PRP Records

Probable Primes Top 10000

(288949 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 ?
9001(25*2^281577-1)/2384764Lelio R Paula02/2014
90022^281574-11154643584763Paul Bourdelais10/2021
900320320^14819+14819^2032084752Hans Havermann07/2020
90042^281500-45584740Yves Minet03/2012
900510^84725+114514191984726Marisa Kirisame03/2015
900610^84725+14204184726Patrick De Geest10/2015
900710^84725-13867784725Patrick De Geest02/2016
900876^45044+7584720Norbert Schneider02/2015
900954^48897-5384709Norbert Schneider08/2014
9010(9913*2^281377-1)/6584706Lelio R Paula04/2015
9011Phi(171124,10)/29946701/7761329021/5856034404184700Maksym Voznyy11/2015
90122^281337-11122384691Enzo Doria05/2014
90132^281308+5461584683Lelio R Paula09/2013
90147*5^121144-684677Lelio R Paula10/2014
9015(2^281270+3858)/284671Stefano Morozzi01/2020
9016(2^281252+47)/384665Lelio R Paula01/2013
901711^81297-315084663Enzo Doria12/2012
90182^281208-30384653Yves Minet02/2012
9019197^36892-284648Lelio R Paula10/2017
9020(21*2^281187+1)/248384644Lelio R Paula01/2013
9021(4*10^84632-61)/384633Robert Price12/2021
902211^81247-8484611Lelio R Paula10/2015
9023(10876^20959-1)/1087584597Serge Batalov08/2020
90242067^25516+25516^206784595Norbert Schneider11/2019
902617^68747-6484590Lelio R Paula11/2015
9025(2^281002+3718)/284590Stefano Morozzi01/2020
90275^121018-1559684588Enzo Doria02/2013
90286^108702+784587Lelio R Paula11/2014
902910^84582+10067784583Patrick De Geest05/2016
903010^84582-800184582Robert Price03/2016
90311828^25929+25929^182884580Norbert Schneider12/2019
9032(2^280968+1446)/284580Stefano Morozzi01/2020
90333*5^121004-884579Lelio R Paula10/2014
90345^120996-8484573Lelio R Paula10/2015
9035(2^280896+1522)/284558Stefano Morozzi01/2020
9036(10223*2^280881+1)/6841984553Lelio R Paula06/2014
90372^280852+9768184545Yves Minet08/2004
90382^280848-120384544Lelio R Paula09/2013
90395^120946-2484538Lelio R Paula10/2015
90402^280810-211184533Yves Minet08/2013
904111^81161-516084521Enzo Doria01/2013
90422^280737-9384511Lelio R Paula08/2012
9043(2^280737+494)/284510Stefano Morozzi01/2020
9044(2^280717+1166)/284504Stefano Morozzi01/2020
90452^280698+31584499Lelio R Paula09/2013
90463^177099-34084498Lelio R Paula12/2015
9047(8201^21589-1)/820084493Serge Batalov08/2020
9048(5*10^84469-107)/384470Robert Price01/2017
9049(3^177002+7)/669602227216174484436Lelio R Paula12/2012
9050(2^280500-1017)/82384436Lelio R Paula01/2013
905124677^2640+2640^2467784435Hans Havermann07/2020
905214^73660-584424Lelio R Paula11/2015
9053(83*10^84413-101)/984414Robert Price08/2021
9054(2^280405+746)/284411Stefano Morozzi01/2020
9056(19*10^84409-61)/384410Robert Price04/2017
905520862^11119+11119^2086284410Hans Havermann07/2020
90572^280388+11784406Lelio R Paula08/2012
90582^280389-56653384406Paul Bourdelais03/2013
905923423^4008+4008^2342384392Hans Havermann07/2020
9060(2^280340+3322)/284391Stefano Morozzi01/2020
9061(141584^16384+1)/6553784390Syoichiro Yamada06/2008
9062(1897^25741-1)/189684378Serge Batalov08/2020
9064119^40652+11884376Norbert Schneider09/2018
9063(2^280291+2274)/284376Stefano Morozzi01/2020
90652^280240-17384361Lelio R Paula08/2012
9066(184*10^84348-1)/384350Robert Price02/2017
906721068^10083+10083^2106884348Hans Havermann07/2020
90684*10^84346+9384347Robert Price01/2017
90697*2^280156-584337Lelio R Paula08/2014
9070(8760^21391-1)/875984331Serge Batalov08/2020
90718*7^99782-384327Lelio R Paula10/2014
9072(38*10^84325+169)/984326Robert Price11/2021
90732^280116+13384324Lelio R Paula08/2012
90742^280118+5461584324Lelio R Paula09/2013
9075(509203*2^280090-1)/384321Lelio R Paula04/2015
90766^108354+4784316Lelio R Paula12/2015
9077(2^280069+462)/284309Stefano Morozzi01/2020
907820657^12058+12058^2065784307Hans Havermann07/2020
907910^84305+14196384306Patrick De Geest07/2013
908010^84305-5784305Robert Price05/2011
90819^88339+3*8^88339-2*4^88339-3*2^8833984297Mike Oakes01/2011
908275843!4-3284295Robert Price11/2019
90833^176648-11280484283Enzo Doria06/2014
90846^108310+11584282Lelio R Paula12/2015
9085(11*2^279968-1)/584280Lelio R Paula02/2014
90866^108288-1664384265Enzo Doria02/2013
90872^279917-5869584264Lelio R Paula08/2013
908865^46477+3684259Lelio R Paula01/2016
9089(2^279883+3230)/284253Stefano Morozzi01/2020
9090(2^279876+1422)/284251Stefano Morozzi01/2020
90912^279866-190784249Yves Minet05/2013
909223140^4373+4373^2314084248Hans Havermann07/2020
909319736^18567+18567^1973684248Hans Havermann07/2020
9094(3^176580-5)/2807684246Lelio R Paula12/2012
9095(p(17530)#+4)/284246Robert Price09/2017
9096(2*10^84239+1)/384239Serge Batalov07/2009
9097(7*10^84236-493)/984236Robert Price04/2021
909818^67103-4184233Lelio R Paula11/2015
909920^64743-4384233Lelio R Paula01/2016
9100(2^279807+2454)/284230Stefano Morozzi01/2020
910119717^18672+18672^1971784216Hans Havermann07/2020
9102(2^279754+3574)/284215Stefano Morozzi01/2020
9103143^39070+39070^14384209Serge Batalov05/2014
910411^80857-540084204Enzo Doria01/2013
910523*10^84185-984187Robert Price10/2021
9106(2^279642+3130)/284181Stefano Morozzi01/2020
9107(13*10^84179+161)/384180Robert Price04/2017
91082^279634-11040584179Enzo Doria05/2014
9109(74*10^84170+313)/984171Robert Price11/2017
91102^279582-101784163Lelio R Paula08/2013
9111(22*10^84159-19)/384160Robert Price02/2017
9112p(17513)#/2+51284156Robert Price05/2017
9113(19*10^84144-43)/384145Robert Price10/2017
9114(9*2^279507-1)/13784139Lelio R Paula02/2014
911511^80792-81084137Enzo Doria11/2012
9116(97*10^84134-1)/384136Serge Batalov12/2014
9117p(17507)#/2+3284125Robert Price12/2016
9118(1750^25939-1)/174984118Serge Batalov08/2020
911921485^8224+8224^2148584116Hans Havermann04/2017
91203^176294-34084114Lelio R Paula12/2015
9121(3^176287+4)/219184107Lelio R Paula12/2012
91222^279388-71984105Yves Minet05/2012
9123(22699*2^279378+1)/22184104Lelio R Paula06/2014
9124(28*10^84095-67)/384096Robert Price10/2020
9125(2^279343+578)/284091Stefano Morozzi01/2020
91262^279332-11044784088Enzo Doria05/2014
91272^279320+784084Lelio R Paula06/2012
9128127^39966-284081Lelio R Paula10/2017
9129(2^279299+2490)/284078Stefano Morozzi01/2020
9130(2^279301+1694)/284078Stefano Morozzi01/2020
9131(2^279285+962)/284073Stefano Morozzi01/2020
9132(2^279269+1122)/284069Stefano Morozzi01/2020
9133(11*2^279240-1)/9584059Lelio R Paula02/2014
91342^279218-11134784053Enzo Doria05/2014
913535^54435+284052Lelio R Paula05/2013
9136(2^279176+2998)/284041Stefano Morozzi01/2020
9137(31*2^279191-1)/1251152384040Lelio R Paula02/2014
913820996^10059+10059^2099684038Hans Havermann05/2017
913997*10^84033-384035Robert Price01/2017
9140(2^279153+1326)/284034Stefano Morozzi01/2020
9141(2^279155+3534)/284034Stefano Morozzi01/2020
914221234^9067+9067^2123484033Hans Havermann05/2017
9143(134569^16384+1)/284033Richard Fischer06/2018
9144(5858^22303-1)/585784029Serge Batalov08/2020
9145(29*10^84024-119)/984025Robert Price12/2021
91462^279095-10971784016Enzo Doria04/2014
9147(2^279054+1438)/284004Stefano Morozzi01/2020
914810^83997+55559783998Patrick De Geest02/2021
914910^83997-4000183997Robert Price01/2021
915014^73282-9983991Lelio R Paula11/2015
915121457^8200+8200^2145783979Hans Havermann06/2017
915289*10^83976-783978Robert Price03/2017
91532^278955+17383974Lelio R Paula06/2012
9154(7*2^278851+1)/3983942Lelio R Paula12/2012
9155(9913*2^278844-1)/4080383940Lelio R Paula04/2015
91565^120076-1484683930Enzo Doria02/2013
9157(85*10^83921-1)/383923Robert Price07/2017
9158(2^278770-3)/2383917Lelio R Paula12/2012
9159(10^83916+449)/983916Serge Batalov12/2014
91612^278715+9983902Lelio R Paula06/2012
9160(132109^16384+1)/283902Richard Fischer05/2018
916240235!2-2^4023583899Robert Price09/2015
91632^278698-17183897Lelio R Paula06/2012
9164(19*10^83894-43)/383895Robert Price10/2017
91656^107802+2583887Lelio R Paula12/2015
91668*10^83880+3983881Robert Price01/2017
9167(58*10^83878+23)/983879Robert Price09/2015
91687^99244-9083871Lelio R Paula10/2015
9169(2^278601+1674)/283867Stefano Morozzi01/2020
91702^278554+425783854Lelio R Paula08/2013
91712^278504-10961983839Enzo Doria04/2014
91722^278499+187043383837Enzo Doria05/2016
9173(2^278487+570)/283833Stefano Morozzi01/2020
9174105^41475+10483829Norbert Schneider11/2016
917515^71276-6883828Lelio R Paula11/2015
91762^278464-21641383827Enzo Doria04/2013
9177(2^278440+1602)/283819Stefano Morozzi01/2020
9178(76*10^83816-211)/983817Robert Price10/2017
9179(2^278429+1950)/283816Stefano Morozzi01/2020
9180(2^278428+1750)/283815Stefano Morozzi01/2020
9181(8*10^83811-101)/383812Robert Price10/2017
91822^278400+4075583807Lelio R Paula08/2013
9183(2^278394+3718)/283805Stefano Morozzi01/2020
9184(2^278388+3586)/283803Stefano Morozzi01/2020
9185(9*2^278381-1)/783802Lelio R Paula02/2014
91863*9^87813+6^87813+2*4^8781383796Mike Oakes12/2010
918719551^19268+19268^1955183773Hans Havermann05/2017
918820625^11522+11522^2062583770Hans Havermann05/2017
9189(44*10^83768-791)/983769Robert Price10/2017
9190(87^43189+1)/8883764Paul Bourdelais08/2017
91912^278235-4983758Lelio R Paula06/2012
919223543^3610+3610^2354383755Hans Havermann05/2017
919418^66711-9183741Lelio R Paula11/2015
91934*10^83740-8983741Robert Price08/2017
9195(3*2^278172-1)/1183738Lelio R Paula02/2014
9196(15*29^57251+2561)/2883724Curtis Bright05/2015
91974*7^99059-983716Lelio R Paula10/2014
9198(2^278128-3)/12684472414983714Lelio R Paula12/2012
91992^278077+186721183710Enzo Doria03/2016
9200(85*10^83708+203)/983709Robert Price09/2020
92012^278059-2783705Lelio R Paula06/2012
9202214^35917+35917^21483702Norbert Schneider12/2014
9203(23*10^83693+7)/383694Robert Price10/2015
920485^43375-283689Lelio R Paula09/2013
92055*3^175360+483669Lelio R Paula07/2014
9206(23^61441-1)/2283665Robert Price01/2012
920720091^14596+14596^2009183664Hans Havermann03/2017
92082^277907-11062983659Enzo Doria05/2014
920919522^19283+19283^1952283656Hans Havermann04/2017
9210(2^277881+2570)/283651Stefano Morozzi01/2020
92118*5^119664-383643Lelio R Paula10/2014
92128*3^175299-783640Lelio R Paula07/2014
9213(26*10^83638-413)/983639Robert Price10/2017
9214(197*10^83636+7)/383638Robert Price12/2020
92153^175250+2283616Robert Price12/2013
921711^80285+3083609Lelio R Paula10/2015
921626870^1293+1293^2687083609Hans Havermann03/2017
9218(6730^21841-1)/672983604Serge Batalov08/2020
9219(2828^24223-1)/282783602Serge Batalov08/2020
92202^277691+187442383594Enzo Doria06/2016
922113^75022-6083571Lelio R Paula11/2015
9222(2^277593+2622)/283564Stefano Morozzi01/2020
922314^72905-5183559Lelio R Paula11/2015
9224(17*2^277565-1)/54383554Lelio R Paula02/2014
92255^119532-1283550Lelio R Paula10/2015
92266^107358-1625383541Enzo Doria02/2013
922710^83534+359303783535Paul Bourdelais10/2021
92282^277478-46021183530Enzo Doria06/2015
9229(2^277474+814)/283528Stefano Morozzi01/2020
9230(22*10^83525-7)/383526Erik Branger09/2014
9231(30^56543+1)/3183520Robert Price07/2013
92322^277417-46078383511Paul Bourdelais04/2013
9233(2^277404+3582)/283507Stefano Morozzi01/2020
9234(22699*2^277387+1)/21983504Lelio R Paula06/2014
9235(31*2^277383-1)/24783500Lelio R Paula02/2014
923621368^8085+8085^2136883500Hans Havermann04/2017
9237(2^277353+3750)/283492Stefano Morozzi01/2020
9238(2^277348+3538)/283490Stefano Morozzi01/2020
9239(9*2^277342+1)/1383489Lelio R Paula12/2012
92405^119439-6683485Lelio R Paula10/2015
9241(14*10^83471-101)/383472Robert Price04/2017
92425*6^107263+783468Lelio R Paula10/2014
9243(64*10^83461-1)/983462Serge Batalov11/2010
92442^277244-17570983459Hans Havermann10/2018
9245(2^277230+1450)/283455Stefano Morozzi01/2020
9246(2^277232+3658)/283455Stefano Morozzi01/2020
924717^67796-9283420Lelio R Paula11/2015
92482^277106-11005783418Enzo Doria04/2014
92496^107200-1983418Lelio R Paula12/2015
92502*10^83416+4783417Robert Price12/2021


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Created by  Henri Lifchitz & Renaud Lifchitz : October, 26 2000, last modification: January, 19 2022 17:15 (Time in France)

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