PRP Records

Probable Primes Top 10000

(295176 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 ?
7001(2^345267-9)/539049127103927Lelio R Paula12/2013
7002(19*10^103907+77)/3103908Robert Price05/2019
7003(78557*2^345163+1)/78589103905Lelio R Paula07/2014
70042^345106-112181103888Enzo Doria06/2014
7005(2^345105+1326)/2103887Stefano Morozzi02/2021
70062^345079+99103880Lelio R Paula09/2011
7007(2^345034+1198)/2103866Stefano Morozzi09/2020
700811^99736-1500103865Enzo Doria12/2012
7009(569^37699-1)/568103863Serge Batalov06/2022
7010(2^345010+2082)/2103859Stefano Morozzi09/2020
701123263^23784-23784^23263103857Norbert Schneider01/2020
70123*10^103844+31103845Robert Price06/2021
7013444*33^68368+19103821Eric Chen05/2023
701423927^21814+21814^23927103813Hans Havermann09/2020
70152^344842-20157103808Enzo Doria06/2013
7016(47*2^344822+1)/1071103801Lelio R Paula05/2015
70172^344802-20765103796Enzo Doria06/2013
70182^344794-3821103794Yves Minet05/2011
70192^344782-109103103790Enzo Doria04/2014
70203^217521-112292103784Enzo Doria06/2014
70212^344759-3505103783Lelio R Paula11/2016
70222^344735-147103776Lelio R Paula09/2011
7023L(496533)-p(496533)103770Robert Price02/2018
70242*10^103749-69103750Robert Price03/2018
7025(55459*2^344617+1)/3103745Lelio R Paula07/2014
70262^344607-108891103738Enzo Doria03/2014
7028(2^344608+3798)/2103738Stefano Morozzi02/2021
7027(1097^34123-1)/1096103738Serge Batalov06/2022
70292^344560+22411103723Enzo Doria09/2023
7030(148*10^103718-1)/3103720Robert Price03/2020
70312^344541-19561103718Enzo Doria05/2013
7032(1017*2^344529-1)/569103714Lelio R Paula05/2015
7033(8896^26263-1)/8895103714Serge Batalov06/2022
7034(2^344503+1758)/2103706Stefano Morozzi09/2020
7035(4*10^103703-1)/3103704Serge Batalov08/2009
70362^344444-455103688Yves Minet03/2012
7037(4*10^103678-43)/3103679Robert Price01/2022
7038(13*53^238539*617^9)/10^307661103673Hans Havermann06/2017
7039(2^344367+2738)/2103665Stefano Morozzi01/2021
70412^344317-109933103650Enzo Doria04/2014
704026055^9508+9508^26055103650Hans Havermann09/2020
70422^344309-1852033103648Enzo Doria08/2015
704325729^10672+10672^25729103643Hans Havermann09/2020
7044(2^344289+1166)/2103642Stefano Morozzi09/2020
70453*10^103637+61103638Robert Price09/2020
7046(2^344246+1614)/2103629Stefano Morozzi09/2020
70472^344213-21253103619Enzo Doria06/2013
70482^344196-465103614Lelio R Paula11/2016
70492^344187-20001103611Enzo Doria06/2013
7050(117191#+(355573#)/(117191#))/(200233679)103602Makoto Morimoto10/2017
7051(237^43627-1)/236103601Serge Batalov06/2022
705220^79621-19^79621103590Jean-Louis Charton03/2011
7053Phi(155391,10)/1243129103586Maksym Voznyy09/2015
7054(9^108553-2^108553)/7103586Jon Grantham07/2023
70552^344085-20365103580Enzo Doria06/2013
70565^148169+54103566Lelio R Paula11/2016
70572^344017-108795103560Enzo Doria03/2014
7058(2^343974+2670)/2103547Stefano Morozzi09/2020
70592^343971-5077103546Lelio R Paula09/2011
7060(7*10^103531+71)/3103532Robert Price05/2018
70612^343899+141103524Lelio R Paula08/2011
7062(2^343933+1)/(3*98294339989393)103520Gord Palameta08/2018
70636^133029-67103517Lelio R Paula11/2016
7064(17*2^343877+1)/13625103515Lelio R Paula12/2013
706566*10^103507+7103509Robert Price07/2020
706626297^8614+8614^26297103485Hans Havermann09/2020
7067(2^343764+2658)/2103483Stefano Morozzi09/2020
706826499^8036+8036^26499103480Hans Havermann09/2020
7069(136*10^103474-1)/9103476Serge Batalov12/2014
70705^148014-24103458Lelio R Paula11/2016
707128316^4503+4503^28316103453Hans Havermann09/2020
7072(22*10^103450+53)/3103451Robert Price07/2019
70732^343604+9931103436Yves Minet01/2011
70742^343601-21189103435Enzo Doria06/2013
7075(10^103423+173)/3103423Robert Price05/2021
70762^343508-115229103407Enzo Doria06/2015
7077(8766^26227-1)/8765103404Serge Batalov06/2022
7078(509203*2^343491-1)/16147103403Lelio R Paula05/2015
70793^216685-113056103386Enzo Doria07/2014
708024829^14580+14580^24829103382Hans Havermann08/2020
708191355!4+1024103381Robert Price09/2019
708244^62903-43^62903103379Jean-Louis Charton08/2012
708311^99262-20103371Lelio R Paula12/2016
7084(509203*2^343357-1)/5103366Lelio R Paula05/2015
7085(2^343363+3570)/2103363Stefano Morozzi09/2020
70862^343356-2791889103361Enzo Doria03/2016
7087(25*10^103360-241)/9103361Robert Price05/2018
7088Phi(104989,10)/2939693103350Maksym Voznyy09/2015
7089(371*33^68040-19)/32103321Eric Chen05/2023
709024826^14511+14511^24826103319Hans Havermann09/2020
70912^343182-171103309Lelio R Paula08/2011
7092(23619^23619+23620^23620)/7187103294David Broadhurst09/2009
7093(16487^24649-1)/(16487^157-1)103287Ryan Propper11/2023
7094(10680^25639-1)/10679103285Serge Batalov06/2022
7095(7427^26683-1)/7426103282Serge Batalov06/2022
70962^343079-1835611103278Enzo Doria05/2015
70972^343063-1147103273Yves Minet06/2013
709824741^14930+14930^24741103271Hans Havermann09/2020
7099(16*10^103255-73)/3103256Robert Price07/2020
7100(219^44119-1)/218103256Serge Batalov06/2022
71019*6^132689+7103254Lelio R Paula11/2014
71022^342979-18085103247Enzo Doria05/2013
7103(16*10^103244-31)/3103245Robert Price03/2019
71042^342966-16995103244Lelio R Paula11/2016
710523797^21774+21774^23797103230Hans Havermann09/2020
710625388^11637+11637^25388103224Hans Havermann09/2020
7107(2^342876+2086)/2103216Stefano Morozzi09/2020
7108(16*10^103214-31)/3103215Robert Price03/2019
7110(37*10^103211+611)/9103212Robert Price11/2018
7109(238*10^103210-1)/3103212Robert Price04/2020
71115^147650+16103203Lelio R Paula11/2016
7112gcd(Phi(852060,10),(10^42603+1)^3*(10^42603+1-10^21302)+(10^85206+10^42603)*(10^21302+1)+10^127809)103201Serge Batalov04/2015
71132^342817+2707067103199Enzo Doria03/2016
711443^63177-42103198Theodore Burton02/2007
71152^342805-21025103195Enzo Doria06/2013
711624129^18890+18890^24129103182Hans Havermann09/2020
7117(622*10^103171-1)/9103173Robert Price11/2021
71182^342714+12285103168Lelio R Paula11/2016
7119(2*10^103161-17)/3103161Serge Batalov11/2022
712018^82178-4481103156Enzo Doria03/2013
71212^342665-17349103153Enzo Doria05/2013
712230408^2467+2467^30408103150Hans Havermann09/2020
7123(5^147571-3^147571)/2103148Kellen Shenton05/2022
7124(2^342615+3090)/2103138Stefano Morozzi09/2020
71252^342612+175103137Lelio R Paula08/2011
71265*2^342585-3103130Lelio R Paula09/2014
7127(16*10^103127+77)/3103128Robert Price03/2019
7128(2^342527+3774)/2103111Stefano Morozzi02/2021
71292^342503-19209103104Enzo Doria05/2013
7130(2^342484+2586)/2103098Stefano Morozzi09/2020
71312^342476+51103096Lelio R Paula08/2011
71322^342460-18885103091Enzo Doria05/2013
7133(2^342442+862)/2103086Stefano Morozzi02/2021
7134(194*10^103074-17)/3103076Robert Price09/2020
71357^121968+82103075Lelio R Paula10/2016
71362^342392-108863103071Enzo Doria03/2014
7137(2^342389+806)/2103070Stefano Morozzi01/2021
71383^216014+28103065Lelio R Paula11/2016
71392^342353-108879103059Enzo Doria03/2014
714010^103055+276081103056Patrick De Geest12/2016
714110^103055-53103055Lelio R Paula11/2016
7142(58*10^103046+419)/9103047Robert Price05/2019
71437^121933+4103046Lelio R Paula11/2014
7144(71*10^103028-143)/9103029Robert Price10/2021
7145(2^342235+3618)/2103023Stefano Morozzi09/2020
714619^80560-68103017Lelio R Paula10/2016
71472^342209+76607103016Enzo Doria05/2016
7149328^40945+40945^328103013Norbert Schneider12/2014
714812^95454-91103013Lelio R Paula10/2016
715025833^9716+9716^25833103009Hans Havermann01/2019
7151(893*10^103004+7)/9103006Robert Price06/2021
7152(1475^32503-1)/1474102993Serge Batalov06/2022
715365^56809-64^56809102990Robert Price08/2013
71545^147338-6102985Lelio R Paula11/2014
71552^342084-112739102978Enzo Doria06/2014
71569*6^132330+7102974Lelio R Paula11/2014
71572^342034-16737102963Enzo Doria05/2013
7158(9787*2^342011-1)/25102959Lelio R Paula05/2015
7159(3^215802-5)/124343756102956Lelio R Paula12/2013
71602^341991-17421102950Enzo Doria05/2013
71612^341969-112225102943Enzo Doria06/2014
7162(9787*2^341864-1)/3102915Lelio R Paula05/2015
71632^341859+1869413102910Enzo Doria05/2016
716410^102909+61102910Lelio R Paula11/2016
716510^102909-67049102909Patrick De Geest12/2016
716623814^20935+20935^23814102898Hans Havermann02/2019
716728345^4264+4264^28345102888Hans Havermann02/2019
716825665^10204+10204^25665102886Hans Havermann02/2019
716926288^8181+8181^26288102860Hans Havermann02/2019
71702^341659+1836773102850Enzo Doria03/2016
71712^341608-110639102835Enzo Doria05/2014
717210^102824+49102825Lelio R Paula11/2016
717310^102824-168011102824Patrick De Geest12/2016
717411^98708-8102794Lelio R Paula10/2016
71752^341466+4429102792Lelio R Paula09/2011
71762^341460-107102790Lelio R Paula08/2011
7177(2^341388+47)/21014943102761Lelio R Paula12/2013
71782^341355+21102759Lelio R Paula08/2011
7179(6496^26947-1)/6495102736Serge Batalov06/2022
71802^341246+40755102726Lelio R Paula11/2016
7181(2^341256-5)/991699102723Lelio R Paula12/2013
71827^121547+78102720Lelio R Paula10/2016
71832^341223-461197102719Enzo Doria06/2015
718427838^4893+4893^27838102711Hans Havermann03/2019
71862^341190-20577102709Enzo Doria06/2013
7185(27*2^341212+1)/84674449102709Lelio R Paula12/2013
7187(25*10^102698+77)/3102699Robert Price09/2022
71886^131976-65102698Lelio R Paula10/2016
71892^341134+2533102692Henri Lifchitz09/2005
719013^92184-54102688Lelio R Paula10/2016
71912^341116-20873102687Enzo Doria06/2013
71922^341094-19953102680Enzo Doria06/2013
719323761^20950+20950^23761102676Hans Havermann03/2019
71952^341053+129102668Lelio R Paula08/2011
7194(4724^27943-1)/4723102668Serge Batalov06/2022
7197(31*2^341006-1)/3102655Lelio R Paula03/2014
71967^121471+94102655Lelio R Paula10/2016
71992^341004-173102653Lelio R Paula08/2011
719820^78901+3102653Lelio R Paula10/2016
7200(2^341001+1674)/2102652Stefano Morozzi09/2020
72015^146853-52102646Lelio R Paula10/2016
72022^340969-216931102642Enzo Doria05/2014
7203122^49196+121102641Norbert Schneider10/2018
72042^340952+1870021102637Enzo Doria05/2016
72055*2^340940-3102634Lelio R Paula08/2014
7206(6^131891+1)/7102631Paul Bourdelais01/2010
7207(11*10^102629-23)/3102630Robert Price09/2021
72083^215094+5*2^215094102626Jon Grantham08/2023
720925876^9239+9239^25876102615Hans Havermann02/2019
7210(4*10^102612+83)/3102613Robert Price02/2018
721175^54717+74102598Norbert Schneider01/2015
7212(17*10^102597+13)/3102598Robert Price01/2019
72132^340806-20393102593Enzo Doria06/2013
7214(2^340790+5)/138267102583Lelio R Paula12/2013
72156^131821+77102577Lelio R Paula10/2016
7216(203*10^102561-11)/3102563Robert Price12/2020
72172^340688-29102558Henri Lifchitz05/2005
72182^340685-109101102557Enzo Doria04/2014
721965^56567-64102552Norbert Schneider11/2014
722026230^8121+8121^26230102550Hans Havermann03/2019
7221(64*10^102547+161)/9102548Robert Price08/2022
7222(8*10^102541+49)/3102542Robert Price05/2020
7223(536*10^102533-23)/9102535Robert Price02/2020
72242^340547-108897102515Enzo Doria03/2014
7225(2^340536+778)/2102512Stefano Morozzi09/2020
722625592^10119+10119^25592102500Hans Havermann02/2019
7227(5*10^102492-23)/9102492Serge Batalov11/2022
72287^121268+82102484Lelio R Paula10/2016
7229(6883*2^340443-1)/162401102483Lelio R Paula05/2015
72302^340434-5955102481Lelio R Paula11/2016
7231(7*10^102480-19)/3102481Robert Price10/2020
7232(2^340381+47)/7102465Lelio R Paula12/2013
7233111^50095+110102461Norbert Schneider04/2017
72342^340291-20301102438Enzo Doria06/2013
723512^94915+89102431Lelio R Paula10/2016
7236(106*10^102422+17)/3102424Robert Price04/2021
723724466^15349+15349^24466102417Hans Havermann03/2019
72382^340212+111546435102415Paul Bourdelais10/2021
72392^340208-20373102413Enzo Doria06/2013
72406^131598-17273102404Enzo Doria02/2013
7241(2^340132+1182)/2102390Stefano Morozzi09/2020
7242(2^340133+1166)/2102390Stefano Morozzi09/2020
72432^340115-21181102385Enzo Doria06/2013
7244(55459*2^340090+1)/1591102379Lelio R Paula07/2014
7245(2^340064+3630)/2102370Stefano Morozzi09/2020
72469348*31^68638+13102369Eric Chen04/2024
724789^52511-88^52511102365Robert Price06/2015
72483^214539-112756102362Enzo Doria07/2014
724923159^23450-23450^23159102353Norbert Schneider12/2019
72502^340000-19877102351Enzo Doria06/2013


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Created by  Henri Lifchitz & Renaud Lifchitz : October, 26 2000, last modification: May, 30 2024 08:39 (Time in France)

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