PRP Records

Probable Primes Top 10000

(218736 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 ?
32512^336369-19753101258Enzo Doria05/2013
32522^336350-344291101252Enzo Doria07/2015
32532^336243-108777101220Enzo Doria03/2014
3254(31*2^336189-1)/19101204Lelio R Paula03/2014
3255(78557*2^336178+1)/1268757101199Lelio R Paula07/2014
32562^336150-20393101192Enzo Doria06/2013
32572^336112-1865249101180Enzo Doria03/2016
32582^336103-109015101178Enzo Doria04/2014
325913^90809-96101157Lelio R Paula10/2016
326019^79098-30101147Lelio R Paula10/2016
326119^79095+88101144Lelio R Paula10/2016
326215^85976+32101116Lelio R Paula10/2016
3263(3^211950+7)/28854513015920697088101107Lelio R Paula11/2013
3264(4^167933+17)/3101106Robert Price02/2017
32652^335858+153101104Lelio R Paula10/2009
32666^129918-35101096Lelio R Paula10/2016
32673^211885-70101095Lelio R Paula09/2016
3268(29*2^335835-1)/550599101093Lelio R Paula03/2014
32692^335818-20033101092Enzo Doria06/2013
32702^335813-110083101090Enzo Doria04/2014
32712^335804+2155101088Lelio R Paula09/2016
32722^335784-16145101082Enzo Doria04/2013
327311^97051+62101069Lelio R Paula10/2016
32743*10^101065+11101066Robert Price07/2018
3275(2^335691-3)/26515101049Lelio R Paula12/2013
32762^335658-94395101044Lelio R Paula09/2016
32772^335586+169101022Lelio R Paula10/2009
3278(56^57787-1)/55101021Paul Bourdelais08/2017
3279(19*10^100997+737)/9100998Robert Price07/2018
328047599!2+1024100991Robert Price02/2015
32812^335468-18629100986Enzo Doria05/2013
32822^335454-20961100982Enzo Doria06/2013
328310^100978+61100979Lelio R Paula09/2016
328410^100978-156437100978Patrick De Geest11/2016
3285(15*2^335417+1)/481100970Lelio R Paula12/2013
32862^335403-1859167100967Enzo Doria03/2016
32879*2^335364-5100956Lelio R Paula08/2014
32882^335349+72287100951Enzo Doria04/2016
32892^335329+16095100945Lelio R Paula09/2016
3290232823#+233663100937Makoto Morimoto10/2017
32912^335237-20893100917Enzo Doria06/2013
32922^335222-19337100912Enzo Doria05/2013
32932^335222-109985100912Enzo Doria04/2014
32942^335182-17237100900Enzo Doria05/2013
32952^335043-16737100858Enzo Doria05/2013
3296(21181*2^335049+1)/1343811100858Lelio R Paula07/2014
32972^335038-20633100857Enzo Doria06/2013
32982^335031+1873373100855Enzo Doria06/2016
32993^211354-8816100842Enzo Doria05/2014
33002^334984-112757100841Enzo Doria06/2014
33022^334857+48527100803Lelio R Paula08/2011
330112^93406+29100803Lelio R Paula10/2016
3303(5*2^334825+1)/47100792Lelio R Paula12/2013
33042^334809-13100788Lelio R Paula04/2011
3305(82*10^100780-1)/9100781Robert Price12/2014
3306(2^334779+47)/5100778Lelio R Paula12/2013
33072^334751+2049100771Lelio R Paula09/2016
330813^90443-98100749Lelio R Paula10/2016
3309(7*10^100737+71)/3100738Robert Price05/2018
3310(24737*2^334628+1)/3100737Lelio R Paula07/2014
331115^85639-28100720Lelio R Paula10/2016
33122^334562+577294575100711Lelio R Paula09/2016
33134*3^211077-5100710Lelio R Paula08/2014
33142^334524+145100702Lelio R Paula07/2009
3315(1017*2^334391-1)/3535100662Lelio R Paula05/2015
33162^334294-113111100633Enzo Doria07/2014
33176^129308-17723100622Enzo Doria03/2013
33186^129305+95100619Lelio R Paula10/2016
33192^334244-1167100618Lelio R Paula09/2016
3320(21*2^334050+1)/935100558Lelio R Paula12/2013
332124885^10984+10984^24885100555Hans Havermann07/2018
3322(78557*2^334018+1)/4326021100548Lelio R Paula07/2014
3323(35*10^100542+1)/9100543Serge Batalov11/2010
332423578^18367+18367^23578100538Hans Havermann07/2018
332513^90251+24100535Lelio R Paula10/2016
33262^333963+789100533Lelio R Paula08/2011
33272^333919-1840087100520Enzo Doria06/2015
33282^333911+72623100518Enzo Doria04/2016
332924605^12168+12168^24605100517Hans Havermann08/2018
333018^80064-67100503Lelio R Paula10/2016
33315^143742-48100472Lelio R Paula10/2016
333224095^14784+14784^24095100472Hans Havermann08/2018
33332^333757-112123100471Enzo Doria06/2014
333427358^4693+4693^27358100444Hans Havermann07/2018
33352^333603-108861100425Enzo Doria03/2014
33369*7^118818-2100414Lelio R Paula11/2014
33372^333546-17097100408Enzo Doria05/2013
333817^81597+72100401Lelio R Paula10/2016
3339p(20559)#/2+8100384Robert Price01/2017
334011^96390-24100380Lelio R Paula10/2016
33414832563059*2^333333+30029100353Donovan Johnson01/2008
334223565^18136+18136^23565100353Hans Havermann07/2018
33432^333354+763100350Lelio R Paula08/2011
33442^333289-109483100330Enzo Doria04/2014
33452^333240-2790209100316Enzo Doria03/2016
334623601^17798+17798^23601100314Hans Havermann05/2018
3348(2^333227-2^166614+1)/510031111/2006
33472^333225+719100311Lelio R Paula08/2011
33492^333221-2785333100310Enzo Doria10/2015
335076^53332-75100308Norbert Schneider02/2015
33516^128892-17573100298Enzo Doria03/2013
33522^333105-113215100275Enzo Doria07/2014
3353(31*2^333102+1)/2375100272Lelio R Paula11/2013
335417^81476-74100253Lelio R Paula10/2016
335523392^19207+19207^23392100199Hans Havermann06/2018
335617^81417-16100180Theodore Burton11/2005
33572^332739-113215100165Enzo Doria07/2014
33582^332730-1865621100162Enzo Doria03/2016
335991^51127-2100160Lelio R Paula09/2013
336015^85159-32100155Lelio R Paula10/2016
33616^128661+97100118Lelio R Paula10/2016
336219^78285+40100108Lelio R Paula07/2016
33636^128640+5100102Lelio R Paula11/2014
336428562^3189+3189^28562100072Hans Havermann05/2018
33656^128565-127100044Lelio R Paula08/2016
33662^332309-133100035Lelio R Paula02/2011
33672^332307+731100035Lelio R Paula07/2011
33682^332301+12927100033Lelio R Paula04/2013
336923406^18781+18781^23406100031Hans Havermann04/2018
337012^92684-13100023Lelio R Paula07/2016
337110^100002+236023100003Stefano Morozzi05/2018
337210^100002+433741100003Stefano Morozzi05/2018
3373(10^100002-1)/9-10^33441100002Akihiko Yoshida03/2018
3374(10^100002-1)/9-10^44692100002Akihiko Yoshida03/2018
337510^100002-249519100002Patrick De Geest07/2018
337610^100001+314199100002Patrick De Geest07/2018
339125206!+p(4114)100001Henri Lifchitz09/2005
339225206!-p(5447)100001Henri Lifchitz10/2005
339325206!-p(12402)100001Henri Lifchitz04/2006
339425206!-p(16290)100001Henri Lifchitz09/2006
339525206!-p(19647)100001Henri Lifchitz02/2007
33962^332194+11473100001Henri Lifchitz03/2007
339010^100000+342909100001Milton L. Brown12/2007
341110^100000+346579100001Robert Price04/2012
341210^100000+829767100001Robert Price05/2012
341310^100000+871899100001Robert Price05/2012
341410^100000+1475997100001Robert Price07/2012
338310^100000+1751769100001Robert Price08/2012
338410^100000+2155489100001Robert Price10/2012
338510^100000+2483527100001Robert Price12/2012
338610^100000+2503087100001Robert Price12/2012
338710^100000+2686179100001Robert Price12/2012
338810^100000+2688933100001Robert Price12/2012
338910^100000+3667159100001Robert Price08/2013
339710^100000+3938473100001Robert Price05/2015
339810^100000+3979761100001Robert Price05/2015
339910^100000+4293973100001Robert Price09/2015
340010^100000+4858267100001Robert Price12/2015
340110^100000+5113299100001Robert Price02/2016
340210^100000+5169411100001Robert Price02/2016
340310^100000+5354043100001Robert Price05/2016
340410^100000+5717979100001Robert Price05/2016
340510^100000+6080631100001Robert Price07/2016
340610^100000+6308469100001Robert Price07/2016
340710^100000+6512023100001Robert Price08/2016
340810^100000+6596557100001Robert Price08/2016
340910^100000+7115409100001Robert Price10/2016
341010^100000+7235803100001Robert Price10/2016
341510^100000+7867333100001Robert Price12/2016
341610^100000+8743093100001Robert Price02/2017
341710^100000+8955391100001Robert Price03/2017
341810^100000+9180019100001Robert Price03/2017
341910^100000+9225987100001Robert Price04/2017
342010^100000+9265587100001Robert Price04/2017
342110^100000+9287049100001Robert Price04/2017
342210^100000+9425053100001Robert Price05/2017
342310^100000+9450769100001Robert Price05/2017
342410^100000+9528747100001Robert Smith05/2017
342510^100000+9548071100001Robert Price06/2017
342610^100000+10064287100001Robert Price08/2017
342710^100000+10229569100001Robert Price10/2017
337710^100000+11187931100001Robert Price03/2018
337810^100000+11264721100001Robert Price04/2018
337910^100000+11477661100001Robert Price05/2018
338010^100000+11644653100001Robert Price07/2018
338110^100001-431439100001Patrick De Geest07/2018
338210^100000+11769399100001Robert Price08/2018
342810^99999+309403100000Daniel Heuer01/2004
342910^100000-260199100000Patrick De Geest01/2010
343010^99999-5951199999Patrick De Geest07/2009
34312^332141-11307399985Enzo Doria07/2014
3432(3^209561+2)/72810125599978Lelio R Paula09/2013
343323827^15702+15702^2382799978Hans Havermann04/2018
34342^332085+186589799968Enzo Doria03/2016
3435(9787*2^332070-1)/93640236999959Lelio R Paula05/2015
34362^332023+19199949Lelio R Paula02/2011
34372^331938+7114999924Enzo Doria04/2016
34382^331932-7879599922Lelio R Paula09/2016
34392^331921+77199919Lelio R Paula01/2013
3440(3^209419-2)/513275599912Lelio R Paula09/2013
34412^331860-11498999900Enzo Doria05/2015
34422^331746-1165599866Lelio R Paula09/2016
344311^95891-2899861Lelio R Paula08/2016
3444(2^331694-5)/1199849Lelio R Paula10/2013
3445(3^209246+7)/6499834Lelio R Paula09/2013
344625062^9617+9617^2506299823Hans Havermann04/2018
344715^84866-5299811Lelio R Paula08/2016
344813^89600+3099810Lelio R Paula08/2016
344922950^22309+22309^2295099798Hans Havermann03/2018
34505^142772-3899794Lelio R Paula08/2016
3451(23*2^331459+1)/47599778Lelio R Paula11/2013
34522^331416-331416+199767Robert Price10/2014
34532^331256-5799718Lelio R Paula12/2012
345428192^3443+3443^2819299714Hans Havermann03/2018
34552^331185+73799697Lelio R Paula01/2013
3456(4*10^99693+149)/999693Robert Price03/2017
34572^331154+188052799688Enzo Doria10/2016
3459(19^77951+1)/2099679Paul Bourdelais03/2010
345824354^12385+12385^2435499679Hans Havermann03/2018
34602^331110+187045999675Enzo Doria05/2016
34615*2^331075+799665Lelio R Paula08/2014
346225776^7351+7351^2577699659Hans Havermann02/2018
3463(16*10^99656-31)/399657Robert Price03/2016
34642^330968+34599632Lelio R Paula09/2016
34662*5^142528-799624Lelio R Paula11/2014
34652^330942+7732999624Enzo Doria05/2016
346714^86914-9999615Lelio R Paula08/2016
3468(19*2^330902+1)/7799611Lelio R Paula11/2013
346922971^21692+21692^2297199610Hans Havermann03/2018
34702^330845+7168799595Enzo Doria04/2016
3471(23*2^330770+1)/399573Lelio R Paula11/2013
347224494^11613+11613^2449499567Hans Havermann03/2018
34732^330735+841599562Lelio R Paula09/2016
34742^330720+7407199557Enzo Doria04/2016
347531^66738-299531Lelio R Paula09/2013
34767*3^208567+499513Lelio R Paula08/2014
3477(13*10^99508+47)/399509Robert Price01/2017
34782^330553+77999507Lelio R Paula01/2013
347915^84606-9499505Lelio R Paula08/2016
34806^127858+4799493Lelio R Paula08/2016
34815^142337+4899490Lelio R Paula08/2016
34827^117724-2099489Lelio R Paula08/2016
3483(29*10^99474-17)/399475Erik Branger09/2014
3484(9*2^330407-1)/799463Lelio R Paula03/2014
3485(68*10^99441+7)/399443Robert Price03/2016
348646^59791-45^5979199418Jean-Louis Charton01/2013
348723839^14802+14802^2383999417Hans Havermann02/2018
3488(2*10^99408+529)/999408Robert Price01/2017
348953^57646-299398Lelio R Paula09/2013
34902^330165+187002599390Enzo Doria05/2016
34912^330142-15599383Lelio R Paula12/2012
34922^330088-11525999367Enzo Doria06/2015
349324216^12671+12671^2421699354Hans Havermann01/2018
3494(746*10^99303+1)/999305Robert Price02/2017
34953^208107+4099293Lelio R Paula08/2016
3496(5*2^329833-1)/36999288Lelio R Paula02/2014
34978*3^208093+599287Lelio R Paula08/2014
34985^142043+5699284Lelio R Paula08/2016
349922*10^99275+799277Robert Price04/2016
35002^329778+187618999274Enzo Doria07/2016


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Created by  Henri Lifchitz & Renaud Lifchitz : October, 26 2000, last modification: August, 14 2018 21:45 (Time in France)

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