula08/2011
304712^93406+29100803Lelio R Paula10/2016
3048(5*2^334825+1)/47100792Lelio R Paula12/2013
30492^334809-13100788Lelio R Paula04/2011
3050(82*10^100780-1)/9100781Robert Price12/2014
3051(2^334779+47)/5100778Lelio R Paula12/2013
30522^334751+2049100771Lelio R Paula09/2016
305313^90443-98100749Lelio R Paula10/2016
3054(24737*2^334628+1)/3100737Lelio R Paula07/2014
305515^85639-28100720Lelio R Paula10/2016
30562^334562+577294575100711Lelio R Paula09/2016
30574*3^211077-5100710Lelio R Paula08/2014
30582^334524+145100702Lelio R Paula07/2009
3059(1017*2^334391-1)/3535100662Lelio R Paula05/2015
30602^334294-113111100633Enzo Doria07/2014
30616^129308-17723100622Enzo Doria03/2013
30626^129305+95100619Lelio R Paula10/2016
30632^334244-1167100618Lelio R Paula09/2016
3064(21*2^334050+1)/935100558Lelio R Paula12/2013
3065(78557*2^334018+1)/4326021100548Lelio R Paula07/2014
3066(35*10^100542+1)/9100543Serge Batalov11/2010
306713^90251+24100535Lelio R Paula10/2016
30682^333963+789100533Lelio R Paula08/2011
30692^333919-1840087100520Enzo Doria06/2015
30702^333911+72623100518Enzo Doria04/2016
307118^80064-67100503Lelio R Paula10/2016
30725^143742-48100472Lelio R Paula10/2016
30732^333757-112123100471Enzo Doria06/2014
30742^333603-108861100425Enzo Doria03/2014
30759*7^118818-2100414Lelio R Paula11/2014
30762^333546-17097100408Enzo Doria05/2013
307717^81597+72100401Lelio R Paula10/2016
3078p(20559)#/2+8100384Robert Price01/2017
307911^96390-24100380Lelio R Paula10/2016
30804832563059*2^333333+30029100353Donovan Johnson01/2008
30812^333354+763100350Lelio R Paula08/2011
30822^333289-109483100330Enzo Doria04/2014
30832^333240-2790209100316Enzo Doria03/2016
3085(2^333227-2^166614+1)/510031111/2006
30842^333225+719100311Lelio R Paula08/2011
30862^333221-2785333100310Enzo Doria10/2015
308776^53332-75100308Norbert Schneider02/2015
30886^128892-17573100298Enzo Doria03/2013
30892^333105-113215100275Enzo Doria07/2014
3090(31*2^333102+1)/2375100272Lelio R Paula11/2013
309117^81476-74100253Lelio R Paula10/2016
309217^81417-16100180Theodore Burton11/2005
30932^332739-113215100165Enzo Doria07/2014
30942^332730-1865621100162Enzo Doria03/2016
309591^51127-2100160Lelio R Paula09/2013
309615^85159-32100155Lelio R Paula10/2016
30976^128661+97100118Lelio R Paula10/2016
309819^78285+40100108Lelio R Paula07/2016
30996^128640+5100102Lelio R Paula11/2014
31006^128565-127100044Lelio R Paula08/2016
31012^332309-133100035Lelio R Paula02/2011
31022^332307+731100035Lelio R Paula07/2011
31032^332301+12927100033Lelio R Paula04/2013
310412^92684-13100023Lelio R Paula07/2016
312925206!+p(4114)100001Henri Lifchitz09/2005
313025206!-p(5447)100001Henri Lifchitz10/2005
313125206!-p(12402)100001Henri Lifchitz04/2006
313225206!-p(16290)100001Henri Lifchitz09/2006
313325206!-p(19647)100001Henri Lifchitz02/2007
31342^332194+11473100001Henri Lifchitz03/2007
313510^100000+342909100001Milton L. Brown12/2007
314610^100000+346579100001Robert Price04/2012
314710^100000+829767100001Robert Price05/2012
314810^100000+871899100001Robert Price05/2012
314910^100000+1475997100001Robert Price07/2012
313610^100000+1751769100001Robert Price08/2012
313710^100000+2155489100001Robert Price10/2012
313810^100000+2483527100001Robert Price12/2012
313910^100000+2503087100001Robert Price12/2012
314010^100000+2686179100001Robert Price12/2012
314110^100000+2688933100001Robert Price12/2012
314210^100000+3667159100001Robert Price08/2013
314310^100000+3938473100001Robert Price05/2015
314410^100000+3979761100001Robert Price05/2015
314510^100000+4293973100001Robert Price09/2015
312610^100000+4858267100001Robert Price12/2015
312710^100000+5113299100001Robert Price02/2016
312810^100000+5169411100001Robert Price02/2016
310510^100000+5354043100001Robert Price05/2016
310610^100000+5717979100001Robert Price05/2016
310710^100000+6080631100001Robert Price07/2016
310810^100000+6308469100001Robert Price07/2016
310910^100000+6512023100001Robert Price08/2016
311010^100000+6596557100001Robert Price08/2016
311110^100000+7115409100001Robert Price10/2016
311210^100000+7235803100001Robert Price10/2016
311310^100000+7867333100001Robert Price12/2016
311410^100000+8743093100001Robert Price02/2017
311510^100000+8955391100001Robert Price03/2017
311610^100000+9180019100001Robert Price03/2017
311710^100000+9225987100001Robert Price04/2017
311810^100000+9265587100001Robert Price04/2017
311910^100000+9287049100001Robert Price04/2017
312010^100000+9425053100001Robert Price05/2017
312110^100000+9450769100001Robert Price05/2017
312210^100000+9528747100001Robert Smith05/2017
312310^100000+9548071100001Robert Price06/2017
312410^100000+10064287100001Robert Price08/2017
312510^100000+10229569100001Robert Price10/2017
315010^99999+309403100000Daniel Heuer01/2004
315110^100000-260199100000Patrick De Geest01/2010
315210^99999-5951199999Patrick De Geest07/2009
31532^332141-11307399985Enzo Doria07/2014
3154(3^209561+2)/72810125599978Lelio R Paula09/2013
31552^332085+186589799968Enzo Doria03/2016
3156(9787*2^332070-1)/93640236999959Lelio R Paula05/2015
31572^332023+19199949Lelio R Paula02/2011
31582^331938+7114999924Enzo Doria04/2016
31592^331932-7879599922Lelio R Paula09/2016
31602^331921+77199919Lelio R Paula01/2013
3161(3^209419-2)/513275599912Lelio R Paula09/2013
31622^331860-11498999900Enzo Doria05/2015
31632^331746-1165599866Lelio R Paula09/2016
316411^95891-2899861Lelio R Paula08/2016
3165(2^331694-5)/1199849Lelio R Paula10/2013
3166(3^209246+7)/6499834Lelio R Paula09/2013
316715^84866-5299811Lelio R Paula08/2016
316813^89600+3099810Lelio R Paula08/2016
31695^142772-3899794Lelio R Paula08/2016
3170(23*2^331459+1)/47599778Lelio R Paula11/2013
31712^331416-331416+199767Robert Price10/2014
31722^331256-5799718Lelio R Paula12/2012
31732^331185+73799697Lelio R Paula01/2013
3174(4*10^99693+149)/999693Robert Price03/2017
31752^331154+188052799688Enzo Doria10/2016
3176(19^77951+1)/2099679Paul Bourdelais03/2010
31772^331110+187045999675Enzo Doria05/2016
31785*2^331075+799665Lelio R Paula08/2014
3179(16*10^99656-31)/399657Robert Price03/2016
31802^330968+34599632Lelio R Paula09/2016
31822*5^142528-799624Lelio R Paula11/2014
31812^330942+7732999624Enzo Doria05/2016
318314^86914-9999615Lelio R Paula08/2016
3184(19*2^330902+1)/7799611Lelio R Paula11/2013
31852^330845+7168799595Enzo Doria04/2016
3186(23*2^330770+1)/399573Lelio R Paula11/2013
31872^330735+841599562Lelio R Paula09/2016
31882^330720+7407199557Enzo Doria04/2016
318931^66738-299531Lelio R Paula09/2013
31907*3^208567+499513Lelio R Paula08/2014
3191(13*10^99508+47)/399509Robert Price01/2017
31922^330553+77999507Lelio R Paula01/2013
319315^84606-9499505Lelio R Paula08/2016
31946^127858+4799493Lelio R Paula08/2016
31955^142337+4899490Lelio R Paula08/2016
31967^117724-2099489Lelio R Paula08/2016
3197(29*10^99474-17)/399475Erik Branger09/2014
3198(9*2^330407-1)/799463Lelio R Paula03/2014
3199(68*10^99441+7)/399443Robert Price03/2016
320046^59791-45^5979199418Jean-Louis Charton01/2013
3201(2*10^99408+529)/999408Robert Price01/2017
320253^57646-299398Lelio R Paula09/2013
32032^330165+187002599390Enzo Doria05/2016
32042^330142-15599383Lelio R Paula12/2012
32052^330088-11525999367Enzo Doria06/2015
3206(746*10^99303+1)/999305Robert Price02/2017
32073^208107+4099293Lelio R Paula08/2016
3208(5*2^329833-1)/36999288Lelio R Paula02/2014
32098*3^208093+599287Lelio R Paula08/2014
32105^142043+5699284Lelio R Paula08/2016
321122*10^99275+799277Robert Price04/2016
32122^329778+187618999274Enzo Doria07/2016
3213(10^99239-13)/399239Robert Price02/2017
32143^207987+6299236Lelio R Paula08/2016
32152^329638+4999231Lelio R Paula12/2012
32167^117413-1899226Lelio R Paula08/2016
32172^329586-45890399216Enzo Doria04/2015
32182^329553+10199206Lelio R Paula12/2012
32192^329551-11289799205Enzo Doria06/2014
3220(3^207925+7)/5099204Lelio R Paula09/2013
32216^127458-1799399182Enzo Doria03/2013
322227197^4428+4428^2719799166Hans Havermann10/2017
3223(46*10^99143-1)/999144Robert Price12/2014
32247*10^99133+6999134Robert Price10/2017
322518^78968-306599127Enzo Doria03/2013
322625927^6654+6654^2592799122Hans Havermann10/2017
32272^329259+18999117Lelio R Paula12/2012
32288*10^99113+3999114Robert Price01/2017
32296^127364+7799109Lelio R Paula08/2016
32306^127285+1399047Lelio R Paula08/2016
3231(228581#+235862)/(2^3*11*71*151)99044Makoto Morimoto10/2017
32322^329007+7328399041Enzo Doria04/2016
32335*3^207543-899024Lelio R Paula08/2014
32342^328885+14999005Lelio R Paula12/2012
323523392^17075+17075^2339299004Hans Havermann09/2017
3236(2^328879-9)/11999001Lelio R Paula10/2013
32375^141618+5498987Lelio R Paula08/2016
32388*10^98982+5198983Robert Price05/2017
3239(21*2^328809-1)/770998979Lelio R Paula03/2014
32402^328794-279760198977Enzo Doria04/2016
32416^127176+598963Lelio R Paula11/2014
324224262^11989+11989^2426298960Hans Havermann09/2017
32432^328700-10970998949Enzo Doria04/2014
324446711!2-2^4671198916Robert Price09/2015
32459*7^117037+498909Lelio R Paula11/2014
3246(10^98890+149)/398890Serge Batalov12/2014
324722775^21978+21978^2277598889Hans Havermann08/2017
32482^328497-21693398888Enzo Doria05/2014
32492^328487+3276998885Lelio R Paula08/2016
32503^207250-11235898884Enzo Doria06/2014


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Created by  Henri Lifchitz & Renaud Lifchitz : October, 26 2000, last modification: December, 12 2017 10:35 (Time in France)

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