PRP Records

Probable Primes Top 10000

(294627 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 ?
67515*10^104326+77104327Robert Price12/2018
6752(2^346564+2026)/2104326Stefano Morozzi09/2020
6753(8925^26569-1)/(8925^163-1)104320Ryan Propper11/2023
67562^346527-111817104316Enzo Doria05/2014
67556^134055+101104316Lelio R Paula11/2016
6754fibonacci(499147)-4104316Jon Grantham08/2023
675792105!4+8104312Robert Price09/2019
6758(7^123407-5^123407)/2104291Jon Grantham08/2023
67596^134013+163104283Lelio R Paula11/2016
676010^(2*52140+1)-10^52140-1104281Robert Price07/2023
6761(22*10^104272-61)/3104273Robert Price03/2022
6762(2^346318+862)/2104252Stefano Morozzi02/2021
676418^83049-89104250Lelio R Paula01/2017
6763(2^346311+606)/2104250Stefano Morozzi09/2020
6765(166*10^104230+11)/3104232Robert Price03/2021
67662^346213+484049104221Enzo Doria04/2017
676718^83021-91104214Lelio R Paula01/2017
676810^104212+128779104213Patrick De Geest05/2016
676910^104212+237447104213Patrick De Geest05/2016
677010^104212+242139104213Patrick De Geest05/2016
677110^104212+269199104213Patrick De Geest05/2016
677224254^19803+19803^24254104213Hans Havermann09/2020
6773(10^104212-71)/1104212Serge Batalov12/2014
677423678^23821-23821^23678104202Norbert Schneider01/2020
67752^346078+7695104180Lelio R Paula12/2016
67762^346055-19537104173Enzo Doria05/2013
6777(3*2^346057+1)/77104173Lelio R Paula12/2013
67782^346037-20125104168Enzo Doria06/2013
6779(34*10^104168-7)/9/13/551179104162Makoto Morimoto05/2016
67806^133854-17993104159Enzo Doria03/2013
67812^345990+1874239104154Enzo Doria06/2016
67822^345988-20373104153Enzo Doria06/2013
6783(2^345965+2214)/2104146Stefano Morozzi09/2020
6784(26*10^104132-503)/9104133Robert Price07/2018
67853*5^148968+8104125Lelio R Paula11/2014
6786(7*10^104113+53)/3104114Robert Price05/2018
6787p(21253)#/2+8104113Robert Price01/2017
678833582^1259+1259^33582104106Hans Havermann09/2020
678932958^1441+1441^32958104104Hans Havermann09/2020
679029127^3748+3748^29127104095Hans Havermann09/2020
6791322^41507+41507^322104094Norbert Schneider12/2014
67926^133768-17423104092Enzo Doria03/2013
67932^345786-19557104092Enzo Doria05/2013
6794171^46606-2104072Lelio R Paula10/2017
6795(29*10^104071+91)/3104072Robert Price04/2020
6796norm(Mod(x,x^3-x-1)^852167-1)104070Paul Vanderveen09/2022
67972^345704-149104068Lelio R Paula09/2011
679825821^10712+10712^25821104056Hans Havermann09/2020
6799(2^345662+2038)/2104055Stefano Morozzi09/2020
68006^133704-17273104042Enzo Doria02/2013
6801(3*2^345590-1)/23104033Lelio R Paula03/2014
6802(19*2^345590+1)/33859104030Lelio R Paula12/2013
68032^345547+11104021Lelio R Paula09/2011
6804(19*10^104014-49)/3104015Robert Price05/2019
6805(2^345519+1794)/2104012Stefano Morozzi01/2021
68062^345504+723104008Lelio R Paula09/2011
68072^345498-20037104006Enzo Doria06/2013
680918^82854-37104005Lelio R Paula01/2017
6808(2^345497+2070)/2104005Stefano Morozzi09/2020
68102^345486-109065104002Enzo Doria04/2014
68112^345487-1851507104002Enzo Doria08/2015
68122^345476+777103999Lelio R Paula09/2011
6813(2^345477+1554)/2103999Stefano Morozzi09/2020
68144*10^103981-83103982Robert Price10/2018
6815(2^345327+3206)/2103954Stefano Morozzi09/2020
6816(5*2^345321-1)/3103953Lelio R Paula03/2014
6817(2^345267-9)/539049127103927Lelio R Paula12/2013
6818(19*10^103907+77)/3103908Robert Price05/2019
6819(78557*2^345163+1)/78589103905Lelio R Paula07/2014
68202^345106-112181103888Enzo Doria06/2014
6821(2^345105+1326)/2103887Stefano Morozzi02/2021
68222^345079+99103880Lelio R Paula09/2011
6823(2^345034+1198)/2103866Stefano Morozzi09/2020
682411^99736-1500103865Enzo Doria12/2012
6825(569^37699-1)/568103863Serge Batalov06/2022
6826(2^345010+2082)/2103859Stefano Morozzi09/2020
682723263^23784-23784^23263103857Norbert Schneider01/2020
68283*10^103844+31103845Robert Price06/2021
6829444*33^68368+19103821Eric Chen05/2023
683023927^21814+21814^23927103813Hans Havermann09/2020
68312^344842-20157103808Enzo Doria06/2013
6832(47*2^344822+1)/1071103801Lelio R Paula05/2015
68332^344802-20765103796Enzo Doria06/2013
68342^344794-3821103794Yves Minet05/2011
68352^344782-109103103790Enzo Doria04/2014
68363^217521-112292103784Enzo Doria06/2014
68372^344759-3505103783Lelio R Paula11/2016
68382^344735-147103776Lelio R Paula09/2011
6839L(496533)-p(496533)103770Robert Price02/2018
68402*10^103749-69103750Robert Price03/2018
6841(55459*2^344617+1)/3103745Lelio R Paula07/2014
68422^344607-108891103738Enzo Doria03/2014
6844(2^344608+3798)/2103738Stefano Morozzi02/2021
6843(1097^34123-1)/1096103738Serge Batalov06/2022
68452^344560+22411103723Enzo Doria09/2023
6846(148*10^103718-1)/3103720Robert Price03/2020
68472^344541-19561103718Enzo Doria05/2013
6848(1017*2^344529-1)/569103714Lelio R Paula05/2015
6849(8896^26263-1)/8895103714Serge Batalov06/2022
6850(2^344503+1758)/2103706Stefano Morozzi09/2020
6851(4*10^103703-1)/3103704Serge Batalov08/2009
68522^344444-455103688Yves Minet03/2012
6853(4*10^103678-43)/3103679Robert Price01/2022
6854(13*53^238539*617^9)/10^307661103673Hans Havermann06/2017
6855(2^344367+2738)/2103665Stefano Morozzi01/2021
68572^344317-109933103650Enzo Doria04/2014
685626055^9508+9508^26055103650Hans Havermann09/2020
68582^344309-1852033103648Enzo Doria08/2015
685925729^10672+10672^25729103643Hans Havermann09/2020
6860(2^344289+1166)/2103642Stefano Morozzi09/2020
68613*10^103637+61103638Robert Price09/2020
6862(2^344246+1614)/2103629Stefano Morozzi09/2020
68632^344213-21253103619Enzo Doria06/2013
68642^344196-465103614Lelio R Paula11/2016
68652^344187-20001103611Enzo Doria06/2013
6866(117191#+(355573#)/(117191#))/(200233679)103602Makoto Morimoto10/2017
6867(237^43627-1)/236103601Serge Batalov06/2022
686820^79621-19^79621103590Jean-Louis Charton03/2011
6869Phi(155391,10)/1243129103586Maksym Voznyy09/2015
6870(9^108553-2^108553)/7103586Jon Grantham07/2023
68712^344085-20365103580Enzo Doria06/2013
68725^148169+54103566Lelio R Paula11/2016
68732^344017-108795103560Enzo Doria03/2014
6874(2^343974+2670)/2103547Stefano Morozzi09/2020
68752^343971-5077103546Lelio R Paula09/2011
6876(7*10^103531+71)/3103532Robert Price05/2018
68772^343899+141103524Lelio R Paula08/2011
6878(2^343933+1)/(3*98294339989393)103520Gord Palameta08/2018
68796^133029-67103517Lelio R Paula11/2016
6880(17*2^343877+1)/13625103515Lelio R Paula12/2013
688166*10^103507+7103509Robert Price07/2020
688226297^8614+8614^26297103485Hans Havermann09/2020
6883(2^343764+2658)/2103483Stefano Morozzi09/2020
688426499^8036+8036^26499103480Hans Havermann09/2020
6885(136*10^103474-1)/9103476Serge Batalov12/2014
68865^148014-24103458Lelio R Paula11/2016
688728316^4503+4503^28316103453Hans Havermann09/2020
6888(22*10^103450+53)/3103451Robert Price07/2019
68892^343604+9931103436Yves Minet01/2011
68902^343601-21189103435Enzo Doria06/2013
6891(10^103423+173)/3103423Robert Price05/2021
68922^343508-115229103407Enzo Doria06/2015
6893(8766^26227-1)/8765103404Serge Batalov06/2022
6894(509203*2^343491-1)/16147103403Lelio R Paula05/2015
68953^216685-113056103386Enzo Doria07/2014
689624829^14580+14580^24829103382Hans Havermann08/2020
689791355!4+1024103381Robert Price09/2019
689844^62903-43^62903103379Jean-Louis Charton08/2012
689911^99262-20103371Lelio R Paula12/2016
6900(509203*2^343357-1)/5103366Lelio R Paula05/2015
6901(2^343363+3570)/2103363Stefano Morozzi09/2020
69022^343356-2791889103361Enzo Doria03/2016
6903(25*10^103360-241)/9103361Robert Price05/2018
6904Phi(104989,10)/2939693103350Maksym Voznyy09/2015
6905(371*33^68040-19)/32103321Eric Chen05/2023
690624826^14511+14511^24826103319Hans Havermann09/2020
69072^343182-171103309Lelio R Paula08/2011
6908(23619^23619+23620^23620)/7187103294David Broadhurst09/2009
6909(16487^24649-1)/(16487^157-1)103287Ryan Propper11/2023
6910(10680^25639-1)/10679103285Serge Batalov06/2022
6911(7427^26683-1)/7426103282Serge Batalov06/2022
69122^343079-1835611103278Enzo Doria05/2015
69132^343063-1147103273Yves Minet06/2013
691424741^14930+14930^24741103271Hans Havermann09/2020
6915(16*10^103255-73)/3103256Robert Price07/2020
6916(219^44119-1)/218103256Serge Batalov06/2022
69179*6^132689+7103254Lelio R Paula11/2014
69182^342979-18085103247Enzo Doria05/2013
6919(16*10^103244-31)/3103245Robert Price03/2019
69202^342966-16995103244Lelio R Paula11/2016
692123797^21774+21774^23797103230Hans Havermann09/2020
692225388^11637+11637^25388103224Hans Havermann09/2020
6923(2^342876+2086)/2103216Stefano Morozzi09/2020
6924(16*10^103214-31)/3103215Robert Price03/2019
6926(37*10^103211+611)/9103212Robert Price11/2018
6925(238*10^103210-1)/3103212Robert Price04/2020
69275^147650+16103203Lelio R Paula11/2016
6928gcd(Phi(852060,10),(10^42603+1)^3*(10^42603+1-10^21302)+(10^85206+10^42603)*(10^21302+1)+10^127809)103201Serge Batalov04/2015
69292^342817+2707067103199Enzo Doria03/2016
693043^63177-42103198Theodore Burton02/2007
69312^342805-21025103195Enzo Doria06/2013
693224129^18890+18890^24129103182Hans Havermann09/2020
6933(622*10^103171-1)/9103173Robert Price11/2021
69342^342714+12285103168Lelio R Paula11/2016
6935(2*10^103161-17)/3103161Serge Batalov11/2022
693618^82178-4481103156Enzo Doria03/2013
69372^342665-17349103153Enzo Doria05/2013
693830408^2467+2467^30408103150Hans Havermann09/2020
6939(5^147571-3^147571)/2103148Kellen Shenton05/2022
6940(2^342615+3090)/2103138Stefano Morozzi09/2020
69412^342612+175103137Lelio R Paula08/2011
69425*2^342585-3103130Lelio R Paula09/2014
6943(16*10^103127+77)/3103128Robert Price03/2019
6944(2^342527+3774)/2103111Stefano Morozzi02/2021
69452^342503-19209103104Enzo Doria05/2013
6946(2^342484+2586)/2103098Stefano Morozzi09/2020
69472^342476+51103096Lelio R Paula08/2011
69482^342460-18885103091Enzo Doria05/2013
6949(2^342442+862)/2103086Stefano Morozzi02/2021
6950(194*10^103074-17)/3103076Robert Price09/2020
69517^121968+82103075Lelio R Paula10/2016
69522^342392-108863103071Enzo Doria03/2014
6953(2^342389+806)/2103070Stefano Morozzi01/2021
69543^216014+28103065Lelio R Paula11/2016
69552^342353-108879103059Enzo Doria03/2014
695610^103055+276081103056Patrick De Geest12/2016
695710^103055-53103055Lelio R Paula11/2016
6958(58*10^103046+419)/9103047Robert Price05/2019
69597^121933+4103046Lelio R Paula11/2014
6960(71*10^103028-143)/9103029Robert Price10/2021
6961(2^342235+3618)/2103023Stefano Morozzi09/2020
696219^80560-68103017Lelio R Paula10/2016
69632^342209+76607103016Enzo Doria05/2016
6965328^40945+40945^328103013Norbert Schneider12/2014
696412^95454-91103013Lelio R Paula10/2016
696625833^9716+9716^25833103009Hans Havermann01/2019
6967(893*10^103004+7)/9103006Robert Price06/2021
6968(1475^32503-1)/1474102993Serge Batalov06/2022
696965^56809-64^56809102990Robert Price08/2013
69705^147338-6102985Lelio R Paula11/2014
69712^342084-112739102978Enzo Doria06/2014
69729*6^132330+7102974Lelio R Paula11/2014
69732^342034-16737102963Enzo Doria05/2013
6974(9787*2^342011-1)/25102959Lelio R Paula05/2015
6975(3^215802-5)/124343756102956Lelio R Paula12/2013
69762^341991-17421102950Enzo Doria05/2013
69772^341969-112225102943Enzo Doria06/2014
6978(9787*2^341864-1)/3102915Lelio R Paula05/2015
69792^341859+1869413102910Enzo Doria05/2016
698010^102909+61102910Lelio R Paula11/2016
698110^102909-67049102909Patrick De Geest12/2016
698223814^20935+20935^23814102898Hans Havermann02/2019
698328345^4264+4264^28345102888Hans Havermann02/2019
698425665^10204+10204^25665102886Hans Havermann02/2019
698526288^8181+8181^26288102860Hans Havermann02/2019
69862^341659+1836773102850Enzo Doria03/2016
69872^341608-110639102835Enzo Doria05/2014
698810^102824+49102825Lelio R Paula11/2016
698910^102824-168011102824Patrick De Geest12/2016
699011^98708-8102794Lelio R Paula10/2016
69912^341466+4429102792Lelio R Paula09/2011
69922^341460-107102790Lelio R Paula08/2011
6993(2^341388+47)/21014943102761Lelio R Paula12/2013
69942^341355+21102759Lelio R Paula08/2011
6995(6496^26947-1)/6495102736Serge Batalov06/2022
69962^341246+40755102726Lelio R Paula11/2016
6997(2^341256-5)/991699102723Lelio R Paula12/2013
69987^121547+78102720Lelio R Paula10/2016
69992^341223-461197102719Enzo Doria06/2015
700027838^4893+4893^27838102711Hans Havermann03/2019


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Created by  Henri Lifchitz & Renaud Lifchitz : October, 26 2000, last modification: March, 12 2024 13:37 (Time in France)

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