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 ?
9251(77*10^93249-257)/993250Robert Price10/2017
925221822^18749+18749^2182293245Hans Havermann09/2020
92533^195430-293244Theodore Burton02/2007
9254(13*10^93236+47)/393237Robert Price01/2017
9255(67*10^93226-7)/393228Robert Price10/2017
9256(86*10^93217-221)/993218Robert Price06/2017
92572^309637-1632993211Enzo Doria04/2013
9258(41*10^93207+49)/993208Robert Price04/2016
925914^81312-5793194Lelio R Paula06/2016
926041^57783-4093192Theodore Burton02/2007
92613*10^93179-9793180Robert Price08/2017
92625*7^110252-493175Lelio R Paula11/2014
926322022^16959+16959^2202293140Hans Havermann08/2020
926483061!4-51293137Robert Price11/2019
926525169^5016+5016^2516993135Hans Havermann08/2020
9266(483641^16384+1)/293135Richard Fischer02/2021
92672^309380-2793133Lelio R Paula11/2012
926825653^4268+4268^2565393127Hans Havermann08/2020
9269(2^309355+1826)/293125Stefano Morozzi02/2021
9270(2^309334+2710)/293119Stefano Morozzi09/2020
927123*10^93116-793118Robert Price03/2016
9272(2^309270+3214)/293100Stefano Morozzi09/2020
9273(29*10^93082+1)/393083Robert Price11/2015
9274(2^309198+3738)/293078Stefano Morozzi09/2020
9275(58*10^93062-13)/993063Robert Price09/2015
9276(2^309138+1794)/293060Stefano Morozzi01/2021
92772^309131+186938393058Enzo Doria05/2016
9278(2^309114+3610)/293053Stefano Morozzi09/2020
92792^309066-9393039Lelio R Paula11/2012
92802^309063-11326993038Enzo Doria07/2014
92813^194965+1693022Robert Price10/2013
9282(89*10^93019-737)/993020Robert Price01/2022
92832^308979+186914393012Enzo Doria05/2016
92845^133064+5493008Lelio R Paula04/2016
9285(2^308947+2750)/293003Stefano Morozzi01/2021
9286(2^308905-509203)/11992988Lelio R Paula06/2013
9287(94*10^92981-49)/9992981Ray Chandler07/2011
9288(2*10^92976-17)/392976Robert Price08/2014
928924783^5642+5642^2478392972Hans Havermann08/2020
9290(472489^16384+1)/292969Richard Fischer01/2021
92912^308809+3796792961Phil Moore03/2008
9292(3^194825+5)/1165692952Lelio R Paula04/2013
9293norm(Mod(x,x^3-x-1)^760951-1)92930Paul Vanderveen08/2022
9294(2^308679+5)/157392919Lelio R Paula06/2013
92952^308650+51392913Lelio R Paula02/2016
92965*7^109936+692908Lelio R Paula10/2014
92972*10^92897+8992898Robert Price07/2016
9298(2^308585+3182)/292894Stefano Morozzi09/2020
9299(467307^16384+1)/292891Richard Fischer01/2021
930012^86073-2992889Lelio R Paula06/2016
93012^308566-11792888Lelio R Paula11/2012
930211594^22851-22851^1159492872Norbert Schneider03/2022
9303(17*10^92869-11)/392870Robert Price07/2015
93042^308459+7543192856Enzo Doria04/2016
93052^308426-186637792846Enzo Doria03/2016
930624810^5521+5521^2481092840Hans Havermann09/2020
9307(96^46831-1)/9592830Paul Bourdelais09/2017
93082^308349-11211192823Enzo Doria06/2014
93099*10^92821+1992822Robert Price05/2016
93102^308337-7592819Lelio R Paula11/2012
93114*3^194508+792805Lelio R Paula08/2014
931222*25^66379-11392796Curtis Bright05/2015
931324538^6047+6047^2453892792Hans Havermann09/2020
931411^89101-108092790Enzo Doria12/2012
93152^308236-186785992789Enzo Doria04/2016
931612^85963+2592770Lelio R Paula06/2016
931723692^8221+8221^2369292753Hans Havermann08/2020
93187^109750-6692750Lelio R Paula04/2016
93199*10^92742+1192743Robert Kinser01/2017
9320(2^308054+778)/292734Stefano Morozzi09/2020
9321(21*2^308046-1)/885792729Lelio R Paula02/2014
93222^307997-11065592717Enzo Doria05/2014
9323L(443609)92709Renaud Lifchitz11/2003
932410^92691+992692Robert Price03/2011
932510^92691-25229192691Patrick De Geest08/2013
9326(2^307883+3506)/292682Stefano Morozzi09/2020
93272^307879-252192681Yves Minet07/2014
932821269^21412+21412^2126992666Norbert Schneider04/2020
9329(2^307780-7)/1995966992644Lelio R Paula06/2013
933014^80831+4792643Lelio R Paula06/2016
933115^78744+9292611Lelio R Paula07/2016
933265^51083-6492610Norbert Schneider11/2014
9333(2^307639+506)/292609Stefano Morozzi09/2020
9334131^43737-13092604Norbert Schneider02/2019
93356^118996-1694392597Enzo Doria02/2013
9336(16*10^92591+41)/392592Robert Price10/2017
9337(2^307566+3094)/292587Stefano Morozzi09/2020
9338(2^307528+1578)/292575Stefano Morozzi09/2020
93399*10^92573+8392574Robert Price11/2020
9340(3^194014-7)/292568Lelio R Paula04/2013
9341(2^307498+570)/292566Stefano Morozzi09/2020
9342(63^51439+1)/6492555Paul Bourdelais08/2017
9343(26*10^92546-77)/392547Robert Price02/2017
93443^193954+34092540Lelio R Paula04/2016
93452^307407-307407^292539Henri Lifchitz05/2005
934624299^6430+6430^2429992536Hans Havermann08/2020
9348(17*10^92513-11)/392514Robert Price07/2015
93472^307322-39907192514Harrison Mesh06/2022
93492^307318-421192512Yves Minet06/2011
93502^307280+19392501Lelio R Paula11/2012
935120^71075-3392471Lelio R Paula05/2016
93522^307126-7879592455Lelio R Paula02/2016
93532^307125-4978992454Henri Lifchitz08/2005
93542^307099+2392447Lelio R Paula11/2012
9355129^43798+12892440Norbert Schneider01/2019
935621826^17181+17181^2182692435Hans Havermann09/2020
9357Phi(277314,10)/332776992430Makoto Kamada05/2019
9358(2^307022+1038)/292423Stefano Morozzi09/2020
93597*10^92414-6992415Robert Price01/2017
9360(9787*2^306975-1)/212915592407Lelio R Paula04/2015
936122280^14037+14037^2228092402Hans Havermann09/2020
93622^306915+187337392391Enzo Doria06/2016
93632^306908+1291592389Lelio R Paula02/2016
936421620^18759+18759^2162092387Hans Havermann09/2020
9365(2^306897+1142)/292385Stefano Morozzi09/2020
936619^72244-8092383Lelio R Paula06/2016
93682^306849+7592371Lelio R Paula11/2012
9367(397*10^92369+53)/992371Robert Price11/2017
93692^306813-86968810592360Lelio R Paula08/2016
9370(2^306797+2694)/292355Stefano Morozzi09/2020
937121713^17914+17914^2171392350Hans Havermann09/2020
93722^306672-10905992318Enzo Doria04/2014
9373(430463^16384+1)/292307Richard Fischer09/2020
93746^118604-1706392292Enzo Doria02/2013
937521969^15878+15878^2196992288Hans Havermann08/2020
937621690^17959+17959^2169092276Hans Havermann08/2020
9377(7613^23773-1)/761292273Serge Batalov08/2020
9378(31*2^306487-1)/229192260Lelio R Paula02/2014
93792^306467-183561192256Enzo Doria04/2015
93802^306433+7642792246Enzo Doria05/2016
93812^306430-11331392245Enzo Doria07/2014
9382(23*10^92244-59)/992245Robert Price03/2017
9383(47*2^306398+1)/138480392231Lelio R Paula04/2015
938421436^20043+20043^2143692217Hans Havermann09/2020
9385(25*10^92186+59)/392187Robert Price05/2016
93862^306213-28618392180Enzo Doria06/2015
938710^92178+6192179Robert Price04/2011
938810^92178-17550992178Patrick De Geest07/2013
93892^306200+118592176Lelio R Paula02/2016
9390(2^306171+1514)/292167Stefano Morozzi09/2020
93912^306153+1192162Lelio R Paula11/2012
9392(2^306141-7)/592157Lelio R Paula06/2013
939321725^17454+17454^2172592156Hans Havermann09/2020
9394(26*10^92152-23)/392153Robert Price08/2016
9395(2*10^92152+67)/392152Robert Price04/2017
939621368^20457+20457^2136892115Hans Havermann08/2020
9397(2^305996+3018)/292114Stefano Morozzi09/2020
93984*10^92099+3*7^9209992100Mike Oakes12/2010
939930504^1045+1045^3050492096Hans Havermann08/2020
940024334^6085+6085^2433492087Hans Havermann08/2020
9401(2^305898+2262)/292085Stefano Morozzi01/2021
9402(4591^25147-1)/459092083Serge Batalov08/2020
9403115^44684+11492081Norbert Schneider07/2018
9404(416771^16384+1)/292077Richard Fischer08/2020
9405(2^305867-2^152934+1)/59207511/2006
94062^305851-10949592071Enzo Doria04/2014
9407(416213^16384+1)/292067Richard Fischer08/2020
940912^85300+3592055Lelio R Paula06/2016
9408((10^46026-1)*1000/9+739)*10^46026+(10^46026-1)/992055Hans Havermann05/2019
941021732^17201+17201^2173292048Hans Havermann08/2020
94117*10^92043-3992044Robert Price07/2020
94123^192911+9292042Lelio R Paula04/2016
94132^305723-27627192032Enzo Doria07/2015
9414(2^305714+3738)/292029Stefano Morozzi09/2020
9415(2^305707+798)/292027Stefano Morozzi01/2021
9416(2^305682+3202)/292020Stefano Morozzi09/2020
94172^305676+9392018Donovan Johnson06/2008
94183^192819+491999Lelio R Paula04/2013
9419(38*10^91997-83)/9991997Ray Chandler07/2011
94202^305539+7291191977Enzo Doria04/2016
9421Phi(212014,10)91960Makoto Kamada04/2019
9422(2^305423+2666)/291942Stefano Morozzi09/2020
9423(2^305427-5)/129799821391934Lelio R Paula06/2013
942482077!4-12891928Robert Price11/2019
942585^47642+8491922Norbert Schneider10/2015
942610^91920+18765191921Patrick De Geest07/2013
942710^91920-3991920Robert Price05/2011
9428(3975^25537-1)/397491913Serge Batalov08/2020
9429(22*10^91903+41)/991904Robert Price02/2015
94312^305275-2791897Lelio R Paula11/2012
94303^192607-772691897Enzo Doria05/2014
9432(2^305243+2274)/291887Stefano Morozzi02/2021
9433(2^305220+1278)/291881Stefano Morozzi01/2021
9435(6958^23911-1)/695791874Serge Batalov08/2020
94349*10^91873-9191874Robert Price06/2021
9436(7*10^91856-61)/991856Erik Branger12/2009
9437(2^305107+1274)/291847Stefano Morozzi01/2021
9438(89*10^91839-53)/991840Robert Price11/2015
94391678^28479+28479^167891839Norbert Schneider08/2020
9440(2^304996+406)/291813Stefano Morozzi02/2021
94418*5^131351+791812Lelio R Paula10/2014
94423^192426-6891811Lelio R Paula04/2016
94432^304979-37560791808Harrison Mesh06/2022
94452^304973+11791807Lelio R Paula11/2012
9444(2^304974+234)/291807Stefano Morozzi09/2020
94462^304939-186372791796Enzo Doria03/2016
94472^304902+841591785Lelio R Paula02/2016
944818^73119+6191785Lelio R Paula06/2016
9449(78557*2^304740+1)/15991739Lelio R Paula06/2014
94502^304747+7135591738Lelio R Paula02/2016
9451(2^304738+2262)/291735Stefano Morozzi01/2021
94528*3^192251+591728Lelio R Paula08/2014
9453(2^304693+3746)/291722Stefano Morozzi01/2021
94542^304674-8791717Lelio R Paula11/2012
9455(28*10^91715+701)/991716Robert Price11/2017
9456(2^304698+9)/136280995391715Lelio R Paula06/2013
9457(2^304671+1046)/291715Stefano Morozzi09/2020
9458(2^304667+3614)/291714Stefano Morozzi09/2020
9459(5*10^91707-119)/391708Robert Price04/2016
94602^304633-11277191704Enzo Doria06/2014
9461(5*10^91702+19)/391703Robert Price07/2022
9462(395347^16384+1)/291701Richard Fischer06/2020
94639*10^91693+2391694Robert Price11/2017
94642^304578-1671391688Enzo Doria05/2013
94656^117824-1871391685Enzo Doria03/2013
9466(17^74509-1)/1691679Paul Bourdelais03/2010
9467(2^304551-7)/891223191673Lelio R Paula06/2013
9468(2^304532-3)/301391670Lelio R Paula06/2013
94692^304507-1664591666Enzo Doria04/2013
9470(29*2^304489+1)/3191661Lelio R Paula09/2013
947121221^20860+20860^2122191661Hans Havermann08/2020
94722^304471-183612791655Enzo Doria04/2015
94732^304433+3276991644Lelio R Paula02/2016
94742^304410-1662591637Enzo Doria04/2013
9475183^40500-291630Lelio R Paula10/2017
9476(2^304373+1850)/291626Stefano Morozzi02/2021
9477(203*10^91613+1)/391615Robert Price09/2017
94784*5^131052+791603Lelio R Paula10/2014
948021725^16458+16458^2172591601Hans Havermann08/2020
9479(2^304290+3270)/291601Stefano Morozzi02/2021
94812^304278-400191597Yves Minet04/2017
94822^304272-186637791595Enzo Doria03/2016
94832^304268+1968391594Lelio R Paula02/2016
948421718^16497+16497^2171891594Hans Havermann08/2020
948522759^10576+10576^2275991590Hans Havermann08/2020
9486(29*10^91584-119)/991585Robert Price12/2021
94872^304162-16191562Lelio R Paula11/2012
94885*7^108331+691552Lelio R Paula10/2014
94892^304082-278782191538Enzo Doria03/2016
94902^304015+6413391518David Broadhurst06/2002
9491(7*2^303963+1)/391503Lelio R Paula09/2013
9492(2^303945-9)/361791494Lelio R Paula06/2013
9493(384007^16384+1)/291494Richard Fischer05/2020
94942^303930+188052791493Enzo Doria10/2016
949524810^4859+4859^2481091464Hans Havermann08/2020
94962*10^91457+2991458Robert Price02/2021
94973^191684-6891457Lelio R Paula04/2016
9498(21*2^303813-1)/16991456Lelio R Paula02/2014
9499(298*10^91446+11)/391448Robert Price11/2020
950011^87797-12091432Enzo Doria07/2012


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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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