PRP Records

Probable Primes Top 10000

(271000 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 ?
40012^344196-465103614Lelio R Paula11/2016
40022^344187-20001103611Enzo Doria06/2013
4003(117191#+(355573#)/(117191#))/(200233679)103602Makoto Morimoto10/2017
400420^79621-19^79621103590Jean-Louis Charton03/2011
4005Phi(155391,10)/1243129103586Maksym Voznyy09/2015
40062^344085-20365103580Enzo Doria06/2013
40075^148169+54103566Lelio R Paula11/2016
40082^344017-108795103560Enzo Doria03/2014
4009(2^343974+2670)/2103547Stefano Morozzi09/2020
40102^343971-5077103546Lelio R Paula09/2011
4011(7*10^103531+71)/3103532Robert Price05/2018
40122^343899+141103524Lelio R Paula08/2011
4013(2^343933+1)/(3*98294339989393)103520Gord Palameta08/2018
40146^133029-67103517Lelio R Paula11/2016
4015(17*2^343877+1)/13625103515Lelio R Paula12/2013
401666*10^103507+7103509Robert Price07/2020
401726297^8614+8614^26297103485Hans Havermann09/2020
4018(2^343764+2658)/2103483Stefano Morozzi09/2020
401926499^8036+8036^26499103480Hans Havermann09/2020
4020(136*10^103474-1)/9103476Serge Batalov12/2014
40215^148014-24103458Lelio R Paula11/2016
402228316^4503+4503^28316103453Hans Havermann09/2020
4023(22*10^103450+53)/3103451Robert Price07/2019
40242^343604+9931103436Yves Minet01/2011
40252^343601-21189103435Enzo Doria06/2013
40262^343508-115229103407Enzo Doria06/2015
4027(509203*2^343491-1)/16147103403Lelio R Paula05/2015
40283^216685-113056103386Enzo Doria07/2014
402924829^14580+14580^24829103382Hans Havermann08/2020
403091355!4+1024103381Robert Price09/2019
403144^62903-43^62903103379Jean-Louis Charton08/2012
403211^99262-20103371Lelio R Paula12/2016
4033(509203*2^343357-1)/5103366Lelio R Paula05/2015
4034(2^343363+3570)/2103363Stefano Morozzi09/2020
40362^343356-2791889103361Enzo Doria03/2016
4035(25*10^103360-241)/9103361Robert Price05/2018
4037Phi(104989,10)/2939693103350Maksym Voznyy09/2015
403824826^14511+14511^24826103319Hans Havermann09/2020
40392^343182-171103309Lelio R Paula08/2011
4040(23619^23619+23620^23620)/7187103294David Broadhurst09/2009
40412^343079-1835611103278Enzo Doria05/2015
40422^343063-1147103273Yves Minet06/2013
404324741^14930+14930^24741103271Hans Havermann09/2020
4044(16*10^103255-73)/3103256Robert Price07/2020
40459*6^132689+7103254Lelio R Paula11/2014
40462^342979-18085103247Enzo Doria05/2013
4047(16*10^103244-31)/3103245Robert Price03/2019
40482^342966-16995103244Lelio R Paula11/2016
404923797^21774+21774^23797103230Hans Havermann09/2020
405025388^11637+11637^25388103224Hans Havermann09/2020
4051(2^342876+2086)/2103216Stefano Morozzi09/2020
4052(16*10^103214-31)/3103215Robert Price03/2019
4054(37*10^103211+611)/9103212Robert Price11/2018
4053(238*10^103210-1)/3103212Robert Price04/2020
40555^147650+16103203Lelio R Paula11/2016
4056gcd(Phi(852060,10),(10^42603+1)^3*(10^42603+1-10^21302)+(10^85206+10^42603)*(10^21302+1)+10^127809)103201Serge Batalov04/2015
40572^342817+2707067103199Enzo Doria03/2016
405843^63177-42103198Theodore Burton02/2007
40592^342805-21025103195Enzo Doria06/2013
40602^342714+12285103168Lelio R Paula11/2016
406118^82178-4481103156Enzo Doria03/2013
40622^342665-17349103153Enzo Doria05/2013
406330408^2467+2467^30408103150Hans Havermann09/2020
4064(2^342615+3090)/2103138Stefano Morozzi09/2020
40652^342612+175103137Lelio R Paula08/2011
40665*2^342585-3103130Lelio R Paula09/2014
4067(16*10^103127+77)/3103128Robert Price03/2019
40682^342503-19209103104Enzo Doria05/2013
4069(2^342484+2586)/2103098Stefano Morozzi09/2020
40702^342476+51103096Lelio R Paula08/2011
40712^342460-18885103091Enzo Doria05/2013
4072(194*10^103074-17)/3103076Robert Price09/2020
40737^121968+82103075Lelio R Paula10/2016
40742^342392-108863103071Enzo Doria03/2014
40753^216014+28103065Lelio R Paula11/2016
40762^342353-108879103059Enzo Doria03/2014
407710^103055+276081103056Patrick De Geest12/2016
407810^103055-53103055Lelio R Paula11/2016
4079(58*10^103046+419)/9103047Robert Price05/2019
40807^121933+4103046Lelio R Paula11/2014
4081(2^342235+3618)/2103023Stefano Morozzi09/2020
408219^80560-68103017Lelio R Paula10/2016
40832^342209+76607103016Enzo Doria05/2016
4085328^40945+40945^328103013Norbert Schneider12/2014
408412^95454-91103013Lelio R Paula10/2016
408625833^9716+9716^25833103009Hans Havermann01/2019
408765^56809-64^56809102990Robert Price08/2013
40885^147338-6102985Lelio R Paula11/2014
40892^342084-112739102978Enzo Doria06/2014
40909*6^132330+7102974Lelio R Paula11/2014
40912^342034-16737102963Enzo Doria05/2013
4092(9787*2^342011-1)/25102959Lelio R Paula05/2015
4093(3^215802-5)/124343756102956Lelio R Paula12/2013
40942^341991-17421102950Enzo Doria05/2013
40952^341969-112225102943Enzo Doria06/2014
4096(9787*2^341864-1)/3102915Lelio R Paula05/2015
40972^341859+1869413102910Enzo Doria05/2016
409810^102909+61102910Lelio R Paula11/2016
409910^102909-67049102909Patrick De Geest12/2016
410023814^20935+20935^23814102898Hans Havermann02/2019
410128345^4264+4264^28345102888Hans Havermann02/2019
410225665^10204+10204^25665102886Hans Havermann02/2019
410326288^8181+8181^26288102860Hans Havermann02/2019
41042^341659+1836773102850Enzo Doria03/2016
41052^341608-110639102835Enzo Doria05/2014
410610^102824+49102825Lelio R Paula11/2016
410710^102824-168011102824Patrick De Geest12/2016
410811^98708-8102794Lelio R Paula10/2016
41092^341466+4429102792Lelio R Paula09/2011
41102^341460-107102790Lelio R Paula08/2011
4111(2^341388+47)/21014943102761Lelio R Paula12/2013
41122^341355+21102759Lelio R Paula08/2011
41132^341246+40755102726Lelio R Paula11/2016
4114(2^341256-5)/991699102723Lelio R Paula12/2013
41157^121547+78102720Lelio R Paula10/2016
41162^341223-461197102719Enzo Doria06/2015
411727838^4893+4893^27838102711Hans Havermann03/2019
41192^341190-20577102709Enzo Doria06/2013
4118(27*2^341212+1)/84674449102709Lelio R Paula12/2013
41206^131976-65102698Lelio R Paula10/2016
41212^341134+2533102692Henri Lifchitz09/2005
412213^92184-54102688Lelio R Paula10/2016
41232^341116-20873102687Enzo Doria06/2013
41242^341094-19953102680Enzo Doria06/2013
412523761^20950+20950^23761102676Hans Havermann03/2019
41262^341053+129102668Lelio R Paula08/2011
4128(31*2^341006-1)/3102655Lelio R Paula03/2014
41277^121471+94102655Lelio R Paula10/2016
41302^341004-173102653Lelio R Paula08/2011
412920^78901+3102653Lelio R Paula10/2016
4131(2^341001+1674)/2102652Stefano Morozzi09/2020
41325^146853-52102646Lelio R Paula10/2016
41332^340969-216931102642Enzo Doria05/2014
4134122^49196+121102641Norbert Schneider10/2018
41352^340952+1870021102637Enzo Doria05/2016
41365*2^340940-3102634Lelio R Paula08/2014
4137(6^131891+1)/7102631Paul Bourdelais01/2010
413825876^9239+9239^25876102615Hans Havermann02/2019
4139(4*10^102612+83)/3102613Robert Price02/2018
414075^54717+74102598Norbert Schneider01/2015
4141(17*10^102597+13)/3102598Robert Price01/2019
41422^340806-20393102593Enzo Doria06/2013
4143(2^340790+5)/138267102583Lelio R Paula12/2013
41446^131821+77102577Lelio R Paula10/2016
41452^340688-29102558Henri Lifchitz05/2005
41462^340685-109101102557Enzo Doria04/2014
414765^56567-64102552Norbert Schneider11/2014
414826230^8121+8121^26230102550Hans Havermann03/2019
4149(8*10^102541+49)/3102542Robert Price05/2020
4150(536*10^102533-23)/9102535Robert Price02/2020
41512^340547-108897102515Enzo Doria03/2014
4152(2^340536+778)/2102512Stefano Morozzi09/2020
415325592^10119+10119^25592102500Hans Havermann02/2019
41547^121268+82102484Lelio R Paula10/2016
4155(6883*2^340443-1)/162401102483Lelio R Paula05/2015
41562^340434-5955102481Lelio R Paula11/2016
4157(2^340381+47)/7102465Lelio R Paula12/2013
4158111^50095+110102461Norbert Schneider04/2017
41592^340291-20301102438Enzo Doria06/2013
416012^94915+89102431Lelio R Paula10/2016
416124466^15349+15349^24466102417Hans Havermann03/2019
41622^340208-20373102413Enzo Doria06/2013
41636^131598-17273102404Enzo Doria02/2013
4164(2^340132+1182)/2102390Stefano Morozzi09/2020
4165(2^340133+1166)/2102390Stefano Morozzi09/2020
41662^340115-21181102385Enzo Doria06/2013
4167(55459*2^340090+1)/1591102379Lelio R Paula07/2014
4168(2^340064+3630)/2102370Stefano Morozzi09/2020
416989^52511-88^52511102365Robert Price06/2015
41703^214539-112756102362Enzo Doria07/2014
417123159^23450-23450^23159102353Norbert Schneider12/2019
41722^340000-19877102351Enzo Doria06/2013
41732^339990-114845102348Enzo Doria05/2015
4174(3^214516-2)/51383102346Lelio R Paula12/2013
417520^78661-99102341Lelio R Paula09/2016
41762^339951-19585102336Enzo Doria05/2013
4177(13*2^339943+1)/45102333Lelio R Paula12/2013
4178(236282#+121441)/(121441*25499429)102332Makoto Morimoto08/2020
41802^339889+29327102317Yves Minet06/2010
4179(167*10^102315-17)/3102317Robert Price03/2020
418126348^7641+7641^26348102314Hans Havermann03/2019
4182Phi(239414,10)/6333218543102303Makoto Kamada08/2019
41832^339834-109493102301Enzo Doria04/2014
4184(16*10^102299-19)/3102300Robert Price02/2019
4185(11^98221-5^98221)/6102286Robert Price01/2013
41863^214365+1820102279Lelio R Paula10/2016
418731978^1579+1579^31978102278Hans Havermann03/2019
4188(11*2^339705-1)/183102261Lelio R Paula03/2014
41892^339694-16995102259Lelio R Paula09/2016
4190(56*10^102255+691)/9102256Robert Price05/2019
4191122^49008+121102249Norbert Schneider10/2018
4192(2^339652+3178)/2102246Stefano Morozzi09/2020
41947^120985-38102245Lelio R Paula10/2016
419310^102244+122961102245Patrick De Geest12/2016
419510^102244-27102244Lelio R Paula09/2016
41967^120982-62102242Lelio R Paula10/2016
4197(2^339640+2670)/2102242Stefano Morozzi09/2020
41984*6^131382-5102236Lelio R Paula11/2014
41992^339586-1091102226Yves Minet11/2012
420011^98161-3072000102225Enzo Doria12/2012
42019*7^120961-4102225Lelio R Paula11/2014
42025*3^214250+2102224Serge Batalov10/2010
420312^94713-59102213Lelio R Paula10/2016
420412^94705+89102204Lelio R Paula10/2016
42052^339407-177102172Lelio R Paula08/2011
42064*10^102163-57102164Robert Price10/2018
42072^339355+65102157Lelio R Paula07/2011
4208(28*10^102142-31)/3102143Robert Price12/2019
4209(2^339323+47)/880715102141Lelio R Paula12/2013
4210(2^339268+1758)/2102130Stefano Morozzi09/2020
4211s(178551)102122Robert Price05/2020
42142^339168+21102100Lelio R Paula07/2011
42132^339167-108807102100Enzo Doria03/2014
4212(2^339169+42)/2102100Stefano Morozzi09/2020
42152^339156+163102097Lelio R Paula08/2011
4216(2^339149+746)/2102094Stefano Morozzi09/2020
4217(25*10^102076-67)/3102077Robert Price06/2019
42182^339081-4543102074Yves Minet03/2019
42192*10^102062+77102063Robert Price08/2020
422024327^15668+15668^24327102053Hans Havermann02/2019
422125080^11711+11711^25080102041Hans Havermann02/2019
4222(2^338982-7)/1754517102038Lelio R Paula12/2013
42232^338891-18885102017Enzo Doria05/2013
42248*10^102000+51102001Robert Price08/2019
4225(2^338832+642)/2101999Stefano Morozzi09/2020
42262^338829-113239101998Enzo Doria07/2014
42272^338828-113297101998Enzo Doria07/2014
42282^338796+93101988Donovan Johnson06/2008
4229lucasU(1373,1,32502)-lucasU(1373,1,32501)101978Mike Oakes05/2009
423025295^10744+10744^25295101969Hans Havermann01/2019
423125712^9243+9243^25712101969Hans Havermann01/2019
4232(71^55079-1)/70101964Paul Bourdelais08/2017
42332^338682-19865101954Enzo Doria06/2013
4234(2^(112895*3+1)+243)/7101954Kevin Acres12/2013
4235(2^338666+3154)/2101949Stefano Morozzi09/2020
423628594^3673+3673^28594101939Hans Havermann02/2019
42372^338568+37101920Lelio R Paula07/2011
42382^338559-1858777101917Enzo Doria04/2016
4239(9*2^338520+1)/365101904Lelio R Paula12/2013
424024502^14419+14419^24502101903Hans Havermann01/2019
42412^338497-17041101898Enzo Doria05/2013
42422^338475+54615101892Lelio R Paula10/2016
42432^338426-19797101877Enzo Doria06/2013
42442^338368-20369101859Enzo Doria06/2013
42452^338366+74179101859Enzo Doria04/2016
424627088^5755+5755^27088101853Hans Havermann01/2019
42472^338280-19745101833Enzo Doria06/2013
4248(3*2^338236-1)/347101818Lelio R Paula03/2014
42496^130841+103101815Lelio R Paula10/2016
42502^338122-20117101785Enzo Doria06/2013


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Created by  Henri Lifchitz & Renaud Lifchitz : October, 26 2000, last modification: September, 29 2020 00:24 (Time in France)

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