PRP Records

Probable Primes Top 10000

(293016 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 ?
95012^309063-11326993038Enzo Doria07/2014
95023^194965+1693022Robert Price10/2013
9503(89*10^93019-737)/993020Robert Price01/2022
95042^308979+186914393012Enzo Doria05/2016
95055^133064+5493008Lelio R Paula04/2016
9506(2^308947+2750)/293003Stefano Morozzi01/2021
9507(2^308905-509203)/11992988Lelio R Paula06/2013
9508(94*10^92981-49)/9992981Ray Chandler07/2011
9509(2*10^92976-17)/392976Robert Price08/2014
951024783^5642+5642^2478392972Hans Havermann08/2020
9511(472489^16384+1)/292969Richard Fischer01/2021
95122^308809+3796792961Phil Moore03/2008
9513(3^194825+5)/1165692952Lelio R Paula04/2013
9514norm(Mod(x,x^3-x-1)^760951-1)92930Paul Vanderveen08/2022
9515(2^308679+5)/157392919Lelio R Paula06/2013
95162^308650+51392913Lelio R Paula02/2016
95175*7^109936+692908Lelio R Paula10/2014
95182*10^92897+8992898Robert Price07/2016
9519(2^308585+3182)/292894Stefano Morozzi09/2020
9520(467307^16384+1)/292891Richard Fischer01/2021
952112^86073-2992889Lelio R Paula06/2016
95222^308566-11792888Lelio R Paula11/2012
952311594^22851-22851^1159492872Norbert Schneider03/2022
9524(17*10^92869-11)/392870Robert Price07/2015
95252^308459+7543192856Enzo Doria04/2016
95262^308426-186637792846Enzo Doria03/2016
952724810^5521+5521^2481092840Hans Havermann09/2020
9528(96^46831-1)/9592830Paul Bourdelais09/2017
95292^308349-11211192823Enzo Doria06/2014
95309*10^92821+1992822Robert Price05/2016
95312^308337-7592819Lelio R Paula11/2012
95324*3^194508+792805Lelio R Paula08/2014
953322*25^66379-11392796Curtis Bright05/2015
953424538^6047+6047^2453892792Hans Havermann09/2020
953511^89101-108092790Enzo Doria12/2012
95362^308236-186785992789Enzo Doria04/2016
953712^85963+2592770Lelio R Paula06/2016
953823692^8221+8221^2369292753Hans Havermann08/2020
95397^109750-6692750Lelio R Paula04/2016
95409*10^92742+1192743Robert Kinser01/2017
9541(2^308054+778)/292734Stefano Morozzi09/2020
9542(21*2^308046-1)/885792729Lelio R Paula02/2014
95432^307997-11065592717Enzo Doria05/2014
9544L(443609)92709Renaud Lifchitz11/2003
954510^92691+992692Robert Price03/2011
954610^92691-25229192691Patrick De Geest08/2013
9547(2^307883+3506)/292682Stefano Morozzi09/2020
95482^307879-252192681Yves Minet07/2014
954921269^21412+21412^2126992666Norbert Schneider04/2020
9550(2^307780-7)/1995966992644Lelio R Paula06/2013
955114^80831+4792643Lelio R Paula06/2016
955215^78744+9292611Lelio R Paula07/2016
955365^51083-6492610Norbert Schneider11/2014
9554(2^307639+506)/292609Stefano Morozzi09/2020
9555131^43737-13092604Norbert Schneider02/2019
95566^118996-1694392597Enzo Doria02/2013
9557(16*10^92591+41)/392592Robert Price10/2017
9558(2^307566+3094)/292587Stefano Morozzi09/2020
9559(2^307528+1578)/292575Stefano Morozzi09/2020
95609*10^92573+8392574Robert Price11/2020
9561(3^194014-7)/292568Lelio R Paula04/2013
9562(2^307498+570)/292566Stefano Morozzi09/2020
9563(63^51439+1)/6492555Paul Bourdelais08/2017
9564(26*10^92546-77)/392547Robert Price02/2017
95653^193954+34092540Lelio R Paula04/2016
95662^307407-307407^292539Henri Lifchitz05/2005
956724299^6430+6430^2429992536Hans Havermann08/2020
9569(17*10^92513-11)/392514Robert Price07/2015
95682^307322-39907192514Harrison Mesh06/2022
95702^307318-421192512Yves Minet06/2011
95712^307280+19392501Lelio R Paula11/2012
957220^71075-3392471Lelio R Paula05/2016
95732^307126-7879592455Lelio R Paula02/2016
95742^307125-4978992454Henri Lifchitz08/2005
95752^307099+2392447Lelio R Paula11/2012
9576129^43798+12892440Norbert Schneider01/2019
957721826^17181+17181^2182692435Hans Havermann09/2020
9578Phi(277314,10)/332776992430Makoto Kamada05/2019
9579(2^307022+1038)/292423Stefano Morozzi09/2020
95807*10^92414-6992415Robert Price01/2017
9581(9787*2^306975-1)/212915592407Lelio R Paula04/2015
958222280^14037+14037^2228092402Hans Havermann09/2020
95832^306915+187337392391Enzo Doria06/2016
95842^306908+1291592389Lelio R Paula02/2016
958521620^18759+18759^2162092387Hans Havermann09/2020
958610^92386+11192387Jeppe Stig Nielsen02/2023
9587(2^306897+1142)/292385Stefano Morozzi09/2020
958819^72244-8092383Lelio R Paula06/2016
95902^306849+7592371Lelio R Paula11/2012
9589(397*10^92369+53)/992371Robert Price11/2017
95912^306813-86968810592360Lelio R Paula08/2016
9592(2^306797+2694)/292355Stefano Morozzi09/2020
959321713^17914+17914^2171392350Hans Havermann09/2020
95942^306672-10905992318Enzo Doria04/2014
9595(430463^16384+1)/292307Richard Fischer09/2020
959698*10^92295-992297Robert Price05/2023
95976^118604-1706392292Enzo Doria02/2013
959821969^15878+15878^2196992288Hans Havermann08/2020
959921690^17959+17959^2169092276Hans Havermann08/2020
9600(7613^23773-1)/761292273Serge Batalov08/2020
9601(31*2^306487-1)/229192260Lelio R Paula02/2014
96022^306467-183561192256Enzo Doria04/2015
96032^306433+7642792246Enzo Doria05/2016
96042^306430-11331392245Enzo Doria07/2014
9605(23*10^92244-59)/992245Robert Price03/2017
9606(47*2^306398+1)/138480392231Lelio R Paula04/2015
960721436^20043+20043^2143692217Hans Havermann09/2020
9608(25*10^92186+59)/392187Robert Price05/2016
96092^306213-28618392180Enzo Doria06/2015
961010^92178+6192179Robert Price04/2011
961110^92178-17550992178Patrick De Geest07/2013
96122^306200+118592176Lelio R Paula02/2016
9613(2^306171+1514)/292167Stefano Morozzi09/2020
96142^306153+1192162Lelio R Paula11/2012
9615(2^306141-7)/592157Lelio R Paula06/2013
961621725^17454+17454^2172592156Hans Havermann09/2020
9617(26*10^92152-23)/392153Robert Price08/2016
9618(2*10^92152+67)/392152Robert Price04/2017
9619640*27^64370+1792140Eric Chen02/2023
962021368^20457+20457^2136892115Hans Havermann08/2020
9621(2^305996+3018)/292114Stefano Morozzi09/2020
96224*10^92099+3*7^9209992100Mike Oakes12/2010
962330504^1045+1045^3050492096Hans Havermann08/2020
962424334^6085+6085^2433492087Hans Havermann08/2020
9625(2^305898+2262)/292085Stefano Morozzi01/2021
9626(4591^25147-1)/459092083Serge Batalov08/2020
9627115^44684+11492081Norbert Schneider07/2018
9628(416771^16384+1)/292077Richard Fischer08/2020
9629(2^305867-2^152934+1)/59207511/2006
96302^305851-10949592071Enzo Doria04/2014
9631(416213^16384+1)/292067Richard Fischer08/2020
963312^85300+3592055Lelio R Paula06/2016
9632((10^46026-1)*1000/9+739)*10^46026+(10^46026-1)/992055Hans Havermann05/2019
963421732^17201+17201^2173292048Hans Havermann08/2020
96357*10^92043-3992044Robert Price07/2020
96363^192911+9292042Lelio R Paula04/2016
96372^305723-27627192032Enzo Doria07/2015
9638(2^305714+3738)/292029Stefano Morozzi09/2020
9639(2^305707+798)/292027Stefano Morozzi01/2021
9640(2^305682+3202)/292020Stefano Morozzi09/2020
96412^305676+9392018Donovan Johnson06/2008
96423^192819+491999Lelio R Paula04/2013
9643(38*10^91997-83)/9991997Ray Chandler07/2011
96442^305539+7291191977Enzo Doria04/2016
9645Phi(212014,10)91960Makoto Kamada04/2019
9646(2^305423+2666)/291942Stefano Morozzi09/2020
9647(2^305427-5)/129799821391934Lelio R Paula06/2013
964882077!4-12891928Robert Price11/2019
964985^47642+8491922Norbert Schneider10/2015
965010^91920+18765191921Patrick De Geest07/2013
965110^91920-3991920Robert Price05/2011
9652(3975^25537-1)/397491913Serge Batalov08/2020
9653(22*10^91903+41)/991904Robert Price02/2015
96552^305275-2791897Lelio R Paula11/2012
96543^192607-772691897Enzo Doria05/2014
9656(2^305243+2274)/291887Stefano Morozzi02/2021
9657(2^305220+1278)/291881Stefano Morozzi01/2021
9659(6958^23911-1)/695791874Serge Batalov08/2020
96589*10^91873-9191874Robert Price06/2021
9660(7*10^91856-61)/991856Erik Branger12/2009
9661(2^305107+1274)/291847Stefano Morozzi01/2021
9662(89*10^91839-53)/991840Robert Price11/2015
96631678^28479+28479^167891839Norbert Schneider08/2020
9664(2^304996+406)/291813Stefano Morozzi02/2021
96658*5^131351+791812Lelio R Paula10/2014
96663^192426-6891811Lelio R Paula04/2016
96672^304979-37560791808Harrison Mesh06/2022
96692^304973+11791807Lelio R Paula11/2012
9668(2^304974+234)/291807Stefano Morozzi09/2020
96702^304939-186372791796Enzo Doria03/2016
96712^304902+841591785Lelio R Paula02/2016
967218^73119+6191785Lelio R Paula06/2016
9673(78557*2^304740+1)/15991739Lelio R Paula06/2014
96742^304747+7135591738Lelio R Paula02/2016
9675(2^304738+2262)/291735Stefano Morozzi01/2021
96768*3^192251+591728Lelio R Paula08/2014
9677(5993*33^60402-25)/1691724Eric Chen05/2023
9678(2^304693+3746)/291722Stefano Morozzi01/2021
96792^304674-8791717Lelio R Paula11/2012
9680(28*10^91715+701)/991716Robert Price11/2017
9682(2^304698+9)/136280995391715Lelio R Paula06/2013
9681(2^304671+1046)/291715Stefano Morozzi09/2020
9683(2^304667+3614)/291714Stefano Morozzi09/2020
9684(5*10^91707-119)/391708Robert Price04/2016
96852^304633-11277191704Enzo Doria06/2014
9686(5*10^91702+19)/391703Robert Price07/2022
9687(395347^16384+1)/291701Richard Fischer06/2020
96889*10^91693+2391694Robert Price11/2017
96892^304578-1671391688Enzo Doria05/2013
96906^117824-1871391685Enzo Doria03/2013
9691(17^74509-1)/1691679Paul Bourdelais03/2010
9692(2^304551-7)/891223191673Lelio R Paula06/2013
9693(2^304532-3)/301391670Lelio R Paula06/2013
96942^304507-1664591666Enzo Doria04/2013
9695(29*2^304489+1)/3191661Lelio R Paula09/2013
969621221^20860+20860^2122191661Hans Havermann08/2020
96972^304471-183612791655Enzo Doria04/2015
96982^304433+3276991644Lelio R Paula02/2016
96992^304410-1662591637Enzo Doria04/2013
9700183^40500-291630Lelio R Paula10/2017
9701(2^304373+1850)/291626Stefano Morozzi02/2021
9702(203*10^91613+1)/391615Robert Price09/2017
97034*5^131052+791603Lelio R Paula10/2014
970521725^16458+16458^2172591601Hans Havermann08/2020
9704(2^304290+3270)/291601Stefano Morozzi02/2021
97062^304278-400191597Yves Minet04/2017
97072^304272-186637791595Enzo Doria03/2016
97082^304268+1968391594Lelio R Paula02/2016
970921718^16497+16497^2171891594Hans Havermann08/2020
971022759^10576+10576^2275991590Hans Havermann08/2020
9711(29*10^91584-119)/991585Robert Price12/2021
97122^304162-16191562Lelio R Paula11/2012
97135*7^108331+691552Lelio R Paula10/2014
97142^304082-278782191538Enzo Doria03/2016
97152^304015+6413391518David Broadhurst06/2002
9716(7*2^303963+1)/391503Lelio R Paula09/2013
9717(2^303945-9)/361791494Lelio R Paula06/2013
9718(384007^16384+1)/291494Richard Fischer05/2020
97192^303930+188052791493Enzo Doria10/2016
972024810^4859+4859^2481091464Hans Havermann08/2020
97212*10^91457+2991458Robert Price02/2021
97223^191684-6891457Lelio R Paula04/2016
9723(21*2^303813-1)/16991456Lelio R Paula02/2014
9724(298*10^91446+11)/391448Robert Price11/2020
972511^87797-12091432Enzo Doria07/2012
97262^303698-184723191423Enzo Doria07/2015
9727(38^28933-1)^2-291416Norbert Schneider06/2016
972825660^3643+3643^2566091388Hans Havermann08/2020
97292^303554+7729991379Enzo Doria05/2016
97302^303542+1270591376Lelio R Paula02/2016
973131^61269-291375Lelio R Paula09/2013
973228*33^60170+2367591371Eric Chen05/2023
9733(2^303525+2774)/291370Stefano Morozzi01/2021
97342^303516-6487591368Lelio R Paula02/2016
9735(2^303497+1266)/291362Stefano Morozzi09/2020
9736(2^303497+3710)/291362Stefano Morozzi09/2020
9737(31*10^91352+257)/991353Robert Price12/2021
973821856^15121+15121^2185691349Hans Havermann09/2020
9739(24737*2^303428+1)/391345Lelio R Paula06/2014
9740(21181*2^303357+1)/3236191320Lelio R Paula06/2014
974123081^9046+9046^2308191319Hans Havermann09/2020
97422^303344-278696991316Enzo Doria03/2016
97436^117346+6591313Lelio R Paula05/2016
97442^303321+85591309Lelio R Paula02/2016
9745(2^303315+3746)/291307Stefano Morozzi01/2021
974612^84606+4791306Lelio R Paula06/2016
97472^303288+187431191299Enzo Doria06/2016
9748197^39788-291293Lelio R Paula10/2017
974911^87663-171091292Enzo Doria12/2012
9750(4*10^91284-61)/391285Robert Price12/2021


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Created by  Henri Lifchitz & Renaud Lifchitz : October, 26 2000, last modification: June, 04 2023 08:38 (Time in France)

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