PRP Records

Probable Primes Top 10000

(252932 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 (> 50000) Who ? When ?
35013*10^101657-37101658Robert Price07/2018
3502(31*2^337677-1)/593101650Lelio R Paula03/2014
350311^97605-24101646Lelio R Paula10/2016
35048^112539-112539101633Robert Price01/2014
350525694^9003+9003^25694101605Hans Havermann12/2018
35062^337515-19869101603Enzo Doria06/2013
35072^337473+719101590Lelio R Paula08/2011
3508(2^337485-509203)/656647157101585Lelio R Paula12/2013
35092^337452-108815101584Enzo Doria03/2014
35102^337453+1185101584Lelio R Paula09/2016
35112^337410-113561101571Enzo Doria08/2014
35122^337387+855101564Lelio R Paula09/2016
35132^337367-17295101558Lelio R Paula09/2016
35142^337342-109035101551Enzo Doria04/2014
351523703^19238+19238^23703101548Hans Havermann12/2018
35162^337267-19101528Lelio R Paula07/2011
35172^337183-19989101503Enzo Doria06/2013
35182^337149+72425101492Enzo Doria04/2016
351924041^16642+16642^24041101483Hans Havermann12/2018
352033982^969+969^33982101482Hans Havermann12/2018
35212^337101-20241101478Enzo Doria06/2013
35222^337035-20001101458Enzo Doria06/2013
35232^337017-16995101453Lelio R Paula09/2016
35242^336979-115315101441Enzo Doria06/2015
35252^336970-20885101439Enzo Doria06/2013
35262^336958+79101435Lelio R Paula10/2009
35272^336942+169101430Lelio R Paula10/2009
3528(15185*2^336894-1)/7939101416Lelio R Paula05/2015
35294*10^101415-89101416Robert Price11/2018
35302^336871+257463101409Tony Prest / Never Odd Or Even04/2016
35312^336871+318105101409Tony Prest / Never Odd Or Even04/2016
35322^336871+1010813101409Tony Prest / Never Odd Or Even04/2016
35332^336871+2302245101409Tony Prest / Never Odd Or Even04/2016
35342^336871+389273101409Tony Prest / Never Odd Or Even04/2016
35352^336871+1685475101409Tony Prest / Never Odd Or Even04/2016
35362^336871+1068119101409Tony Prest / Never Odd Or Even04/2016
35372^336871+586905101409Tony Prest / Never Odd Or Even04/2016
35382^336871+674571101409Tony Prest / Never Odd Or Even04/2016
35392^336871+707009101409Tony Prest / Never Odd Or Even04/2016
35402^336871+1210299101409Tony Prest / Never Odd Or Even04/2016
35412^336871+1921185101409Tony Prest / Never Odd Or Even04/2016
35422^336871+2003973101409Tony Prest / Never Odd Or Even04/2016
35432^336871+2656475101409Tony Prest / Never Odd Or Even04/2016
35442^336871+2703023101409Tony Prest / Never Odd Or Even04/2016
35452^336871+2704545101409Tony Prest / Never Odd Or Even04/2016
35462^336871+2766801101409Tony Prest / Never Odd Or Even04/2016
35472^336871+2127735101409Tony Prest / Never Odd Or Even04/2016
3548(2^336871+821089)/3101408Tony Prest / Never Odd Or Even05/2016
3549(2^336871+119567)/5101408Tony Prest / Never Odd Or Even05/2016
3550(2^336871+398161)/3101408Tony Prest / Never Odd Or Even05/2016
3551(2^336871+625889)/7101408Tony Prest / Never Odd Or Even05/2016
355224097^16150+16150^24097101405Hans Havermann12/2018
35532^336842+94065101400Lelio R Paula09/2016
3554(2^336871+904417)/3/3/3/5/19/9287177/9690011663/29993043103101378Tony Prest / Never Odd Or Even04/2016
3555(2^336871+631971)/13/251/1601/294277/614362921/30324278867101377Tony Prest / Never Odd Or Even04/2016
3556(2^336871+1443541)/3/89/1655197/11018131/47972707/468862691879101374Tony Prest / Never Odd Or Even04/2016
3557(2^336871+689863)/3/11/109/137/1867/7151/20800501/29243857/127778489101373Tony Prest / Never Odd Or Even04/2016
3558(2^336871+219839)/191/643/3011/9479/117127/175750007/4578271757101373Tony Prest / Never Odd Or Even04/2016
3559(2^336871+272895)/19/661/977572033/95853078653/520779768241101373Tony Prest / Never Odd Or Even04/2016
3560(2^336871+1023429)/2311/415873/991889/3630648341/207732189179101373Tony Prest / Never Odd Or Even04/2016
356110^101369+203811101370Patrick De Geest11/2016
356210^101369-99101369Lelio R Paula09/2016
3563(2^336871+1832627)/5/5/23/181/4397/91373/3746673331/115602484097/279351383917101363Tony Prest / Never Odd Or Even04/2016
35642^336701-113563101358Enzo Doria08/2014
35652^336644-109023101340Enzo Doria04/2014
35662^336601-21081101327Enzo Doria06/2013
356720^77869+63101310Lelio R Paula09/2016
3568(13*2^336523-1)/19101304Lelio R Paula03/2014
35706^130179-137101299Lelio R Paula10/2016
3569(2^336506+lucasV(1,2,336506)+1)/2101299Mike Oakes11/2016
3571(24737*2^336485+1)/7285101293Lelio R Paula07/2014
3572(2^336448+9)/497405101276Lelio R Paula12/2013
35732^336369-19753101258Enzo Doria05/2013
357423842^17653+17653^23842101253Hans Havermann11/2018
35752^336350-344291101252Enzo Doria07/2015
3576(56*10^101222-47)/9101223Robert Price02/2019
35772^336243-108777101220Enzo Doria03/2014
3578(31*2^336189-1)/19101204Lelio R Paula03/2014
357923535^19954+19954^23535101202Hans Havermann11/2018
3580(78557*2^336178+1)/1268757101199Lelio R Paula07/2014
35812^336150-20393101192Enzo Doria06/2013
358223996^16473+16473^23996101186Hans Havermann11/2018
35832^336112-1865249101180Enzo Doria03/2016
35842^336103-109015101178Enzo Doria04/2014
358513^90809-96101157Lelio R Paula10/2016
358626199^7258+7258^26199101150Hans Havermann11/2018
358719^79098-30101147Lelio R Paula10/2016
358819^79095+88101144Lelio R Paula10/2016
358915^85976+32101116Lelio R Paula10/2016
35902^335872-2776215101108Tony Prest / Never Odd Or Even01/2019
3591(3^211950+7)/28854513015920697088101107Lelio R Paula11/2013
3592(4^167933+17)/3101106Robert Price02/2017
35932^335858+153101104Lelio R Paula10/2009
3594(2^335872-2776871)/5/5/479101104Tony Prest / Never Odd Or Even01/2019
3595(2^335872-2758787)/23/31/20809101101Tony Prest / Never Odd Or Even01/2019
3596(2^335872-2795083)/3/3/113/283/148367101097Tony Prest / Never Odd Or Even01/2019
35976^129918-35101096Lelio R Paula10/2016
35983^211885-70101095Lelio R Paula09/2016
3599(29*2^335835-1)/550599101093Lelio R Paula03/2014
3600(2^335872-2794771)/3/5/5/61/232312440293101093Tony Prest / Never Odd Or Even01/2019
36012^335818-20033101092Enzo Doria06/2013
36022^335813-110083101090Enzo Doria04/2014
36032^335804+2155101088Lelio R Paula09/2016
3604(2^335872-2756679)/7/7/7/13/31/4987/437653/8734021101087Tony Prest / Never Odd Or Even01/2019
36052^335784-16145101082Enzo Doria04/2013
360611^97051+62101069Lelio R Paula10/2016
36073*10^101065+11101066Robert Price07/2018
360827820^4293+4293^27820101064Hans Havermann10/2018
3609(2^335691-3)/26515101049Lelio R Paula12/2013
36102^335658-94395101044Lelio R Paula09/2016
361124514^13215+13215^24514101024Hans Havermann11/2018
36122^335586+169101022Lelio R Paula10/2009
3613(56^57787-1)/55101021Paul Bourdelais08/2017
3614(19*10^100997+737)/9100998Robert Price07/2018
361547599!2+1024100991Robert Price02/2015
36162^335468-18629100986Enzo Doria05/2013
36172^335454-20961100982Enzo Doria06/2013
361810^100978+61100979Lelio R Paula09/2016
361910^100978-156437100978Patrick De Geest11/2016
3620(15*2^335417+1)/481100970Lelio R Paula12/2013
36212^335403-1859167100967Enzo Doria03/2016
362223599^18976+18976^23599100962Hans Havermann10/2018
36239*2^335364-5100956Lelio R Paula08/2014
36242^335349+72287100951Enzo Doria04/2016
36252^335329+16095100945Lelio R Paula09/2016
3626232823#+233663100937Makoto Morimoto10/2017
3627(232823#+10141)/(10141*1674461)100927Makoto Morimoto06/2019
36282^335237-20893100917Enzo Doria06/2013
36292^335222-19337100912Enzo Doria05/2013
36302^335222-109985100912Enzo Doria04/2014
36312^335182-17237100900Enzo Doria05/2013
36322^335043-16737100858Enzo Doria05/2013
3633(21181*2^335049+1)/1343811100858Lelio R Paula07/2014
36342^335038-20633100857Enzo Doria06/2013
36352^335031+1873373100855Enzo Doria06/2016
363623489^19650+19650^23489100847Hans Havermann10/2018
36373^211354-8816100842Enzo Doria05/2014
36382^334984-112757100841Enzo Doria06/2014
363929451^2648+2648^29451100809Hans Havermann09/2018
364025583^8716+8716^25583100806Hans Havermann08/2018
36422^334857+48527100803Lelio R Paula08/2011
364112^93406+29100803Lelio R Paula10/2016
364328780^3179+3179^28780100796Hans Havermann09/2018
3644(5*2^334825+1)/47100792Lelio R Paula12/2013
36452^334809-13100788Lelio R Paula04/2011
3646(82*10^100780-1)/9100781Robert Price12/2014
364731395^1622+1622^31395100780Hans Havermann09/2018
3648(2^334779+47)/5100778Lelio R Paula12/2013
36492^334751+2049100771Lelio R Paula09/2016
365013^90443-98100749Lelio R Paula10/2016
3651(7*10^100737+71)/3100738Robert Price05/2018
3652(24737*2^334628+1)/3100737Lelio R Paula07/2014
365315^85639-28100720Lelio R Paula10/2016
365427068^5259+5259^27068100718Hans Havermann08/2018
36552^334562+577294575100711Lelio R Paula09/2016
36564*3^211077-5100710Lelio R Paula08/2014
36572^334524+145100702Lelio R Paula07/2009
365827648^4375+4375^27648100666Hans Havermann09/2018
3659(1017*2^334391-1)/3535100662Lelio R Paula05/2015
36602^334294-113111100633Enzo Doria07/2014
366125581^8582+8582^25581100626Hans Havermann08/2018
36626^129308-17723100622Enzo Doria03/2013
36636^129305+95100619Lelio R Paula10/2016
36642^334244-1167100618Lelio R Paula09/2016
3665(21*2^334050+1)/935100558Lelio R Paula12/2013
366624885^10984+10984^24885100555Hans Havermann07/2018
3667(78557*2^334018+1)/4326021100548Lelio R Paula07/2014
3668(35*10^100542+1)/9100543Serge Batalov11/2010
366923578^18367+18367^23578100538Hans Havermann07/2018
367013^90251+24100535Lelio R Paula10/2016
36712^333963+789100533Lelio R Paula08/2011
36722^333919-1840087100520Enzo Doria06/2015
36732^333911+72623100518Enzo Doria04/2016
367424605^12168+12168^24605100517Hans Havermann08/2018
367518^80064-67100503Lelio R Paula10/2016
36765^143742-48100472Lelio R Paula10/2016
367724095^14784+14784^24095100472Hans Havermann08/2018
36782^333757-112123100471Enzo Doria06/2014
367927358^4693+4693^27358100444Hans Havermann07/2018
36802^333603-108861100425Enzo Doria03/2014
36819*7^118818-2100414Lelio R Paula11/2014
36822^333546-17097100408Enzo Doria05/2013
368317^81597+72100401Lelio R Paula10/2016
3684p(20559)#/2+8100384Robert Price01/2017
368511^96390-24100380Lelio R Paula10/2016
36874832563059*2^333333+30029100353Donovan Johnson01/2008
368623565^18136+18136^23565100353Hans Havermann07/2018
36882^333354+763100350Lelio R Paula08/2011
36892^333289-109483100330Enzo Doria04/2014
36902^333240-2790209100316Enzo Doria03/2016
369123601^17798+17798^23601100314Hans Havermann05/2018
3693(2^333227-2^166614+1)/510031111/2006
36922^333225+719100311Lelio R Paula08/2011
36942^333221-2785333100310Enzo Doria10/2015
369576^53332-75100308Norbert Schneider02/2015
36966^128892-17573100298Enzo Doria03/2013
3697(47*10^100283-119)/9100284Robert Price05/2019
36982^333105-113215100275Enzo Doria07/2014
3699(31*2^333102+1)/2375100272Lelio R Paula11/2013
37004*10^100257-83100258Robert Price10/2018
370117^81476-74100253Lelio R Paula10/2016
370223392^19207+19207^23392100199Hans Havermann06/2018
370317^81417-16100180Theodore Burton11/2005
37042^332739-113215100165Enzo Doria07/2014
37052^332730-1865621100162Enzo Doria03/2016
370691^51127-2100160Lelio R Paula09/2013
370715^85159-32100155Lelio R Paula10/2016
37086^128661+97100118Lelio R Paula10/2016
370919^78285+40100108Lelio R Paula07/2016
37106^128640+5100102Lelio R Paula11/2014
3711(14*10^100075+61)/3100076Robert Price12/2018
371228562^3189+3189^28562100072Hans Havermann05/2018
37136^128565-127100044Lelio R Paula08/2016
37142^332309-133100035Lelio R Paula02/2011
37152^332307+731100035Lelio R Paula07/2011
37162^332301+12927100033Lelio R Paula04/2013
371723406^18781+18781^23406100031Hans Havermann04/2018
37182^332277-4573100026Yves Minet03/2019
371912^92684-13100023Lelio R Paula07/2016
372078557*2^332193+55669100005Jorge Menendez04/2019
372178557*2^332192+72689100005Jorge Menendez04/2019
372210^100003+45799100004Stefano Morozzi04/2019
372310^100003+155461100004Stefano Morozzi04/2019
372410^100003+211389100004Stefano Morozzi04/2019
372510^100003+381027100004Stefano Morozzi04/2019
372610^100003+540703100004Stefano Morozzi04/2019
372710^100003+823977100004Stefano Morozzi04/2019
373810^100002+236023100003Stefano Morozzi05/2018
373910^100002+433741100003Stefano Morozzi05/2018
37282^332202+104659100003Stefano Morozzi04/2019
37292^332202+857539100003Stefano Morozzi04/2019
37302^332202+181773100003Stefano Morozzi04/2019
37312^332202+687543100003Stefano Morozzi04/2019
37322^332202+941595100003Stefano Morozzi04/2019
37332^332202+445813100003Stefano Morozzi04/2019
37342^332202+1599727100003Stefano Morozzi04/2019
37352^332202+1389567100003Stefano Morozzi04/2019
37362^332202+1206315100003Stefano Morozzi04/2019
37372^332202+1958647100003Stefano Morozzi04/2019
3740(10^100002-1)/9-10^33441100002Akihiko Yoshida03/2018
3741(10^100002-1)/9-10^44692100002Akihiko Yoshida03/2018
374210^100002-249519100002Patrick De Geest07/2018
374310^100001+314199100002Patrick De Geest07/2018
374410^100000+11187931100001Robert Price03/2018
374510^100000+11264721100001Robert Price04/2018
374610^100000+11477661100001Robert Price05/2018
374710^100000+11644653100001Robert Price07/2018
374810^100001-431439100001Patrick De Geest07/2018
374910^100000+11769399100001Robert Price08/2018
375010^100000+11848159100001Robert Price08/2018


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Created by  Henri Lifchitz & Renaud Lifchitz : October, 26 2000, last modification: June, 18 2019 07:14 (Time in France)

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