PRP Records

Probable Primes Top 10000

(294687 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(893*10^103004+7)/9103006Robert Price06/2021
7002(1475^32503-1)/1474102993Serge Batalov06/2022
700365^56809-64^56809102990Robert Price08/2013
70045^147338-6102985Lelio R Paula11/2014
70052^342084-112739102978Enzo Doria06/2014
70069*6^132330+7102974Lelio R Paula11/2014
70072^342034-16737102963Enzo Doria05/2013
7008(9787*2^342011-1)/25102959Lelio R Paula05/2015
7009(3^215802-5)/124343756102956Lelio R Paula12/2013
70102^341991-17421102950Enzo Doria05/2013
70112^341969-112225102943Enzo Doria06/2014
7012(9787*2^341864-1)/3102915Lelio R Paula05/2015
70132^341859+1869413102910Enzo Doria05/2016
701410^102909+61102910Lelio R Paula11/2016
701510^102909-67049102909Patrick De Geest12/2016
701623814^20935+20935^23814102898Hans Havermann02/2019
701728345^4264+4264^28345102888Hans Havermann02/2019
701825665^10204+10204^25665102886Hans Havermann02/2019
701926288^8181+8181^26288102860Hans Havermann02/2019
70202^341659+1836773102850Enzo Doria03/2016
70212^341608-110639102835Enzo Doria05/2014
702210^102824+49102825Lelio R Paula11/2016
702310^102824-168011102824Patrick De Geest12/2016
702411^98708-8102794Lelio R Paula10/2016
70252^341466+4429102792Lelio R Paula09/2011
70262^341460-107102790Lelio R Paula08/2011
7027(2^341388+47)/21014943102761Lelio R Paula12/2013
70282^341355+21102759Lelio R Paula08/2011
7029(6496^26947-1)/6495102736Serge Batalov06/2022
70302^341246+40755102726Lelio R Paula11/2016
7031(2^341256-5)/991699102723Lelio R Paula12/2013
70327^121547+78102720Lelio R Paula10/2016
70332^341223-461197102719Enzo Doria06/2015
703427838^4893+4893^27838102711Hans Havermann03/2019
70362^341190-20577102709Enzo Doria06/2013
7035(27*2^341212+1)/84674449102709Lelio R Paula12/2013
7037(25*10^102698+77)/3102699Robert Price09/2022
70386^131976-65102698Lelio R Paula10/2016
70392^341134+2533102692Henri Lifchitz09/2005
704013^92184-54102688Lelio R Paula10/2016
70412^341116-20873102687Enzo Doria06/2013
70422^341094-19953102680Enzo Doria06/2013
704323761^20950+20950^23761102676Hans Havermann03/2019
70452^341053+129102668Lelio R Paula08/2011
7044(4724^27943-1)/4723102668Serge Batalov06/2022
7047(31*2^341006-1)/3102655Lelio R Paula03/2014
70467^121471+94102655Lelio R Paula10/2016
70492^341004-173102653Lelio R Paula08/2011
704820^78901+3102653Lelio R Paula10/2016
7050(2^341001+1674)/2102652Stefano Morozzi09/2020
70515^146853-52102646Lelio R Paula10/2016
70522^340969-216931102642Enzo Doria05/2014
7053122^49196+121102641Norbert Schneider10/2018
70542^340952+1870021102637Enzo Doria05/2016
70555*2^340940-3102634Lelio R Paula08/2014
7056(6^131891+1)/7102631Paul Bourdelais01/2010
7057(11*10^102629-23)/3102630Robert Price09/2021
70583^215094+5*2^215094102626Jon Grantham08/2023
705925876^9239+9239^25876102615Hans Havermann02/2019
7060(4*10^102612+83)/3102613Robert Price02/2018
706175^54717+74102598Norbert Schneider01/2015
7062(17*10^102597+13)/3102598Robert Price01/2019
70632^340806-20393102593Enzo Doria06/2013
7064(2^340790+5)/138267102583Lelio R Paula12/2013
70656^131821+77102577Lelio R Paula10/2016
7066(203*10^102561-11)/3102563Robert Price12/2020
70672^340688-29102558Henri Lifchitz05/2005
70682^340685-109101102557Enzo Doria04/2014
706965^56567-64102552Norbert Schneider11/2014
707026230^8121+8121^26230102550Hans Havermann03/2019
7071(64*10^102547+161)/9102548Robert Price08/2022
7072(8*10^102541+49)/3102542Robert Price05/2020
7073(536*10^102533-23)/9102535Robert Price02/2020
70742^340547-108897102515Enzo Doria03/2014
7075(2^340536+778)/2102512Stefano Morozzi09/2020
707625592^10119+10119^25592102500Hans Havermann02/2019
7077(5*10^102492-23)/9102492Serge Batalov11/2022
70787^121268+82102484Lelio R Paula10/2016
7079(6883*2^340443-1)/162401102483Lelio R Paula05/2015
70802^340434-5955102481Lelio R Paula11/2016
7081(7*10^102480-19)/3102481Robert Price10/2020
7082(2^340381+47)/7102465Lelio R Paula12/2013
7083111^50095+110102461Norbert Schneider04/2017
70842^340291-20301102438Enzo Doria06/2013
708512^94915+89102431Lelio R Paula10/2016
7086(106*10^102422+17)/3102424Robert Price04/2021
708724466^15349+15349^24466102417Hans Havermann03/2019
70882^340212+111546435102415Paul Bourdelais10/2021
70892^340208-20373102413Enzo Doria06/2013
70906^131598-17273102404Enzo Doria02/2013
7091(2^340132+1182)/2102390Stefano Morozzi09/2020
7092(2^340133+1166)/2102390Stefano Morozzi09/2020
70932^340115-21181102385Enzo Doria06/2013
7094(55459*2^340090+1)/1591102379Lelio R Paula07/2014
7095(2^340064+3630)/2102370Stefano Morozzi09/2020
709689^52511-88^52511102365Robert Price06/2015
70973^214539-112756102362Enzo Doria07/2014
709823159^23450-23450^23159102353Norbert Schneider12/2019
70992^340000-19877102351Enzo Doria06/2013
71002^339990-114845102348Enzo Doria05/2015
7101(3^214516-2)/51383102346Lelio R Paula12/2013
710220^78661-99102341Lelio R Paula09/2016
71042^339951-19585102336Enzo Doria05/2013
7103(17*10^102335-167)/3102336Robert Price05/2022
7105(13*2^339943+1)/45102333Lelio R Paula12/2013
7106(236282#+121441)/(121441*25499429)102332Makoto Morimoto08/2020
71075*10^102323-91102324Robert Price03/2021
71092^339889+29327102317Yves Minet06/2010
7108(167*10^102315-17)/3102317Robert Price03/2020
711026348^7641+7641^26348102314Hans Havermann03/2019
7111Phi(239414,10)/6333218543102303Makoto Kamada08/2019
71122^339834-109493102301Enzo Doria04/2014
7113(16*10^102299-19)/3102300Robert Price02/2019
7114(11^98221-5^98221)/6102286Robert Price01/2013
71153^214365+1820102279Lelio R Paula10/2016
711631978^1579+1579^31978102278Hans Havermann03/2019
7117(89*10^102262-467)/9102263Robert Price04/2022
7118(11*2^339705-1)/183102261Lelio R Paula03/2014
71192^339694-16995102259Lelio R Paula09/2016
7120(56*10^102255+691)/9102256Robert Price05/2019
7121122^49008+121102249Norbert Schneider10/2018
7122(2^339652+3178)/2102246Stefano Morozzi09/2020
71237^120985-38102245Lelio R Paula10/2016
712410^102244+122961102245Patrick De Geest12/2016
712510^102244-27102244Lelio R Paula09/2016
71267^120982-62102242Lelio R Paula10/2016
7127(2^339640+2670)/2102242Stefano Morozzi09/2020
71284*6^131382-5102236Lelio R Paula11/2014
7129(2^339607+3290)/2102232Stefano Morozzi02/2021
71302^339586-1091102226Yves Minet11/2012
713111^98161-3072000102225Enzo Doria12/2012
71329*7^120961-4102225Lelio R Paula11/2014
71335*3^214250+2102224Serge Batalov10/2010
713412^94713-59102213Lelio R Paula10/2016
713512^94705+89102204Lelio R Paula10/2016
71362^339407-177102172Lelio R Paula08/2011
71374*10^102163-57102164Robert Price10/2018
71382^339355+65102157Lelio R Paula07/2011
7139(28*10^102142-31)/3102143Robert Price12/2019
7140(2^339323+47)/880715102141Lelio R Paula12/2013
7141(2^339268+1758)/2102130Stefano Morozzi09/2020
7142s(178551)102122Robert Price05/2020
7143(797*10^102112-23)/9102114Robert Price01/2022
7144(5*10^102107+7)/3102108Tyler Busby02/2023
7145(2^339175+2790)/2102102Stefano Morozzi02/2021
71472^339168+21102100Lelio R Paula07/2011
71482^339167-108807102100Enzo Doria03/2014
7146(2^339169+42)/2102100Stefano Morozzi09/2020
71492^339156+163102097Lelio R Paula08/2011
7150(2^339149+746)/2102094Stefano Morozzi09/2020
7151(25*10^102076-67)/3102077Robert Price06/2019
71522^339081-4543102074Yves Minet03/2019
7153(3435^28867-1)/3434102069Serge Batalov06/2022
71542*10^102062+77102063Robert Price08/2020
715624327^15668+15668^24327102053Hans Havermann02/2019
715510^102052+66793102053Patrick De Geest09/2022
715710^102052-7000001102052Robert Price06/2021
715810^102052-618623102052Patrick De Geest09/2022
71592^339000-175635102050Stefano Morozzi12/2021
71602^339000-151667102050Stefano Morozzi12/2021
71612^338999+79289102049Stefano Morozzi01/2022
71622^338998-63897102049Stefano Morozzi12/2022
71632^338997+99659102049Stefano Morozzi02/2023
71642^338994+188757102048Stefano Morozzi05/2022
71652^338995+70785102048Stefano Morozzi11/2022
71662^338994-12183102048Stefano Morozzi12/2022
71672^338992+181591102047Stefano Morozzi01/2022
71682^338992+136171102047Stefano Morozzi03/2022
71692^338991-109435102047Stefano Morozzi04/2022
71702^338991+193611102047Stefano Morozzi09/2022
71712^338988-134619102046Stefano Morozzi04/2022
71722^338987-62557102046Stefano Morozzi12/2022
71732^338986-60141102045Stefano Morozzi06/2022
71742^338986+98209102045Stefano Morozzi11/2022
71752^338981+106391102044Stefano Morozzi01/2022
71762^338982+34069102044Stefano Morozzi03/2022
71772^338982-58781102044Stefano Morozzi04/2022
71782^338980+70833102044Stefano Morozzi11/2022
71792^338982-92111102044Stefano Morozzi02/2023
71802^338977+83007102043Stefano Morozzi02/2022
71812^338979-83601102043Stefano Morozzi04/2022
71822^338975+28355102042Stefano Morozzi01/2022
71832^338973+134619102042Stefano Morozzi03/2022
71842^338974+183777102042Stefano Morozzi03/2022
71852^338975+69293102042Stefano Morozzi09/2022
719325080^11711+11711^25080102041Hans Havermann02/2019
71862^338972+152343102041Stefano Morozzi12/2021
71872^338972-180623102041Stefano Morozzi02/2022
71882^338972+84441102041Stefano Morozzi03/2022
71892^338971+64875102041Stefano Morozzi05/2022
71902^338971+44985102041Stefano Morozzi11/2022
71912^338971+145065102041Stefano Morozzi11/2022
71922^338972-16635102041Stefano Morozzi01/2023
71942^338968+53461102040Stefano Morozzi01/2022
71952^338969+160175102040Stefano Morozzi03/2022
71962^338967+13409102040Stefano Morozzi04/2022
71972^338969+67635102040Stefano Morozzi09/2022
71982^338969-15913102040Stefano Morozzi01/2023
71992^338963-127455102039Stefano Morozzi12/2021
72002^338963+132195102039Stefano Morozzi02/2022
72012^338966+137919102039Stefano Morozzi04/2022
72022^338963-87529102039Stefano Morozzi12/2022
72032^338963-116859102039Stefano Morozzi02/2023
7210(2^338982-7)/1754517102038Lelio R Paula12/2013
72042^338960+53935102038Stefano Morozzi01/2022
72052^338962+83157102038Stefano Morozzi02/2022
72062^338961+12341102038Stefano Morozzi04/2022
72072^338960+63933102038Stefano Morozzi05/2022
72082^338960+170791102038Stefano Morozzi11/2022
72092^338962+21679102038Stefano Morozzi11/2022
72112^338959-30919102037Stefano Morozzi02/2022
72122^338959+164769102037Stefano Morozzi05/2022
72132^338958-43161102037Stefano Morozzi02/2023
72142^338954-177003102036Stefano Morozzi12/2021
72152^338954+154207102036Stefano Morozzi01/2022
72162^338956+182493102036Stefano Morozzi02/2022
72172^338954+162715102036Stefano Morozzi04/2022
72182^338955-158241102036Stefano Morozzi04/2022
72192^338956-33395102036Stefano Morozzi04/2022
72202^338954+190915102036Stefano Morozzi06/2022
72212^338955+41643102036Stefano Morozzi09/2022
72222^338954+194427102036Stefano Morozzi09/2022
72232^338956+117967102036Stefano Morozzi09/2022
72242^338956+195495102036Stefano Morozzi11/2022
72252^338954-186371102036Stefano Morozzi12/2022
72262^338950+175077102035Stefano Morozzi12/2021
72272^338951-51687102035Stefano Morozzi12/2021
72282^338951+66123102035Stefano Morozzi06/2022
72292^338950+19317102035Stefano Morozzi09/2022
72302^338951-161479102035Stefano Morozzi12/2022
72312^338950-66335102035Stefano Morozzi01/2023
72322^338951-41611102035Stefano Morozzi02/2023
72332^338952-142887102035Stefano Morozzi02/2023
72342^338949+85449102034Stefano Morozzi03/2022
72352^338949-184585102034Stefano Morozzi04/2022
72362^338949-88555102034Stefano Morozzi12/2022
72372^338948+49393102034Stefano Morozzi02/2023
72382^338949-17601102034Stefano Morozzi02/2023
72392^338943+127103102033Stefano Morozzi12/2021
72402^338944-84003102033Stefano Morozzi04/2022
72412^338945+138605102033Stefano Morozzi05/2022
72422^338943+95133102033Stefano Morozzi11/2022
72432^338943+147435102033Stefano Morozzi11/2022
72442^338943-116067102033Stefano Morozzi01/2023
72452^338940+78607102032Stefano Morozzi01/2022
72462^338942-86687102032Stefano Morozzi12/2022
72472^338939+151569102031Stefano Morozzi12/2021
72482^338938+183975102031Stefano Morozzi03/2022
72492^338937-33429102031Stefano Morozzi04/2022
72502^338939-183259102031Stefano Morozzi04/2022


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Created by  Henri Lifchitz & Renaud Lifchitz : October, 26 2000, last modification: March, 27 2024 11:51 (Time in France)

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