PRP Records

Probable Primes Top 10000

(300944 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 ?
85012^341246+40755102726Lelio R Paula11/2016
8502(2^341256-5)/991699102723Lelio R Paula12/2013
85037^121547+78102720Lelio R Paula10/2016
85042^341223-461197102719Enzo Doria06/2015
850527838^4893+4893^27838102711Hans Havermann03/2019
85072^341190-20577102709Enzo Doria06/2013
8506(27*2^341212+1)/84674449102709Lelio R Paula12/2013
8508(25*10^102698+77)/3102699Robert Price09/2022
85096^131976-65102698Lelio R Paula10/2016
85102^341134+2533102692Henri Lifchitz09/2005
851113^92184-54102688Lelio R Paula10/2016
85122^341116-20873102687Enzo Doria06/2013
85132^341094-19953102680Enzo Doria06/2013
851423761^20950+20950^23761102676Hans Havermann03/2019
85162^341053+129102668Lelio R Paula08/2011
8515(4724^27943-1)/4723102668Serge Batalov06/2022
8518(31*2^341006-1)/3102655Lelio R Paula03/2014
85177^121471+94102655Lelio R Paula10/2016
85202^341004-173102653Lelio R Paula08/2011
851920^78901+3102653Lelio R Paula10/2016
8521(2^341001+1674)/2102652Stefano Morozzi09/2020
85225^146853-52102646Lelio R Paula10/2016
85232^340969-216931102642Enzo Doria05/2014
8524122^49196+121102641Norbert Schneider10/2018
85252^340952+1870021102637Enzo Doria05/2016
85265*2^340940-3102634Lelio R Paula08/2014
8527(6^131891+1)/7102631Paul Bourdelais01/2010
8528(11*10^102629-23)/3102630Robert Price09/2021
85293^215094+5*2^215094102626Jon Grantham08/2023
853025876^9239+9239^25876102615Hans Havermann02/2019
8531(4*10^102612+83)/3102613Robert Price02/2018
853275^54717+74102598Norbert Schneider01/2015
8533(17*10^102597+13)/3102598Robert Price01/2019
85342^340806-20393102593Enzo Doria06/2013
8535(2^340790+5)/138267102583Lelio R Paula12/2013
85366^131821+77102577Lelio R Paula10/2016
8537(203*10^102561-11)/3102563Robert Price12/2020
85382^340688-29102558Henri Lifchitz05/2005
85392^340685-109101102557Enzo Doria04/2014
854065^56567-64102552Norbert Schneider11/2014
854126230^8121+8121^26230102550Hans Havermann03/2019
8542(64*10^102547+161)/9102548Robert Price08/2022
8543(8*10^102541+49)/3102542Robert Price05/2020
8544(536*10^102533-23)/9102535Robert Price02/2020
85452^340547-108897102515Enzo Doria03/2014
8546(2^340536+778)/2102512Stefano Morozzi09/2020
854725592^10119+10119^25592102500Hans Havermann02/2019
8548(5*10^102492-23)/9102492Serge Batalov11/2022
85497^121268+82102484Lelio R Paula10/2016
8550(6883*2^340443-1)/162401102483Lelio R Paula05/2015
85512^340434-5955102481Lelio R Paula11/2016
8552(7*10^102480-19)/3102481Robert Price10/2020
8553(2^340381+47)/7102465Lelio R Paula12/2013
8554111^50095+110102461Norbert Schneider04/2017
8555180^45427-45427^180102451Norman Luhn09/2024
85562^340291-20301102438Enzo Doria06/2013
855712^94915+89102431Lelio R Paula10/2016
8558(106*10^102422+17)/3102424Robert Price04/2021
855924466^15349+15349^24466102417Hans Havermann03/2019
85602^340212+111546435102415Paul Bourdelais10/2021
85612^340208-20373102413Enzo Doria06/2013
85626^131598-17273102404Enzo Doria02/2013
8563(2^340132+1182)/2102390Stefano Morozzi09/2020
8564(2^340133+1166)/2102390Stefano Morozzi09/2020
85652^340115-21181102385Enzo Doria06/2013
8566(55459*2^340090+1)/1591102379Lelio R Paula07/2014
8567(2^340064+3630)/2102370Stefano Morozzi09/2020
85689348*31^68638+13102369Eric Chen04/2024
856989^52511-88^52511102365Robert Price06/2015
85703^214539-112756102362Enzo Doria07/2014
857123159^23450-23450^23159102353Norbert Schneider12/2019
85722^340000-19877102351Enzo Doria06/2013
85732^339990-114845102348Enzo Doria05/2015
8574311^41058-41058^311102348Norman Luhn09/2024
8575(3^214516-2)/51383102346Lelio R Paula12/2013
857620^78661-99102341Lelio R Paula09/2016
85782^339951-19585102336Enzo Doria05/2013
8577(17*10^102335-167)/3102336Robert Price05/2022
8579(13*2^339943+1)/45102333Lelio R Paula12/2013
8580(236282#+121441)/(121441*25499429)102332Makoto Morimoto08/2020
85815*10^102323-91102324Robert Price03/2021
85832^339889+29327102317Yves Minet06/2010
8582(167*10^102315-17)/3102317Robert Price03/2020
858426348^7641+7641^26348102314Hans Havermann03/2019
8585Phi(239414,10)/6333218543102303Makoto Kamada08/2019
85862^339834-109493102301Enzo Doria04/2014
8587(16*10^102299-19)/3102300Robert Price02/2019
8588(11^98221-5^98221)/6102286Robert Price01/2013
85893^214365+1820102279Lelio R Paula10/2016
859031978^1579+1579^31978102278Hans Havermann03/2019
8591(89*10^102262-467)/9102263Robert Price04/2022
8592(11*2^339705-1)/183102261Lelio R Paula03/2014
85932^339694-16995102259Lelio R Paula09/2016
8594(56*10^102255+691)/9102256Robert Price05/2019
8595122^49008+121102249Norbert Schneider10/2018
8596(2^339652+3178)/2102246Stefano Morozzi09/2020
85977^120985-38102245Lelio R Paula10/2016
859810^102244+122961102245Patrick De Geest12/2016
859910^102244-27102244Lelio R Paula09/2016
86007^120982-62102242Lelio R Paula10/2016
8601(2^339640+2670)/2102242Stefano Morozzi09/2020
86024*6^131382-5102236Lelio R Paula11/2014
8603(2^339607+3290)/2102232Stefano Morozzi02/2021
86042^339586-1091102226Yves Minet11/2012
860511^98161-3072000102225Enzo Doria12/2012
86069*7^120961-4102225Lelio R Paula11/2014
86075*3^214250+2102224Serge Batalov10/2010
860812^94713-59102213Lelio R Paula10/2016
860912^94705+89102204Lelio R Paula10/2016
86102^339407-177102172Lelio R Paula08/2011
86114*10^102163-57102164Robert Price10/2018
86122^339355+65102157Lelio R Paula07/2011
8613(28*10^102142-31)/3102143Robert Price12/2019
8614(2^339323+47)/880715102141Lelio R Paula12/2013
8615(2^339268+1758)/2102130Stefano Morozzi09/2020
8616U(610865)102130Serge Batalov07/2024
8617s(178551)102122Robert Price05/2020
8618(797*10^102112-23)/9102114Robert Price01/2022
8619(5*10^102107+7)/3102108Tyler Busby02/2023
8620(2^339175+2790)/2102102Stefano Morozzi02/2021
86222^339168+21102100Lelio R Paula07/2011
86232^339167-108807102100Enzo Doria03/2014
8621(2^339169+42)/2102100Stefano Morozzi09/2020
86242^339156+163102097Lelio R Paula08/2011
8625(2^339149+746)/2102094Stefano Morozzi09/2020
8626(25*10^102076-67)/3102077Robert Price06/2019
86272^339081-4543102074Yves Minet03/2019
8628(3435^28867-1)/3434102069Serge Batalov06/2022
86292*10^102062+77102063Robert Price08/2020
863124327^15668+15668^24327102053Hans Havermann02/2019
863010^102052+66793102053Patrick De Geest09/2022
863210^102052-7000001102052Robert Price06/2021
863310^102052-618623102052Patrick De Geest09/2022
86342^339000-175635102050Stefano Morozzi12/2021
86352^339000-151667102050Stefano Morozzi12/2021
86362^338999+79289102049Stefano Morozzi01/2022
86372^338998-63897102049Stefano Morozzi12/2022
86382^338997+99659102049Stefano Morozzi02/2023
86392^338994+188757102048Stefano Morozzi05/2022
86402^338995+70785102048Stefano Morozzi11/2022
86412^338994-12183102048Stefano Morozzi12/2022
86422^338992+181591102047Stefano Morozzi01/2022
86432^338992+136171102047Stefano Morozzi03/2022
86442^338991-109435102047Stefano Morozzi04/2022
86452^338991+193611102047Stefano Morozzi09/2022
86462^338988-134619102046Stefano Morozzi04/2022
86472^338987-62557102046Stefano Morozzi12/2022
86482^338986-60141102045Stefano Morozzi06/2022
86492^338986+98209102045Stefano Morozzi11/2022
86502^338981+106391102044Stefano Morozzi01/2022
86512^338982+34069102044Stefano Morozzi03/2022
86522^338982-58781102044Stefano Morozzi04/2022
86532^338980+70833102044Stefano Morozzi11/2022
86542^338982-92111102044Stefano Morozzi02/2023
86552^338977+83007102043Stefano Morozzi02/2022
86562^338979-83601102043Stefano Morozzi04/2022
86572^338975+28355102042Stefano Morozzi01/2022
86582^338973+134619102042Stefano Morozzi03/2022
86592^338974+183777102042Stefano Morozzi03/2022
86602^338975+69293102042Stefano Morozzi09/2022
866825080^11711+11711^25080102041Hans Havermann02/2019
86612^338972+152343102041Stefano Morozzi12/2021
86622^338972-180623102041Stefano Morozzi02/2022
86632^338972+84441102041Stefano Morozzi03/2022
86642^338971+64875102041Stefano Morozzi05/2022
86652^338971+44985102041Stefano Morozzi11/2022
86662^338971+145065102041Stefano Morozzi11/2022
86672^338972-16635102041Stefano Morozzi01/2023
86692^338968+53461102040Stefano Morozzi01/2022
86702^338969+160175102040Stefano Morozzi03/2022
86712^338967+13409102040Stefano Morozzi04/2022
86722^338969+67635102040Stefano Morozzi09/2022
86732^338969-15913102040Stefano Morozzi01/2023
86742^338963-127455102039Stefano Morozzi12/2021
86752^338963+132195102039Stefano Morozzi02/2022
86762^338966+137919102039Stefano Morozzi04/2022
86772^338963-87529102039Stefano Morozzi12/2022
86782^338963-116859102039Stefano Morozzi02/2023
8685(2^338982-7)/1754517102038Lelio R Paula12/2013
86792^338960+53935102038Stefano Morozzi01/2022
86802^338962+83157102038Stefano Morozzi02/2022
86812^338961+12341102038Stefano Morozzi04/2022
86822^338960+63933102038Stefano Morozzi05/2022
86832^338960+170791102038Stefano Morozzi11/2022
86842^338962+21679102038Stefano Morozzi11/2022
86862^338959-30919102037Stefano Morozzi02/2022
86872^338959+164769102037Stefano Morozzi05/2022
86882^338958-43161102037Stefano Morozzi02/2023
86892^338954-177003102036Stefano Morozzi12/2021
86902^338954+154207102036Stefano Morozzi01/2022
86912^338956+182493102036Stefano Morozzi02/2022
86922^338954+162715102036Stefano Morozzi04/2022
86932^338955-158241102036Stefano Morozzi04/2022
86942^338956-33395102036Stefano Morozzi04/2022
86952^338954+190915102036Stefano Morozzi06/2022
86962^338955+41643102036Stefano Morozzi09/2022
86972^338954+194427102036Stefano Morozzi09/2022
86982^338956+117967102036Stefano Morozzi09/2022
86992^338956+195495102036Stefano Morozzi11/2022
87002^338954-186371102036Stefano Morozzi12/2022
87012^338950+175077102035Stefano Morozzi12/2021
87022^338951-51687102035Stefano Morozzi12/2021
87032^338951+66123102035Stefano Morozzi06/2022
87042^338950+19317102035Stefano Morozzi09/2022
87052^338951-161479102035Stefano Morozzi12/2022
87062^338950-66335102035Stefano Morozzi01/2023
87072^338951-41611102035Stefano Morozzi02/2023
87082^338952-142887102035Stefano Morozzi02/2023
87092^338949+85449102034Stefano Morozzi03/2022
87102^338949-184585102034Stefano Morozzi04/2022
87112^338949-88555102034Stefano Morozzi12/2022
87122^338948+49393102034Stefano Morozzi02/2023
87132^338949-17601102034Stefano Morozzi02/2023
87142^338943+127103102033Stefano Morozzi12/2021
87152^338944-84003102033Stefano Morozzi04/2022
87162^338945+138605102033Stefano Morozzi05/2022
87172^338943+95133102033Stefano Morozzi11/2022
87182^338943+147435102033Stefano Morozzi11/2022
87192^338943-116067102033Stefano Morozzi01/2023
87202^338940+78607102032Stefano Morozzi01/2022
87212^338942-86687102032Stefano Morozzi12/2022
87222^338939+151569102031Stefano Morozzi12/2021
87232^338938+183975102031Stefano Morozzi03/2022
87242^338937-33429102031Stefano Morozzi04/2022
87252^338939-183259102031Stefano Morozzi04/2022
87262^338937-139951102031Stefano Morozzi01/2023
87272^338938-40151102031Stefano Morozzi01/2023
87282^338938+74449102031Stefano Morozzi02/2023
87292^338935+179999102030Stefano Morozzi01/2022
87302^338936+84147102030Stefano Morozzi03/2022
87312^338935+171261102030Stefano Morozzi11/2022
87322^338936-41355102030Stefano Morozzi01/2023
87332^338931+2349102029Stefano Morozzi12/2021
87342^338933+79935102029Stefano Morozzi01/2022
87352^338930+33819102029Stefano Morozzi03/2022
87362^338931-31555102029Stefano Morozzi03/2022
87372^338933+64169102029Stefano Morozzi05/2022
87382^338932-184965102029Stefano Morozzi06/2022
87392^338932+66943102029Stefano Morozzi09/2022
87402^338932+92995102029Stefano Morozzi09/2022
87412^338931+97001102029Stefano Morozzi11/2022
87422^338932-165453102029Stefano Morozzi01/2023
87432^338933-40899102029Stefano Morozzi01/2023
87442^338928+2367102028Stefano Morozzi12/2021
87452^338927+52779102028Stefano Morozzi01/2022
87462^338927-79539102028Stefano Morozzi02/2022
87472^338929+60819102028Stefano Morozzi03/2022
87482^338928-156959102028Stefano Morozzi03/2022
87492^338927-63919102028Stefano Morozzi12/2022
87502^338925+106631102027Stefano Morozzi01/2022


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Created by  Henri Lifchitz & Renaud Lifchitz : October, 26 2000, last modification: February, 15 2025 11:08 (Time in France)

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