PRP Records

Probable Primes Top 10000

(202632 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 ?
30012^337017-16995101453Lelio R Paula09/2016
30022^336979-115315101441Enzo Doria06/2015
30032^336970-20885101439Enzo Doria06/2013
30042^336958+79101435Lelio R Paula10/2009
30052^336942+169101430Lelio R Paula10/2009
3006(15185*2^336894-1)/7939101416Lelio R Paula05/2015
30072^336871+257463101409Tony Prest / Never Odd Or Even04/2016
30082^336871+318105101409Tony Prest / Never Odd Or Even04/2016
30092^336871+1010813101409Tony Prest / Never Odd Or Even04/2016
30102^336871+2302245101409Tony Prest / Never Odd Or Even04/2016
30112^336871+389273101409Tony Prest / Never Odd Or Even04/2016
30122^336871+1685475101409Tony Prest / Never Odd Or Even04/2016
30132^336871+1068119101409Tony Prest / Never Odd Or Even04/2016
30142^336871+586905101409Tony Prest / Never Odd Or Even04/2016
30152^336871+674571101409Tony Prest / Never Odd Or Even04/2016
30162^336871+707009101409Tony Prest / Never Odd Or Even04/2016
30172^336871+1210299101409Tony Prest / Never Odd Or Even04/2016
30182^336871+1921185101409Tony Prest / Never Odd Or Even04/2016
30192^336871+2003973101409Tony Prest / Never Odd Or Even04/2016
30202^336871+2656475101409Tony Prest / Never Odd Or Even04/2016
30212^336871+2703023101409Tony Prest / Never Odd Or Even04/2016
30222^336871+2704545101409Tony Prest / Never Odd Or Even04/2016
30232^336871+2766801101409Tony Prest / Never Odd Or Even04/2016
30242^336871+2127735101409Tony Prest / Never Odd Or Even04/2016
3025(2^336871+821089)/3101408Tony Prest / Never Odd Or Even05/2016
3026(2^336871+119567)/5101408Tony Prest / Never Odd Or Even05/2016
3027(2^336871+398161)/3101408Tony Prest / Never Odd Or Even05/2016
3028(2^336871+625889)/7101408Tony Prest / Never Odd Or Even05/2016
30292^336842+94065101400Lelio R Paula09/2016
3030(2^336871+904417)/3/3/3/5/19/9287177/9690011663/29993043103101378Tony Prest / Never Odd Or Even04/2016
3031(2^336871+631971)/13/251/1601/294277/614362921/30324278867101377Tony Prest / Never Odd Or Even04/2016
3032(2^336871+1443541)/3/89/1655197/11018131/47972707/468862691879101374Tony Prest / Never Odd Or Even04/2016
3033(2^336871+689863)/3/11/109/137/1867/7151/20800501/29243857/127778489101373Tony Prest / Never Odd Or Even04/2016
3034(2^336871+219839)/191/643/3011/9479/117127/175750007/4578271757101373Tony Prest / Never Odd Or Even04/2016
3035(2^336871+272895)/19/661/977572033/95853078653/520779768241101373Tony Prest / Never Odd Or Even04/2016
3036(2^336871+1023429)/2311/415873/991889/3630648341/207732189179101373Tony Prest / Never Odd Or Even04/2016
303710^101369+203811101370Patrick De Geest11/2016
303810^101369-99101369Lelio R Paula09/2016
3039(2^336871+1832627)/5/5/23/181/4397/91373/3746673331/115602484097/279351383917101363Tony Prest / Never Odd Or Even04/2016
30402^336701-113563101358Enzo Doria08/2014
30412^336644-109023101340Enzo Doria04/2014
30422^336601-21081101327Enzo Doria06/2013
304320^77869+63101310Lelio R Paula09/2016
3044(13*2^336523-1)/19101304Lelio R Paula03/2014
30456^130179-137101299Lelio R Paula10/2016
3046(2^336506+lucasV(1,2,336506)+1)/2101299Mike Oakes11/2016
3047(24737*2^336485+1)/7285101293Lelio R Paula07/2014
3048(2^336448+9)/497405101276Lelio R Paula12/2013
30492^336369-19753101258Enzo Doria05/2013
30502^336350-344291101252Enzo Doria07/2015
30512^336243-108777101220Enzo Doria03/2014
3052(31*2^336189-1)/19101204Lelio R Paula03/2014
3053(78557*2^336178+1)/1268757101199Lelio R Paula07/2014
30542^336150-20393101192Enzo Doria06/2013
30552^336112-1865249101180Enzo Doria03/2016
30562^336103-109015101178Enzo Doria04/2014
305713^90809-96101157Lelio R Paula10/2016
305819^79098-30101147Lelio R Paula10/2016
305919^79095+88101144Lelio R Paula10/2016
306015^85976+32101116Lelio R Paula10/2016
3061(3^211950+7)/28854513015920697088101107Lelio R Paula11/2013
3062(4^167933+17)/3101106Robert Price02/2017
30632^335858+153101104Lelio R Paula10/2009
30646^129918-35101096Lelio R Paula10/2016
30653^211885-70101095Lelio R Paula09/2016
3066(29*2^335835-1)/550599101093Lelio R Paula03/2014
30672^335818-20033101092Enzo Doria06/2013
30682^335813-110083101090Enzo Doria04/2014
30692^335804+2155101088Lelio R Paula09/2016
30702^335784-16145101082Enzo Doria04/2013
307111^97051+62101069Lelio R Paula10/2016
3072(2^335691-3)/26515101049Lelio R Paula12/2013
30732^335658-94395101044Lelio R Paula09/2016
30742^335586+169101022Lelio R Paula10/2009
3075(56^57787-1)/55101021Paul Bourdelais08/2017
307647599!2+1024100991Robert Price02/2015
30772^335468-18629100986Enzo Doria05/2013
30782^335454-20961100982Enzo Doria06/2013
307910^100978+61100979Lelio R Paula09/2016
308010^100978-156437100978Patrick De Geest11/2016
3081(15*2^335417+1)/481100970Lelio R Paula12/2013
30822^335403-1859167100967Enzo Doria03/2016
30839*2^335364-5100956Lelio R Paula08/2014
30842^335349+72287100951Enzo Doria04/2016
30852^335329+16095100945Lelio R Paula09/2016
3086232823#+233663100937Makoto Morimoto10/2017
30872^335237-20893100917Enzo Doria06/2013
30882^335222-19337100912Enzo Doria05/2013
30892^335222-109985100912Enzo Doria04/2014
30902^335182-17237100900Enzo Doria05/2013
30912^335043-16737100858Enzo Doria05/2013
3092(21181*2^335049+1)/1343811100858Lelio R Paula07/2014
30932^335038-20633100857Enzo Doria06/2013
30942^335031+1873373100855Enzo Doria06/2016
30953^211354-8816100842Enzo Doria05/2014
30962^334984-112757100841Enzo Doria06/2014
30982^334857+48527100803Lelio R Paula08/2011
309712^93406+29100803Lelio R Paula10/2016
3099(5*2^334825+1)/47100792Lelio R Paula12/2013
31002^334809-13100788Lelio R Paula04/2011
3101(82*10^100780-1)/9100781Robert Price12/2014
3102(2^334779+47)/5100778Lelio R Paula12/2013
31032^334751+2049100771Lelio R Paula09/2016
310413^90443-98100749Lelio R Paula10/2016
3105(24737*2^334628+1)/3100737Lelio R Paula07/2014
310615^85639-28100720Lelio R Paula10/2016
31072^334562+577294575100711Lelio R Paula09/2016
31084*3^211077-5100710Lelio R Paula08/2014
31092^334524+145100702Lelio R Paula07/2009
3110(1017*2^334391-1)/3535100662Lelio R Paula05/2015
31112^334294-113111100633Enzo Doria07/2014
31126^129308-17723100622Enzo Doria03/2013
31136^129305+95100619Lelio R Paula10/2016
31142^334244-1167100618Lelio R Paula09/2016
3115(21*2^334050+1)/935100558Lelio R Paula12/2013
3116(78557*2^334018+1)/4326021100548Lelio R Paula07/2014
3117(35*10^100542+1)/9100543Serge Batalov11/2010
311813^90251+24100535Lelio R Paula10/2016
31192^333963+789100533Lelio R Paula08/2011
31202^333919-1840087100520Enzo Doria06/2015
31212^333911+72623100518Enzo Doria04/2016
312218^80064-67100503Lelio R Paula10/2016
31235^143742-48100472Lelio R Paula10/2016
31242^333757-112123100471Enzo Doria06/2014
31252^333603-108861100425Enzo Doria03/2014
31269*7^118818-2100414Lelio R Paula11/2014
31272^333546-17097100408Enzo Doria05/2013
312817^81597+72100401Lelio R Paula10/2016
3129p(20559)#/2+8100384Robert Price01/2017
313011^96390-24100380Lelio R Paula10/2016
31314832563059*2^333333+30029100353Donovan Johnson01/2008
31322^333354+763100350Lelio R Paula08/2011
31332^333289-109483100330Enzo Doria04/2014
31342^333240-2790209100316Enzo Doria03/2016
3136(2^333227-2^166614+1)/510031111/2006
31352^333225+719100311Lelio R Paula08/2011
31372^333221-2785333100310Enzo Doria10/2015
313876^53332-75100308Norbert Schneider02/2015
31396^128892-17573100298Enzo Doria03/2013
31402^333105-113215100275Enzo Doria07/2014
3141(31*2^333102+1)/2375100272Lelio R Paula11/2013
314217^81476-74100253Lelio R Paula10/2016
314317^81417-16100180Theodore Burton11/2005
31442^332739-113215100165Enzo Doria07/2014
31452^332730-1865621100162Enzo Doria03/2016
314691^51127-2100160Lelio R Paula09/2013
314715^85159-32100155Lelio R Paula10/2016
31486^128661+97100118Lelio R Paula10/2016
314919^78285+40100108Lelio R Paula07/2016
31506^128640+5100102Lelio R Paula11/2014
31516^128565-127100044Lelio R Paula08/2016
31522^332309-133100035Lelio R Paula02/2011
31532^332307+731100035Lelio R Paula07/2011
31542^332301+12927100033Lelio R Paula04/2013
315512^92684-13100023Lelio R Paula07/2016
317225206!+p(4114)100001Henri Lifchitz09/2005
317325206!-p(5447)100001Henri Lifchitz10/2005
317425206!-p(12402)100001Henri Lifchitz04/2006
317525206!-p(16290)100001Henri Lifchitz09/2006
317625206!-p(19647)100001Henri Lifchitz02/2007
31772^332194+11473100001Henri Lifchitz03/2007
317110^100000+342909100001Milton L. Brown12/2007
316410^100000+346579100001Robert Price04/2012
316510^100000+829767100001Robert Price05/2012
316610^100000+871899100001Robert Price05/2012
316710^100000+1475997100001Robert Price07/2012
317810^100000+1751769100001Robert Price08/2012
317910^100000+2155489100001Robert Price10/2012
318010^100000+2483527100001Robert Price12/2012
318110^100000+2503087100001Robert Price12/2012
318210^100000+2686179100001Robert Price12/2012
318310^100000+2688933100001Robert Price12/2012
318410^100000+3667159100001Robert Price08/2013
316810^100000+3938473100001Robert Price05/2015
316910^100000+3979761100001Robert Price05/2015
317010^100000+4293973100001Robert Price09/2015
319810^100000+4858267100001Robert Price12/2015
319910^100000+5113299100001Robert Price02/2016
320010^100000+5169411100001Robert Price02/2016
315610^100000+5354043100001Robert Price05/2016
315710^100000+5717979100001Robert Price05/2016
315810^100000+6080631100001Robert Price07/2016
315910^100000+6308469100001Robert Price07/2016
316010^100000+6512023100001Robert Price08/2016
316110^100000+6596557100001Robert Price08/2016
316210^100000+7115409100001Robert Price10/2016
316310^100000+7235803100001Robert Price10/2016
318510^100000+7867333100001Robert Price12/2016
318610^100000+8743093100001Robert Price02/2017
318710^100000+8955391100001Robert Price03/2017
318810^100000+9180019100001Robert Price03/2017
318910^100000+9225987100001Robert Price04/2017
319010^100000+9265587100001Robert Price04/2017
319110^100000+9287049100001Robert Price04/2017
319210^100000+9425053100001Robert Price05/2017
319310^100000+9450769100001Robert Price05/2017
319410^100000+9528747100001Robert Smith05/2017
319510^100000+9548071100001Robert Price06/2017
319610^100000+10064287100001Robert Price08/2017
319710^100000+10229569100001Robert Price10/2017
320210^99999+309403100000Daniel Heuer01/2004
320110^100000-260199100000Patrick De Geest01/2010
320310^99999-5951199999Patrick De Geest07/2009
32042^332141-11307399985Enzo Doria07/2014
3205(3^209561+2)/72810125599978Lelio R Paula09/2013
32062^332085+186589799968Enzo Doria03/2016
3207(9787*2^332070-1)/93640236999959Lelio R Paula05/2015
32082^332023+19199949Lelio R Paula02/2011
32092^331938+7114999924Enzo Doria04/2016
32102^331932-7879599922Lelio R Paula09/2016
32112^331921+77199919Lelio R Paula01/2013
3212(3^209419-2)/513275599912Lelio R Paula09/2013
32132^331860-11498999900Enzo Doria05/2015
32142^331746-1165599866Lelio R Paula09/2016
321511^95891-2899861Lelio R Paula08/2016
3216(2^331694-5)/1199849Lelio R Paula10/2013
3217(3^209246+7)/6499834Lelio R Paula09/2013
321815^84866-5299811Lelio R Paula08/2016
321913^89600+3099810Lelio R Paula08/2016
32205^142772-3899794Lelio R Paula08/2016
3221(23*2^331459+1)/47599778Lelio R Paula11/2013
32222^331416-331416+199767Robert Price10/2014
32232^331256-5799718Lelio R Paula12/2012
32242^331185+73799697Lelio R Paula01/2013
3225(4*10^99693+149)/999693Robert Price03/2017
32262^331154+188052799688Enzo Doria10/2016
3227(19^77951+1)/2099679Paul Bourdelais03/2010
32282^331110+187045999675Enzo Doria05/2016
32295*2^331075+799665Lelio R Paula08/2014
3230(16*10^99656-31)/399657Robert Price03/2016
32312^330968+34599632Lelio R Paula09/2016
32332*5^142528-799624Lelio R Paula11/2014
32322^330942+7732999624Enzo Doria05/2016
323414^86914-9999615Lelio R Paula08/2016
3235(19*2^330902+1)/7799611Lelio R Paula11/2013
32362^330845+7168799595Enzo Doria04/2016
3237(23*2^330770+1)/399573Lelio R Paula11/2013
32382^330735+841599562Lelio R Paula09/2016
32392^330720+7407199557Enzo Doria04/2016
324031^66738-299531Lelio R Paula09/2013
32417*3^208567+499513Lelio R Paula08/2014
3242(13*10^99508+47)/399509Robert Price01/2017
32432^330553+77999507Lelio R Paula01/2013
324415^84606-9499505Lelio R Paula08/2016
32456^127858+4799493Lelio R Paula08/2016
32465^142337+4899490Lelio R Paula08/2016
32477^117724-2099489Lelio R Paula08/2016
3248(29*10^99474-17)/399475Erik Branger09/2014
3249(9*2^330407-1)/799463Lelio R Paula03/2014
3250(68*10^99441+7)/399443Robert Price03/2016


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Created by  Henri Lifchitz & Renaud Lifchitz : October, 26 2000, last modification: February, 20 2018 10:36 (Time in France)

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