PRP Records

Probable Primes Top 10000

(271023 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 ?
70022^281780-11489384825Enzo Doria05/2015
7001(7654^21841-1)/765384825Serge Batalov08/2020
70033^177719+6484794Lelio R Paula12/2015
70052^281675-19984793Lelio R Paula08/2012
70042^281673-11122384793Enzo Doria05/2014
7006(4*10^84779+149)/984779Robert Price03/2017
7007129^40167-12884777Norbert Schneider01/2019
7008(2^281622+3970)/284777Stefano Morozzi01/2020
7009(72*10^84772-27)/984773Ray Chandler01/2011
701011^81398-63084768Enzo Doria11/2012
7011(25*2^281577-1)/2384764Lelio R Paula02/2014
701220320^14819+14819^2032084752Hans Havermann07/2020
70132^281500-45584740Yves Minet03/2012
701410^84725+114514191984726Marisa Kirisame03/2015
701510^84725+14204184726Patrick De Geest10/2015
701610^84725-13867784725Patrick De Geest02/2016
701776^45044+7584720Norbert Schneider02/2015
701854^48897-5384709Norbert Schneider08/2014
7019(9913*2^281377-1)/6584706Lelio R Paula04/2015
7020Phi(171124,10)/29946701/7761329021/5856034404184700Maksym Voznyy11/2015
70212^281337-11122384691Enzo Doria05/2014
70222^281308+5461584683Lelio R Paula09/2013
70237*5^121144-684677Lelio R Paula10/2014
7024(2^281270+3858)/284671Stefano Morozzi01/2020
7025(2^281252+47)/384665Lelio R Paula01/2013
702611^81297-315084663Enzo Doria12/2012
70272^281208-30384653Yves Minet02/2012
7028197^36892-284648Lelio R Paula10/2017
7029(21*2^281187+1)/248384644Lelio R Paula01/2013
703011^81247-8484611Lelio R Paula10/2015
7031(10876^20959-1)/1087584597Serge Batalov08/2020
70322067^25516+25516^206784595Norbert Schneider11/2019
703417^68747-6484590Lelio R Paula11/2015
7033(2^281002+3718)/284590Stefano Morozzi01/2020
70355^121018-1559684588Enzo Doria02/2013
70366^108702+784587Lelio R Paula11/2014
703710^84582+10067784583Patrick De Geest05/2016
703810^84582-800184582Robert Price03/2016
70391828^25929+25929^182884580Norbert Schneider12/2019
7040(2^280968+1446)/284580Stefano Morozzi01/2020
70413*5^121004-884579Lelio R Paula10/2014
70425^120996-8484573Lelio R Paula10/2015
7043(2^280896+1522)/284558Stefano Morozzi01/2020
7044(10223*2^280881+1)/6841984553Lelio R Paula06/2014
70452^280852+9768184545Yves Minet08/2004
70462^280848-120384544Lelio R Paula09/2013
70475^120946-2484538Lelio R Paula10/2015
70482^280810-211184533Yves Minet08/2013
704911^81161-516084521Enzo Doria01/2013
70502^280737-9384511Lelio R Paula08/2012
7051(2^280737+494)/284510Stefano Morozzi01/2020
7052(2^280717+1166)/284504Stefano Morozzi01/2020
70532^280698+31584499Lelio R Paula09/2013
70543^177099-34084498Lelio R Paula12/2015
7055(8201^21589-1)/820084493Serge Batalov08/2020
7056(5*10^84469-107)/384470Robert Price01/2017
7057(3^177002+7)/669602227216174484436Lelio R Paula12/2012
7058(2^280500-1017)/82384436Lelio R Paula01/2013
705924677^2640+2640^2467784435Hans Havermann07/2020
706014^73660-584424Lelio R Paula11/2015
7061(2^280405+746)/284411Stefano Morozzi01/2020
7063(19*10^84409-61)/384410Robert Price04/2017
706220862^11119+11119^2086284410Hans Havermann07/2020
70642^280388+11784406Lelio R Paula08/2012
70652^280389-56653384406Paul Bourdelais03/2013
706623423^4008+4008^2342384392Hans Havermann07/2020
7067(2^280340+3322)/284391Stefano Morozzi01/2020
7068(141584^16384+1)/6553784390Syoichiro Yamada06/2008
7069(1897^25741-1)/189684378Serge Batalov08/2020
7071119^40652+11884376Norbert Schneider09/2018
7070(2^280291+2274)/284376Stefano Morozzi01/2020
70722^280240-17384361Lelio R Paula08/2012
7073(184*10^84348-1)/384350Robert Price02/2017
707421068^10083+10083^2106884348Hans Havermann07/2020
70754*10^84346+9384347Robert Price01/2017
70767*2^280156-584337Lelio R Paula08/2014
7077(8760^21391-1)/875984331Serge Batalov08/2020
70788*7^99782-384327Lelio R Paula10/2014
70792^280116+13384324Lelio R Paula08/2012
70802^280118+5461584324Lelio R Paula09/2013
7081(509203*2^280090-1)/384321Lelio R Paula04/2015
70826^108354+4784316Lelio R Paula12/2015
7083(2^280069+462)/284309Stefano Morozzi01/2020
708420657^12058+12058^2065784307Hans Havermann07/2020
708510^84305+14196384306Patrick De Geest07/2013
708610^84305-5784305Robert Price05/2011
70879^88339+3*8^88339-2*4^88339-3*2^8833984297Mike Oakes01/2011
708875843!4-3284295Robert Price11/2019
70893^176648-11280484283Enzo Doria06/2014
70906^108310+11584282Lelio R Paula12/2015
7091(11*2^279968-1)/584280Lelio R Paula02/2014
70926^108288-1664384265Enzo Doria02/2013
70932^279917-5869584264Lelio R Paula08/2013
709465^46477+3684259Lelio R Paula01/2016
7095(2^279883+3230)/284253Stefano Morozzi01/2020
7096(2^279876+1422)/284251Stefano Morozzi01/2020
70972^279866-190784249Yves Minet05/2013
709823140^4373+4373^2314084248Hans Havermann07/2020
709919736^18567+18567^1973684248Hans Havermann07/2020
7101(3^176580-5)/2807684246Lelio R Paula12/2012
7100(p(17530)#+4)/284246Robert Price09/2017
7102(2*10^84239+1)/384239Serge Batalov07/2009
710418^67103-4184233Lelio R Paula11/2015
710320^64743-4384233Lelio R Paula01/2016
7105(2^279807+2454)/284230Stefano Morozzi01/2020
710619717^18672+18672^1971784216Hans Havermann07/2020
7107(2^279754+3574)/284215Stefano Morozzi01/2020
7108143^39070+39070^14384209Serge Batalov05/2014
710911^80857-540084204Enzo Doria01/2013
7110(2^279642+3130)/284181Stefano Morozzi01/2020
7111(13*10^84179+161)/384180Robert Price04/2017
71122^279634-11040584179Enzo Doria05/2014
7113(74*10^84170+313)/984171Robert Price11/2017
71142^279582-101784163Lelio R Paula08/2013
7115(22*10^84159-19)/384160Robert Price02/2017
7116p(17513)#/2+51284156Robert Price05/2017
7117(19*10^84144-43)/384145Robert Price10/2017
7118(9*2^279507-1)/13784139Lelio R Paula02/2014
711911^80792-81084137Enzo Doria11/2012
7120(97*10^84134-1)/384136Serge Batalov12/2014
7121p(17507)#/2+3284125Robert Price12/2016
7122(1750^25939-1)/174984118Serge Batalov08/2020
712321485^8224+8224^2148584116Hans Havermann04/2017
71243^176294-34084114Lelio R Paula12/2015
7125(3^176287+4)/219184107Lelio R Paula12/2012
71262^279388-71984105Yves Minet05/2012
7127(22699*2^279378+1)/22184104Lelio R Paula06/2014
7128(2^279343+578)/284091Stefano Morozzi01/2020
71292^279332-11044784088Enzo Doria05/2014
71302^279320+784084Lelio R Paula06/2012
7131127^39966-284081Lelio R Paula10/2017
7132(2^279299+2490)/284078Stefano Morozzi01/2020
7133(2^279301+1694)/284078Stefano Morozzi01/2020
7134(2^279285+962)/284073Stefano Morozzi01/2020
7135(2^279269+1122)/284069Stefano Morozzi01/2020
7136(11*2^279240-1)/9584059Lelio R Paula02/2014
71372^279218-11134784053Enzo Doria05/2014
713835^54435+284052Lelio R Paula05/2013
7139(2^279176+2998)/284041Stefano Morozzi01/2020
7140(31*2^279191-1)/1251152384040Lelio R Paula02/2014
714120996^10059+10059^2099684038Hans Havermann05/2017
714297*10^84033-384035Robert Price01/2017
7143(2^279153+1326)/284034Stefano Morozzi01/2020
7144(2^279155+3534)/284034Stefano Morozzi01/2020
714521234^9067+9067^2123484033Hans Havermann05/2017
7146(134569^16384+1)/284033Richard Fischer06/2018
7147(5858^22303-1)/585784029Serge Batalov08/2020
71482^279095-10971784016Enzo Doria04/2014
7149(2^279054+1438)/284004Stefano Morozzi01/2020
715014^73282-9983991Lelio R Paula11/2015
715121457^8200+8200^2145783979Hans Havermann06/2017
715289*10^83976-783978Robert Price03/2017
71532^278955+17383974Lelio R Paula06/2012
7154(7*2^278851+1)/3983942Lelio R Paula12/2012
7155(9913*2^278844-1)/4080383940Lelio R Paula04/2015
71565^120076-1484683930Enzo Doria02/2013
7157(85*10^83921-1)/383923Robert Price07/2017
7158(2^278770-3)/2383917Lelio R Paula12/2012
7159(10^83916+449)/983916Serge Batalov12/2014
71612^278715+9983902Lelio R Paula06/2012
7160(132109^16384+1)/283902Richard Fischer05/2018
716240235!2-2^4023583899Robert Price09/2015
71632^278698-17183897Lelio R Paula06/2012
7164(19*10^83894-43)/383895Robert Price10/2017
71656^107802+2583887Lelio R Paula12/2015
71668*10^83880+3983881Robert Price01/2017
7167(58*10^83878+23)/983879Robert Price09/2015
71687^99244-9083871Lelio R Paula10/2015
7169(2^278601+1674)/283867Stefano Morozzi01/2020
71702^278554+425783854Lelio R Paula08/2013
71712^278504-10961983839Enzo Doria04/2014
71722^278499+187043383837Enzo Doria05/2016
7173(2^278487+570)/283833Stefano Morozzi01/2020
7174105^41475+10483829Norbert Schneider11/2016
717515^71276-6883828Lelio R Paula11/2015
71762^278464-21641383827Enzo Doria04/2013
7177(2^278440+1602)/283819Stefano Morozzi01/2020
7178(76*10^83816-211)/983817Robert Price10/2017
7179(2^278429+1950)/283816Stefano Morozzi01/2020
7180(2^278428+1750)/283815Stefano Morozzi01/2020
7181(8*10^83811-101)/383812Robert Price10/2017
71822^278400+4075583807Lelio R Paula08/2013
7183(2^278394+3718)/283805Stefano Morozzi01/2020
7184(2^278388+3586)/283803Stefano Morozzi01/2020
7185(9*2^278381-1)/783802Lelio R Paula02/2014
71863*9^87813+6^87813+2*4^8781383796Mike Oakes12/2010
718719551^19268+19268^1955183773Hans Havermann05/2017
718820625^11522+11522^2062583770Hans Havermann05/2017
7189(44*10^83768-791)/983769Robert Price10/2017
7190(87^43189+1)/8883764Paul Bourdelais08/2017
71912^278235-4983758Lelio R Paula06/2012
719223543^3610+3610^2354383755Hans Havermann05/2017
719418^66711-9183741Lelio R Paula11/2015
71934*10^83740-8983741Robert Price08/2017
7195(3*2^278172-1)/1183738Lelio R Paula02/2014
7196(15*29^57251+2561)/2883724Curtis Bright05/2015
71974*7^99059-983716Lelio R Paula10/2014
7198(2^278128-3)/12684472414983714Lelio R Paula12/2012
71992^278077+186721183710Enzo Doria03/2016
7200(85*10^83708+203)/983709Robert Price09/2020
72012^278059-2783705Lelio R Paula06/2012
7202214^35917+35917^21483702Norbert Schneider12/2014
7203(23*10^83693+7)/383694Robert Price10/2015
720485^43375-283689Lelio R Paula09/2013
72055*3^175360+483669Lelio R Paula07/2014
7206(23^61441-1)/2283665Robert Price01/2012
720720091^14596+14596^2009183664Hans Havermann03/2017
72082^277907-11062983659Enzo Doria05/2014
720919522^19283+19283^1952283656Hans Havermann04/2017
7210(2^277881+2570)/283651Stefano Morozzi01/2020
72118*5^119664-383643Lelio R Paula10/2014
72128*3^175299-783640Lelio R Paula07/2014
7213(26*10^83638-413)/983639Robert Price10/2017
72143^175250+2283616Robert Price12/2013
721611^80285+3083609Lelio R Paula10/2015
721526870^1293+1293^2687083609Hans Havermann03/2017
7217(6730^21841-1)/672983604Serge Batalov08/2020
7218(2828^24223-1)/282783602Serge Batalov08/2020
72192^277691+187442383594Enzo Doria06/2016
722013^75022-6083571Lelio R Paula11/2015
7221(2^277593+2622)/283564Stefano Morozzi01/2020
722214^72905-5183559Lelio R Paula11/2015
7223(17*2^277565-1)/54383554Lelio R Paula02/2014
72245^119532-1283550Lelio R Paula10/2015
72256^107358-1625383541Enzo Doria02/2013
72262^277478-46021183530Enzo Doria06/2015
7227(2^277474+814)/283528Stefano Morozzi01/2020
7228(22*10^83525-7)/383526Erik Branger09/2014
7229(30^56543+1)/3183520Robert Price07/2013
72302^277417-46078383511Paul Bourdelais04/2013
7231(2^277404+3582)/283507Stefano Morozzi01/2020
7232(22699*2^277387+1)/21983504Lelio R Paula06/2014
7233(31*2^277383-1)/24783500Lelio R Paula02/2014
723421368^8085+8085^2136883500Hans Havermann04/2017
7235(2^277353+3750)/283492Stefano Morozzi01/2020
7236(2^277348+3538)/283490Stefano Morozzi01/2020
7237(9*2^277342+1)/1383489Lelio R Paula12/2012
72385^119439-6683485Lelio R Paula10/2015
7239(14*10^83471-101)/383472Robert Price04/2017
72405*6^107263+783468Lelio R Paula10/2014
7241(64*10^83461-1)/983462Serge Batalov11/2010
72422^277244-17570983459Hans Havermann10/2018
7243(2^277230+1450)/283455Stefano Morozzi01/2020
7244(2^277232+3658)/283455Stefano Morozzi01/2020
724517^67796-9283420Lelio R Paula11/2015
72462^277106-11005783418Enzo Doria04/2014
72476^107200-1983418Lelio R Paula12/2015
724811^80096-183083412Enzo Doria12/2012
72493^174801+5683402Lelio R Paula12/2015
72502^277033-11197383396Enzo Doria05/2014


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Created by  Henri Lifchitz & Renaud Lifchitz : October, 26 2000, last modification: September, 30 2020 00:02 (Time in France)

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