PRP Records

Probable Primes Top 10000

(277054 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 ?
450123814^20935+20935^23814102898Hans Havermann02/2019
450228345^4264+4264^28345102888Hans Havermann02/2019
450325665^10204+10204^25665102886Hans Havermann02/2019
450426288^8181+8181^26288102860Hans Havermann02/2019
45052^341659+1836773102850Enzo Doria03/2016
45062^341608-110639102835Enzo Doria05/2014
450710^102824+49102825Lelio R Paula11/2016
450810^102824-168011102824Patrick De Geest12/2016
450911^98708-8102794Lelio R Paula10/2016
45102^341466+4429102792Lelio R Paula09/2011
45112^341460-107102790Lelio R Paula08/2011
4512(2^341388+47)/21014943102761Lelio R Paula12/2013
45132^341355+21102759Lelio R Paula08/2011
45142^341246+40755102726Lelio R Paula11/2016
4515(2^341256-5)/991699102723Lelio R Paula12/2013
45167^121547+78102720Lelio R Paula10/2016
45172^341223-461197102719Enzo Doria06/2015
451827838^4893+4893^27838102711Hans Havermann03/2019
45202^341190-20577102709Enzo Doria06/2013
4519(27*2^341212+1)/84674449102709Lelio R Paula12/2013
45216^131976-65102698Lelio R Paula10/2016
45222^341134+2533102692Henri Lifchitz09/2005
452313^92184-54102688Lelio R Paula10/2016
45242^341116-20873102687Enzo Doria06/2013
45252^341094-19953102680Enzo Doria06/2013
452623761^20950+20950^23761102676Hans Havermann03/2019
45272^341053+129102668Lelio R Paula08/2011
4529(31*2^341006-1)/3102655Lelio R Paula03/2014
45287^121471+94102655Lelio R Paula10/2016
45312^341004-173102653Lelio R Paula08/2011
453020^78901+3102653Lelio R Paula10/2016
4532(2^341001+1674)/2102652Stefano Morozzi09/2020
45335^146853-52102646Lelio R Paula10/2016
45342^340969-216931102642Enzo Doria05/2014
4535122^49196+121102641Norbert Schneider10/2018
45362^340952+1870021102637Enzo Doria05/2016
45375*2^340940-3102634Lelio R Paula08/2014
4538(6^131891+1)/7102631Paul Bourdelais01/2010
453925876^9239+9239^25876102615Hans Havermann02/2019
4540(4*10^102612+83)/3102613Robert Price02/2018
454175^54717+74102598Norbert Schneider01/2015
4542(17*10^102597+13)/3102598Robert Price01/2019
45432^340806-20393102593Enzo Doria06/2013
4544(2^340790+5)/138267102583Lelio R Paula12/2013
45456^131821+77102577Lelio R Paula10/2016
4546(203*10^102561-11)/3102563Robert Price12/2020
45472^340688-29102558Henri Lifchitz05/2005
45482^340685-109101102557Enzo Doria04/2014
454965^56567-64102552Norbert Schneider11/2014
455026230^8121+8121^26230102550Hans Havermann03/2019
4551(8*10^102541+49)/3102542Robert Price05/2020
4552(536*10^102533-23)/9102535Robert Price02/2020
45532^340547-108897102515Enzo Doria03/2014
4554(2^340536+778)/2102512Stefano Morozzi09/2020
455525592^10119+10119^25592102500Hans Havermann02/2019
45567^121268+82102484Lelio R Paula10/2016
4557(6883*2^340443-1)/162401102483Lelio R Paula05/2015
45592^340434-5955102481Lelio R Paula11/2016
4558(7*10^102480-19)/3102481Robert Price10/2020
4560(2^340381+47)/7102465Lelio R Paula12/2013
4561111^50095+110102461Norbert Schneider04/2017
45622^340291-20301102438Enzo Doria06/2013
456312^94915+89102431Lelio R Paula10/2016
456424466^15349+15349^24466102417Hans Havermann03/2019
45652^340208-20373102413Enzo Doria06/2013
45666^131598-17273102404Enzo Doria02/2013
4567(2^340132+1182)/2102390Stefano Morozzi09/2020
4568(2^340133+1166)/2102390Stefano Morozzi09/2020
45692^340115-21181102385Enzo Doria06/2013
4570(55459*2^340090+1)/1591102379Lelio R Paula07/2014
4571(2^340064+3630)/2102370Stefano Morozzi09/2020
457289^52511-88^52511102365Robert Price06/2015
45733^214539-112756102362Enzo Doria07/2014
457423159^23450-23450^23159102353Norbert Schneider12/2019
45752^340000-19877102351Enzo Doria06/2013
45762^339990-114845102348Enzo Doria05/2015
4577(3^214516-2)/51383102346Lelio R Paula12/2013
457820^78661-99102341Lelio R Paula09/2016
45792^339951-19585102336Enzo Doria05/2013
4580(13*2^339943+1)/45102333Lelio R Paula12/2013
4581(236282#+121441)/(121441*25499429)102332Makoto Morimoto08/2020
45832^339889+29327102317Yves Minet06/2010
4582(167*10^102315-17)/3102317Robert Price03/2020
458426348^7641+7641^26348102314Hans Havermann03/2019
4585Phi(239414,10)/6333218543102303Makoto Kamada08/2019
45862^339834-109493102301Enzo Doria04/2014
4587(16*10^102299-19)/3102300Robert Price02/2019
4588(11^98221-5^98221)/6102286Robert Price01/2013
45893^214365+1820102279Lelio R Paula10/2016
459031978^1579+1579^31978102278Hans Havermann03/2019
4591(11*2^339705-1)/183102261Lelio R Paula03/2014
45922^339694-16995102259Lelio R Paula09/2016
4593(56*10^102255+691)/9102256Robert Price05/2019
4594122^49008+121102249Norbert Schneider10/2018
4595(2^339652+3178)/2102246Stefano Morozzi09/2020
45977^120985-38102245Lelio R Paula10/2016
459610^102244+122961102245Patrick De Geest12/2016
459810^102244-27102244Lelio R Paula09/2016
45997^120982-62102242Lelio R Paula10/2016
4600(2^339640+2670)/2102242Stefano Morozzi09/2020
46014*6^131382-5102236Lelio R Paula11/2014
46022^339586-1091102226Yves Minet11/2012
460311^98161-3072000102225Enzo Doria12/2012
46049*7^120961-4102225Lelio R Paula11/2014
46055*3^214250+2102224Serge Batalov10/2010
460612^94713-59102213Lelio R Paula10/2016
460712^94705+89102204Lelio R Paula10/2016
46082^339407-177102172Lelio R Paula08/2011
46094*10^102163-57102164Robert Price10/2018
46102^339355+65102157Lelio R Paula07/2011
4611(28*10^102142-31)/3102143Robert Price12/2019
4612(2^339323+47)/880715102141Lelio R Paula12/2013
4613(2^339268+1758)/2102130Stefano Morozzi09/2020
4614s(178551)102122Robert Price05/2020
46172^339168+21102100Lelio R Paula07/2011
46162^339167-108807102100Enzo Doria03/2014
4615(2^339169+42)/2102100Stefano Morozzi09/2020
46182^339156+163102097Lelio R Paula08/2011
4619(2^339149+746)/2102094Stefano Morozzi09/2020
4620(25*10^102076-67)/3102077Robert Price06/2019
46212^339081-4543102074Yves Minet03/2019
46222*10^102062+77102063Robert Price08/2020
462324327^15668+15668^24327102053Hans Havermann02/2019
462425080^11711+11711^25080102041Hans Havermann02/2019
4625(2^338982-7)/1754517102038Lelio R Paula12/2013
46262^338891-18885102017Enzo Doria05/2013
46278*10^102000+51102001Robert Price08/2019
4628(2^338832+642)/2101999Stefano Morozzi09/2020
46292^338829-113239101998Enzo Doria07/2014
46302^338828-113297101998Enzo Doria07/2014
46312^338796+93101988Donovan Johnson06/2008
4632lucasU(1373,1,32502)-lucasU(1373,1,32501)101978Mike Oakes05/2009
463325295^10744+10744^25295101969Hans Havermann01/2019
463425712^9243+9243^25712101969Hans Havermann01/2019
4635(71^55079-1)/70101964Paul Bourdelais08/2017
46362^338682-19865101954Enzo Doria06/2013
4637(2^(112895*3+1)+243)/7101954Kevin Acres12/2013
4638(2^338666+3154)/2101949Stefano Morozzi09/2020
463928594^3673+3673^28594101939Hans Havermann02/2019
46402^338568+37101920Lelio R Paula07/2011
46412^338559-1858777101917Enzo Doria04/2016
4642(9*2^338520+1)/365101904Lelio R Paula12/2013
464324502^14419+14419^24502101903Hans Havermann01/2019
46442^338497-17041101898Enzo Doria05/2013
46452^338475+54615101892Lelio R Paula10/2016
46462^338426-19797101877Enzo Doria06/2013
46472^338368-20369101859Enzo Doria06/2013
46482^338366+74179101859Enzo Doria04/2016
464927088^5755+5755^27088101853Hans Havermann01/2019
46502^338280-19745101833Enzo Doria06/2013
4651(3*2^338236-1)/347101818Lelio R Paula03/2014
46526^130841+103101815Lelio R Paula10/2016
46532^338122-20117101785Enzo Doria06/2013
4654(2^338139+5)/905333101785Lelio R Paula12/2013
465535^65917-7092101781Enzo Doria03/2013
46562^338010-19833101752Enzo Doria06/2013
46573^213215-76101730Lelio R Paula09/2016
465823907^17998+17998^23907101730Hans Havermann01/2019
465910^101728+154953101729Patrick De Geest02/2020
46622^337930+63101728Lelio R Paula07/2011
466010^101728-987654321101728Robert Price12/2019
466110^101728-60741101728Patrick De Geest02/2020
46632^337920+1869661101725Enzo Doria05/2016
466424116^16509+16509^24116101715Hans Havermann01/2019
4665(2^337875+3174)/2101711Stefano Morozzi09/2020
46662^337859-19645101706Enzo Doria05/2013
46672^337754+1869169101675Enzo Doria05/2016
46683*10^101657-37101658Robert Price07/2018
4669(31*2^337677-1)/593101650Lelio R Paula03/2014
467011^97605-24101646Lelio R Paula10/2016
4671(2^337624+3606)/2101635Stefano Morozzi09/2020
46728^112539-112539101633Robert Price01/2014
467325694^9003+9003^25694101605Hans Havermann12/2018
46742^337515-19869101603Enzo Doria06/2013
46752^337473+719101590Lelio R Paula08/2011
4676(2^337485-509203)/656647157101585Lelio R Paula12/2013
46772^337452-108815101584Enzo Doria03/2014
46782^337453+1185101584Lelio R Paula09/2016
46792^337410-113561101571Enzo Doria08/2014
46802^337387+855101564Lelio R Paula09/2016
46812^337367-17295101558Lelio R Paula09/2016
46822^337342-109035101551Enzo Doria04/2014
468323703^19238+19238^23703101548Hans Havermann12/2018
4684(26*10^101537-167)/3101538Robert Price10/2019
46852^337267-19101528Lelio R Paula07/2011
4686(2^337259+1766)/2101525Stefano Morozzi09/2020
4687(2^337195+2646)/2101506Stefano Morozzi09/2020
46882^337183-19989101503Enzo Doria06/2013
46892^337149+72425101492Enzo Doria04/2016
469024041^16642+16642^24041101483Hans Havermann12/2018
469133982^969+969^33982101482Hans Havermann12/2018
46922^337101-20241101478Enzo Doria06/2013
46932^337035-20001101458Enzo Doria06/2013
4694(7*10^101456+89)/3101457Robert Price08/2020
46952^337017-16995101453Lelio R Paula09/2016
46962^336979-115315101441Enzo Doria06/2015
46972^336970-20885101439Enzo Doria06/2013
46982^336958+79101435Lelio R Paula10/2009
46992^336942+169101430Lelio R Paula10/2009
4700(15185*2^336894-1)/7939101416Lelio R Paula05/2015
47014*10^101415-89101416Robert Price11/2018
4702(14*10^101410-89)/3101411Robert Price05/2020
47032^336871+257463101409Tony Prest / Never Odd Or Even04/2016
47042^336871+318105101409Tony Prest / Never Odd Or Even04/2016
47052^336871+1010813101409Tony Prest / Never Odd Or Even04/2016
47062^336871+2302245101409Tony Prest / Never Odd Or Even04/2016
47072^336871+389273101409Tony Prest / Never Odd Or Even04/2016
47082^336871+1685475101409Tony Prest / Never Odd Or Even04/2016
47092^336871+1068119101409Tony Prest / Never Odd Or Even04/2016
47102^336871+586905101409Tony Prest / Never Odd Or Even04/2016
47112^336871+674571101409Tony Prest / Never Odd Or Even04/2016
47122^336871+707009101409Tony Prest / Never Odd Or Even04/2016
47132^336871+1210299101409Tony Prest / Never Odd Or Even04/2016
47142^336871+1921185101409Tony Prest / Never Odd Or Even04/2016
47152^336871+2003973101409Tony Prest / Never Odd Or Even04/2016
47162^336871+2656475101409Tony Prest / Never Odd Or Even04/2016
47172^336871+2703023101409Tony Prest / Never Odd Or Even04/2016
47182^336871+2704545101409Tony Prest / Never Odd Or Even04/2016
47192^336871+2766801101409Tony Prest / Never Odd Or Even04/2016
47202^336871+2127735101409Tony Prest / Never Odd Or Even04/2016
4721(2^336871+821089)/3101408Tony Prest / Never Odd Or Even05/2016
4722(2^336871+119567)/5101408Tony Prest / Never Odd Or Even05/2016
4723(2^336871+398161)/3101408Tony Prest / Never Odd Or Even05/2016
4724(2^336871+625889)/7101408Tony Prest / Never Odd Or Even05/2016
472524097^16150+16150^24097101405Hans Havermann12/2018
47262^336842+94065101400Lelio R Paula09/2016
4727(2^336871+904417)/3/3/3/5/19/9287177/9690011663/29993043103101378Tony Prest / Never Odd Or Even04/2016
4728(2^336871+631971)/13/251/1601/294277/614362921/30324278867101377Tony Prest / Never Odd Or Even04/2016
4729(2^336871+1443541)/3/89/1655197/11018131/47972707/468862691879101374Tony Prest / Never Odd Or Even04/2016
4730(2^336871+689863)/3/11/109/137/1867/7151/20800501/29243857/127778489101373Tony Prest / Never Odd Or Even04/2016
4731(2^336871+219839)/191/643/3011/9479/117127/175750007/4578271757101373Tony Prest / Never Odd Or Even04/2016
4732(2^336871+272895)/19/661/977572033/95853078653/520779768241101373Tony Prest / Never Odd Or Even04/2016
4733(2^336871+1023429)/2311/415873/991889/3630648341/207732189179101373Tony Prest / Never Odd Or Even04/2016
473410^101369+203811101370Patrick De Geest11/2016
473510^101369-99101369Lelio R Paula09/2016
4736(2^336871+1832627)/5/5/23/181/4397/91373/3746673331/115602484097/279351383917101363Tony Prest / Never Odd Or Even04/2016
47372^336701-113563101358Enzo Doria08/2014
473889717!4-512101351Robert Price11/2019
47392^336644-109023101340Enzo Doria04/2014
47402^336601-21081101327Enzo Doria06/2013
474120^77869+63101310Lelio R Paula09/2016
4742(13*2^336523-1)/19101304Lelio R Paula03/2014
47446^130179-137101299Lelio R Paula10/2016
4743(2^336506+lucasV(1,2,336506)+1)/2101299Mike Oakes11/2016
4745(24737*2^336485+1)/7285101293Lelio R Paula07/2014
4746(2^336448+9)/497405101276Lelio R Paula12/2013
47472^336369-19753101258Enzo Doria05/2013
474823842^17653+17653^23842101253Hans Havermann11/2018
47492^336350-344291101252Enzo Doria07/2015
4750(56*10^101222-47)/9101223Robert Price02/2019


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Created by  Henri Lifchitz & Renaud Lifchitz : October, 26 2000, last modification: January, 25 2021 11:23 (Time in France)

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