PRP Records

Probable Primes Top 10000

(291910 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 ?
6001(25*10^103360-241)/9103361Robert Price05/2018
6002Phi(104989,10)/2939693103350Maksym Voznyy09/2015
600324826^14511+14511^24826103319Hans Havermann09/2020
60042^343182-171103309Lelio R Paula08/2011
6005(23619^23619+23620^23620)/7187103294David Broadhurst09/2009
6006(10680^25639-1)/10679103285Serge Batalov06/2022
6007(7427^26683-1)/7426103282Serge Batalov06/2022
60082^343079-1835611103278Enzo Doria05/2015
60092^343063-1147103273Yves Minet06/2013
601024741^14930+14930^24741103271Hans Havermann09/2020
6011(16*10^103255-73)/3103256Robert Price07/2020
6012(219^44119-1)/218103256Serge Batalov06/2022
60139*6^132689+7103254Lelio R Paula11/2014
60142^342979-18085103247Enzo Doria05/2013
6015(16*10^103244-31)/3103245Robert Price03/2019
60162^342966-16995103244Lelio R Paula11/2016
601723797^21774+21774^23797103230Hans Havermann09/2020
601825388^11637+11637^25388103224Hans Havermann09/2020
6019(2^342876+2086)/2103216Stefano Morozzi09/2020
6020(16*10^103214-31)/3103215Robert Price03/2019
6022(37*10^103211+611)/9103212Robert Price11/2018
6021(238*10^103210-1)/3103212Robert Price04/2020
60235^147650+16103203Lelio R Paula11/2016
6024gcd(Phi(852060,10),(10^42603+1)^3*(10^42603+1-10^21302)+(10^85206+10^42603)*(10^21302+1)+10^127809)103201Serge Batalov04/2015
60252^342817+2707067103199Enzo Doria03/2016
602643^63177-42103198Theodore Burton02/2007
60272^342805-21025103195Enzo Doria06/2013
602824129^18890+18890^24129103182Hans Havermann09/2020
6029(622*10^103171-1)/9103173Robert Price11/2021
60302^342714+12285103168Lelio R Paula11/2016
6031(2*10^103161-17)/3103161Serge Batalov11/2022
603218^82178-4481103156Enzo Doria03/2013
60332^342665-17349103153Enzo Doria05/2013
603430408^2467+2467^30408103150Hans Havermann09/2020
6035(5^147571-3^147571)/2103148Kellen Shenton05/2022
6036(2^342615+3090)/2103138Stefano Morozzi09/2020
60372^342612+175103137Lelio R Paula08/2011
60385*2^342585-3103130Lelio R Paula09/2014
6039(16*10^103127+77)/3103128Robert Price03/2019
6040(2^342527+3774)/2103111Stefano Morozzi02/2021
60412^342503-19209103104Enzo Doria05/2013
6042(2^342484+2586)/2103098Stefano Morozzi09/2020
60432^342476+51103096Lelio R Paula08/2011
60442^342460-18885103091Enzo Doria05/2013
6045(2^342442+862)/2103086Stefano Morozzi02/2021
6046(194*10^103074-17)/3103076Robert Price09/2020
60477^121968+82103075Lelio R Paula10/2016
60482^342392-108863103071Enzo Doria03/2014
6049(2^342389+806)/2103070Stefano Morozzi01/2021
60503^216014+28103065Lelio R Paula11/2016
60512^342353-108879103059Enzo Doria03/2014
605210^103055+276081103056Patrick De Geest12/2016
605310^103055-53103055Lelio R Paula11/2016
6054(58*10^103046+419)/9103047Robert Price05/2019
60557^121933+4103046Lelio R Paula11/2014
6056(71*10^103028-143)/9103029Robert Price10/2021
6057(2^342235+3618)/2103023Stefano Morozzi09/2020
605819^80560-68103017Lelio R Paula10/2016
60592^342209+76607103016Enzo Doria05/2016
6061328^40945+40945^328103013Norbert Schneider12/2014
606012^95454-91103013Lelio R Paula10/2016
606225833^9716+9716^25833103009Hans Havermann01/2019
6063(893*10^103004+7)/9103006Robert Price06/2021
6064(1475^32503-1)/1474102993Serge Batalov06/2022
606565^56809-64^56809102990Robert Price08/2013
60665^147338-6102985Lelio R Paula11/2014
60672^342084-112739102978Enzo Doria06/2014
60689*6^132330+7102974Lelio R Paula11/2014
60692^342034-16737102963Enzo Doria05/2013
6070(9787*2^342011-1)/25102959Lelio R Paula05/2015
6071(3^215802-5)/124343756102956Lelio R Paula12/2013
60722^341991-17421102950Enzo Doria05/2013
60732^341969-112225102943Enzo Doria06/2014
6074(9787*2^341864-1)/3102915Lelio R Paula05/2015
60752^341859+1869413102910Enzo Doria05/2016
607610^102909+61102910Lelio R Paula11/2016
607710^102909-67049102909Patrick De Geest12/2016
607823814^20935+20935^23814102898Hans Havermann02/2019
607928345^4264+4264^28345102888Hans Havermann02/2019
608025665^10204+10204^25665102886Hans Havermann02/2019
608126288^8181+8181^26288102860Hans Havermann02/2019
60822^341659+1836773102850Enzo Doria03/2016
60832^341608-110639102835Enzo Doria05/2014
608410^102824+49102825Lelio R Paula11/2016
608510^102824-168011102824Patrick De Geest12/2016
608611^98708-8102794Lelio R Paula10/2016
60872^341466+4429102792Lelio R Paula09/2011
60882^341460-107102790Lelio R Paula08/2011
6089(2^341388+47)/21014943102761Lelio R Paula12/2013
60902^341355+21102759Lelio R Paula08/2011
6091(6496^26947-1)/6495102736Serge Batalov06/2022
60922^341246+40755102726Lelio R Paula11/2016
6093(2^341256-5)/991699102723Lelio R Paula12/2013
60947^121547+78102720Lelio R Paula10/2016
60952^341223-461197102719Enzo Doria06/2015
609627838^4893+4893^27838102711Hans Havermann03/2019
60982^341190-20577102709Enzo Doria06/2013
6097(27*2^341212+1)/84674449102709Lelio R Paula12/2013
6099(25*10^102698+77)/3102699Robert Price09/2022
61006^131976-65102698Lelio R Paula10/2016
61012^341134+2533102692Henri Lifchitz09/2005
610213^92184-54102688Lelio R Paula10/2016
61032^341116-20873102687Enzo Doria06/2013
61042^341094-19953102680Enzo Doria06/2013
610523761^20950+20950^23761102676Hans Havermann03/2019
61072^341053+129102668Lelio R Paula08/2011
6106(4724^27943-1)/4723102668Serge Batalov06/2022
6109(31*2^341006-1)/3102655Lelio R Paula03/2014
61087^121471+94102655Lelio R Paula10/2016
61112^341004-173102653Lelio R Paula08/2011
611020^78901+3102653Lelio R Paula10/2016
6112(2^341001+1674)/2102652Stefano Morozzi09/2020
61135^146853-52102646Lelio R Paula10/2016
61142^340969-216931102642Enzo Doria05/2014
6115122^49196+121102641Norbert Schneider10/2018
61162^340952+1870021102637Enzo Doria05/2016
61175*2^340940-3102634Lelio R Paula08/2014
6118(6^131891+1)/7102631Paul Bourdelais01/2010
6119(11*10^102629-23)/3102630Robert Price09/2021
612025876^9239+9239^25876102615Hans Havermann02/2019
6121(4*10^102612+83)/3102613Robert Price02/2018
612275^54717+74102598Norbert Schneider01/2015
6123(17*10^102597+13)/3102598Robert Price01/2019
61242^340806-20393102593Enzo Doria06/2013
6125(2^340790+5)/138267102583Lelio R Paula12/2013
61266^131821+77102577Lelio R Paula10/2016
6127(203*10^102561-11)/3102563Robert Price12/2020
61282^340688-29102558Henri Lifchitz05/2005
61292^340685-109101102557Enzo Doria04/2014
613065^56567-64102552Norbert Schneider11/2014
613126230^8121+8121^26230102550Hans Havermann03/2019
6132(64*10^102547+161)/9102548Robert Price08/2022
6133(8*10^102541+49)/3102542Robert Price05/2020
6134(536*10^102533-23)/9102535Robert Price02/2020
61352^340547-108897102515Enzo Doria03/2014
6136(2^340536+778)/2102512Stefano Morozzi09/2020
613725592^10119+10119^25592102500Hans Havermann02/2019
6138(5*10^102492-23)/9102492Serge Batalov11/2022
61397^121268+82102484Lelio R Paula10/2016
6140(6883*2^340443-1)/162401102483Lelio R Paula05/2015
61412^340434-5955102481Lelio R Paula11/2016
6142(7*10^102480-19)/3102481Robert Price10/2020
6143(2^340381+47)/7102465Lelio R Paula12/2013
6144111^50095+110102461Norbert Schneider04/2017
61452^340291-20301102438Enzo Doria06/2013
614612^94915+89102431Lelio R Paula10/2016
6147(106*10^102422+17)/3102424Robert Price04/2021
614824466^15349+15349^24466102417Hans Havermann03/2019
61492^340212+111546435102415Paul Bourdelais10/2021
61502^340208-20373102413Enzo Doria06/2013
61516^131598-17273102404Enzo Doria02/2013
6152(2^340132+1182)/2102390Stefano Morozzi09/2020
6153(2^340133+1166)/2102390Stefano Morozzi09/2020
61542^340115-21181102385Enzo Doria06/2013
6155(55459*2^340090+1)/1591102379Lelio R Paula07/2014
6156(2^340064+3630)/2102370Stefano Morozzi09/2020
615789^52511-88^52511102365Robert Price06/2015
61583^214539-112756102362Enzo Doria07/2014
615923159^23450-23450^23159102353Norbert Schneider12/2019
61602^340000-19877102351Enzo Doria06/2013
61612^339990-114845102348Enzo Doria05/2015
6162(3^214516-2)/51383102346Lelio R Paula12/2013
616320^78661-99102341Lelio R Paula09/2016
61642^339951-19585102336Enzo Doria05/2013
6165(17*10^102335-167)/3102336Robert Price05/2022
6166(13*2^339943+1)/45102333Lelio R Paula12/2013
6167(236282#+121441)/(121441*25499429)102332Makoto Morimoto08/2020
61685*10^102323-91102324Robert Price03/2021
61702^339889+29327102317Yves Minet06/2010
6169(167*10^102315-17)/3102317Robert Price03/2020
617126348^7641+7641^26348102314Hans Havermann03/2019
6172Phi(239414,10)/6333218543102303Makoto Kamada08/2019
61732^339834-109493102301Enzo Doria04/2014
6174(16*10^102299-19)/3102300Robert Price02/2019
6175(11^98221-5^98221)/6102286Robert Price01/2013
61763^214365+1820102279Lelio R Paula10/2016
617731978^1579+1579^31978102278Hans Havermann03/2019
6178(89*10^102262-467)/9102263Robert Price04/2022
6179(11*2^339705-1)/183102261Lelio R Paula03/2014
61802^339694-16995102259Lelio R Paula09/2016
6181(56*10^102255+691)/9102256Robert Price05/2019
6182122^49008+121102249Norbert Schneider10/2018
6183(2^339652+3178)/2102246Stefano Morozzi09/2020
61847^120985-38102245Lelio R Paula10/2016
618510^102244+122961102245Patrick De Geest12/2016
618610^102244-27102244Lelio R Paula09/2016
61877^120982-62102242Lelio R Paula10/2016
6188(2^339640+2670)/2102242Stefano Morozzi09/2020
61894*6^131382-5102236Lelio R Paula11/2014
6190(2^339607+3290)/2102232Stefano Morozzi02/2021
61912^339586-1091102226Yves Minet11/2012
619211^98161-3072000102225Enzo Doria12/2012
61939*7^120961-4102225Lelio R Paula11/2014
61945*3^214250+2102224Serge Batalov10/2010
619512^94713-59102213Lelio R Paula10/2016
619612^94705+89102204Lelio R Paula10/2016
61972^339407-177102172Lelio R Paula08/2011
61984*10^102163-57102164Robert Price10/2018
61992^339355+65102157Lelio R Paula07/2011
6200(28*10^102142-31)/3102143Robert Price12/2019
6201(2^339323+47)/880715102141Lelio R Paula12/2013
6202(2^339268+1758)/2102130Stefano Morozzi09/2020
6203s(178551)102122Robert Price05/2020
6204(797*10^102112-23)/9102114Robert Price01/2022
6205(2^339175+2790)/2102102Stefano Morozzi02/2021
62072^339168+21102100Lelio R Paula07/2011
62082^339167-108807102100Enzo Doria03/2014
6206(2^339169+42)/2102100Stefano Morozzi09/2020
62092^339156+163102097Lelio R Paula08/2011
6210(2^339149+746)/2102094Stefano Morozzi09/2020
6211(25*10^102076-67)/3102077Robert Price06/2019
62122^339081-4543102074Yves Minet03/2019
6213(3435^28867-1)/3434102069Serge Batalov06/2022
62142*10^102062+77102063Robert Price08/2020
621624327^15668+15668^24327102053Hans Havermann02/2019
621510^102052+66793102053Patrick De Geest09/2022
621810^102052-7000001102052Robert Price06/2021
621710^102052-618623102052Patrick De Geest09/2022
62192^339000-175635102050Stefano Morozzi12/2021
62202^339000-151667102050Stefano Morozzi12/2021
62212^338999+79289102049Stefano Morozzi01/2022
62222^338998-63897102049Stefano Morozzi12/2022
62232^338994+188757102048Stefano Morozzi05/2022
62242^338995+70785102048Stefano Morozzi11/2022
62252^338994-12183102048Stefano Morozzi12/2022
62262^338992+181591102047Stefano Morozzi01/2022
62272^338992+136171102047Stefano Morozzi03/2022
62282^338991-109435102047Stefano Morozzi04/2022
62292^338991+193611102047Stefano Morozzi09/2022
62302^338988-134619102046Stefano Morozzi04/2022
62312^338987-62557102046Stefano Morozzi12/2022
62322^338986-60141102045Stefano Morozzi06/2022
62332^338986+98209102045Stefano Morozzi11/2022
62342^338981+106391102044Stefano Morozzi01/2022
62352^338982+34069102044Stefano Morozzi03/2022
62362^338982-58781102044Stefano Morozzi04/2022
62372^338980+70833102044Stefano Morozzi11/2022
62382^338977+83007102043Stefano Morozzi02/2022
62392^338979-83601102043Stefano Morozzi04/2022
62402^338975+28355102042Stefano Morozzi01/2022
62412^338973+134619102042Stefano Morozzi03/2022
62422^338974+183777102042Stefano Morozzi03/2022
62432^338975+69293102042Stefano Morozzi09/2022
62442^338972+152343102041Stefano Morozzi12/2021
62452^338972-180623102041Stefano Morozzi02/2022
62462^338972+84441102041Stefano Morozzi03/2022
62472^338971+64875102041Stefano Morozzi05/2022
62482^338971+44985102041Stefano Morozzi11/2022
62492^338971+145065102041Stefano Morozzi11/2022
62502^338972-16635102041Stefano Morozzi01/2023


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Created by  Henri Lifchitz & Renaud Lifchitz : October, 26 2000, last modification: February, 02 2023 13:22 (Time in France)

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