PRP Records

Probable Primes Top 10000

(291192 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 ?
8751(2^309138+1794)/293060Stefano Morozzi01/2021
87522^309131+186938393058Enzo Doria05/2016
8753(2^309114+3610)/293053Stefano Morozzi09/2020
87542^309066-9393039Lelio R Paula11/2012
87552^309063-11326993038Enzo Doria07/2014
87563^194965+1693022Robert Price10/2013
8757(89*10^93019-737)/993020Robert Price01/2022
87582^308979+186914393012Enzo Doria05/2016
87595^133064+5493008Lelio R Paula04/2016
8760(2^308947+2750)/293003Stefano Morozzi01/2021
8761(2^308905-509203)/11992988Lelio R Paula06/2013
8762(94*10^92981-49)/9992981Ray Chandler07/2011
8763(2*10^92976-17)/392976Robert Price08/2014
876424783^5642+5642^2478392972Hans Havermann08/2020
8765(472489^16384+1)/292969Richard Fischer01/2021
87662^308809+3796792961Phil Moore03/2008
8767(3^194825+5)/1165692952Lelio R Paula04/2013
8768norm(Mod(x,x^3-x-1)^760951-1)92930Paul Vanderveen08/2022
8769(2^308679+5)/157392919Lelio R Paula06/2013
87702^308650+51392913Lelio R Paula02/2016
87715*7^109936+692908Lelio R Paula10/2014
87722*10^92897+8992898Robert Price07/2016
8773(2^308585+3182)/292894Stefano Morozzi09/2020
8774(467307^16384+1)/292891Richard Fischer01/2021
877512^86073-2992889Lelio R Paula06/2016
87762^308566-11792888Lelio R Paula11/2012
877711594^22851-22851^1159492872Norbert Schneider03/2022
8778(17*10^92869-11)/392870Robert Price07/2015
87792^308459+7543192856Enzo Doria04/2016
87802^308426-186637792846Enzo Doria03/2016
878124810^5521+5521^2481092840Hans Havermann09/2020
8782(96^46831-1)/9592830Paul Bourdelais09/2017
87832^308349-11211192823Enzo Doria06/2014
87849*10^92821+1992822Robert Price05/2016
87852^308337-7592819Lelio R Paula11/2012
87864*3^194508+792805Lelio R Paula08/2014
878722*25^66379-11392796Curtis Bright05/2015
878824538^6047+6047^2453892792Hans Havermann09/2020
878911^89101-108092790Enzo Doria12/2012
87902^308236-186785992789Enzo Doria04/2016
879112^85963+2592770Lelio R Paula06/2016
879223692^8221+8221^2369292753Hans Havermann08/2020
87937^109750-6692750Lelio R Paula04/2016
87949*10^92742+1192743Robert Kinser01/2017
8795(2^308054+778)/292734Stefano Morozzi09/2020
8796(21*2^308046-1)/885792729Lelio R Paula02/2014
87972^307997-11065592717Enzo Doria05/2014
8798L(443609)92709Renaud Lifchitz11/2003
879910^92691+992692Robert Price03/2011
880010^92691-25229192691Patrick De Geest08/2013
8801(2^307883+3506)/292682Stefano Morozzi09/2020
88022^307879-252192681Yves Minet07/2014
880321269^21412+21412^2126992666Norbert Schneider04/2020
8804(2^307780-7)/1995966992644Lelio R Paula06/2013
880514^80831+4792643Lelio R Paula06/2016
880615^78744+9292611Lelio R Paula07/2016
880765^51083-6492610Norbert Schneider11/2014
8808(2^307639+506)/292609Stefano Morozzi09/2020
8809131^43737-13092604Norbert Schneider02/2019
88106^118996-1694392597Enzo Doria02/2013
8811(16*10^92591+41)/392592Robert Price10/2017
8812(2^307566+3094)/292587Stefano Morozzi09/2020
8813(2^307528+1578)/292575Stefano Morozzi09/2020
88149*10^92573+8392574Robert Price11/2020
8815(3^194014-7)/292568Lelio R Paula04/2013
8816(2^307498+570)/292566Stefano Morozzi09/2020
8817(63^51439+1)/6492555Paul Bourdelais08/2017
8818(26*10^92546-77)/392547Robert Price02/2017
88193^193954+34092540Lelio R Paula04/2016
88202^307407-307407^292539Henri Lifchitz05/2005
882124299^6430+6430^2429992536Hans Havermann08/2020
8823(17*10^92513-11)/392514Robert Price07/2015
88222^307322-39907192514Harrison Mesh06/2022
88242^307318-421192512Yves Minet06/2011
88252^307280+19392501Lelio R Paula11/2012
882620^71075-3392471Lelio R Paula05/2016
88272^307126-7879592455Lelio R Paula02/2016
88282^307125-4978992454Henri Lifchitz08/2005
88292^307099+2392447Lelio R Paula11/2012
8830129^43798+12892440Norbert Schneider01/2019
883121826^17181+17181^2182692435Hans Havermann09/2020
8832Phi(277314,10)/332776992430Makoto Kamada05/2019
8833(2^307022+1038)/292423Stefano Morozzi09/2020
88347*10^92414-6992415Robert Price01/2017
8835(9787*2^306975-1)/212915592407Lelio R Paula04/2015
883622280^14037+14037^2228092402Hans Havermann09/2020
88372^306915+187337392391Enzo Doria06/2016
88382^306908+1291592389Lelio R Paula02/2016
883921620^18759+18759^2162092387Hans Havermann09/2020
8840(2^306897+1142)/292385Stefano Morozzi09/2020
884119^72244-8092383Lelio R Paula06/2016
88432^306849+7592371Lelio R Paula11/2012
8842(397*10^92369+53)/992371Robert Price11/2017
88442^306813-86968810592360Lelio R Paula08/2016
8845(2^306797+2694)/292355Stefano Morozzi09/2020
884621713^17914+17914^2171392350Hans Havermann09/2020
88472^306672-10905992318Enzo Doria04/2014
8848(430463^16384+1)/292307Richard Fischer09/2020
88496^118604-1706392292Enzo Doria02/2013
885021969^15878+15878^2196992288Hans Havermann08/2020
885121690^17959+17959^2169092276Hans Havermann08/2020
8852(7613^23773-1)/761292273Serge Batalov08/2020
8853(31*2^306487-1)/229192260Lelio R Paula02/2014
88542^306467-183561192256Enzo Doria04/2015
88552^306433+7642792246Enzo Doria05/2016
88562^306430-11331392245Enzo Doria07/2014
8857(23*10^92244-59)/992245Robert Price03/2017
8858(47*2^306398+1)/138480392231Lelio R Paula04/2015
885921436^20043+20043^2143692217Hans Havermann09/2020
8860(25*10^92186+59)/392187Robert Price05/2016
88612^306213-28618392180Enzo Doria06/2015
886210^92178+6192179Robert Price04/2011
886310^92178-17550992178Patrick De Geest07/2013
88642^306200+118592176Lelio R Paula02/2016
8865(2^306171+1514)/292167Stefano Morozzi09/2020
88662^306153+1192162Lelio R Paula11/2012
8867(2^306141-7)/592157Lelio R Paula06/2013
886821725^17454+17454^2172592156Hans Havermann09/2020
8869(26*10^92152-23)/392153Robert Price08/2016
8870(2*10^92152+67)/392152Robert Price04/2017
887121368^20457+20457^2136892115Hans Havermann08/2020
8872(2^305996+3018)/292114Stefano Morozzi09/2020
88734*10^92099+3*7^9209992100Mike Oakes12/2010
887430504^1045+1045^3050492096Hans Havermann08/2020
887524334^6085+6085^2433492087Hans Havermann08/2020
8876(2^305898+2262)/292085Stefano Morozzi01/2021
8877(4591^25147-1)/459092083Serge Batalov08/2020
8878115^44684+11492081Norbert Schneider07/2018
8879(416771^16384+1)/292077Richard Fischer08/2020
8880(2^305867-2^152934+1)/59207511/2006
88812^305851-10949592071Enzo Doria04/2014
8882(416213^16384+1)/292067Richard Fischer08/2020
888412^85300+3592055Lelio R Paula06/2016
8883((10^46026-1)*1000/9+739)*10^46026+(10^46026-1)/992055Hans Havermann05/2019
888521732^17201+17201^2173292048Hans Havermann08/2020
88867*10^92043-3992044Robert Price07/2020
88873^192911+9292042Lelio R Paula04/2016
88882^305723-27627192032Enzo Doria07/2015
8889(2^305714+3738)/292029Stefano Morozzi09/2020
8890(2^305707+798)/292027Stefano Morozzi01/2021
8891(2^305682+3202)/292020Stefano Morozzi09/2020
88922^305676+9392018Donovan Johnson06/2008
88933^192819+491999Lelio R Paula04/2013
8894(38*10^91997-83)/9991997Ray Chandler07/2011
88952^305539+7291191977Enzo Doria04/2016
8896Phi(212014,10)91960Makoto Kamada04/2019
8897(2^305423+2666)/291942Stefano Morozzi09/2020
8898(2^305427-5)/129799821391934Lelio R Paula06/2013
889982077!4-12891928Robert Price11/2019
890085^47642+8491922Norbert Schneider10/2015
890110^91920+18765191921Patrick De Geest07/2013
890210^91920-3991920Robert Price05/2011
8903(3975^25537-1)/397491913Serge Batalov08/2020
8904(22*10^91903+41)/991904Robert Price02/2015
89062^305275-2791897Lelio R Paula11/2012
89053^192607-772691897Enzo Doria05/2014
8907(2^305243+2274)/291887Stefano Morozzi02/2021
8908(2^305220+1278)/291881Stefano Morozzi01/2021
8910(6958^23911-1)/695791874Serge Batalov08/2020
89099*10^91873-9191874Robert Price06/2021
8911(7*10^91856-61)/991856Erik Branger12/2009
8912(2^305107+1274)/291847Stefano Morozzi01/2021
8913(89*10^91839-53)/991840Robert Price11/2015
89141678^28479+28479^167891839Norbert Schneider08/2020
8915(2^304996+406)/291813Stefano Morozzi02/2021
89168*5^131351+791812Lelio R Paula10/2014
89173^192426-6891811Lelio R Paula04/2016
89182^304979-37560791808Harrison Mesh06/2022
89202^304973+11791807Lelio R Paula11/2012
8919(2^304974+234)/291807Stefano Morozzi09/2020
89212^304939-186372791796Enzo Doria03/2016
89222^304902+841591785Lelio R Paula02/2016
892318^73119+6191785Lelio R Paula06/2016
8924(78557*2^304740+1)/15991739Lelio R Paula06/2014
89252^304747+7135591738Lelio R Paula02/2016
8926(2^304738+2262)/291735Stefano Morozzi01/2021
89278*3^192251+591728Lelio R Paula08/2014
8928(2^304693+3746)/291722Stefano Morozzi01/2021
89292^304674-8791717Lelio R Paula11/2012
8930(28*10^91715+701)/991716Robert Price11/2017
8931(2^304698+9)/136280995391715Lelio R Paula06/2013
8932(2^304671+1046)/291715Stefano Morozzi09/2020
8933(2^304667+3614)/291714Stefano Morozzi09/2020
8934(5*10^91707-119)/391708Robert Price04/2016
89352^304633-11277191704Enzo Doria06/2014
8936(5*10^91702+19)/391703Robert Price07/2022
8937(395347^16384+1)/291701Richard Fischer06/2020
89389*10^91693+2391694Robert Price11/2017
89392^304578-1671391688Enzo Doria05/2013
89406^117824-1871391685Enzo Doria03/2013
8941(17^74509-1)/1691679Paul Bourdelais03/2010
8942(2^304551-7)/891223191673Lelio R Paula06/2013
8943(2^304532-3)/301391670Lelio R Paula06/2013
89442^304507-1664591666Enzo Doria04/2013
8945(29*2^304489+1)/3191661Lelio R Paula09/2013
894621221^20860+20860^2122191661Hans Havermann08/2020
89472^304471-183612791655Enzo Doria04/2015
89482^304433+3276991644Lelio R Paula02/2016
89492^304410-1662591637Enzo Doria04/2013
8950183^40500-291630Lelio R Paula10/2017
8951(2^304373+1850)/291626Stefano Morozzi02/2021
8952(203*10^91613+1)/391615Robert Price09/2017
89534*5^131052+791603Lelio R Paula10/2014
895521725^16458+16458^2172591601Hans Havermann08/2020
8954(2^304290+3270)/291601Stefano Morozzi02/2021
89562^304278-400191597Yves Minet04/2017
89572^304272-186637791595Enzo Doria03/2016
89582^304268+1968391594Lelio R Paula02/2016
895921718^16497+16497^2171891594Hans Havermann08/2020
896022759^10576+10576^2275991590Hans Havermann08/2020
8961(29*10^91584-119)/991585Robert Price12/2021
89622^304162-16191562Lelio R Paula11/2012
89635*7^108331+691552Lelio R Paula10/2014
89642^304082-278782191538Enzo Doria03/2016
89652^304015+6413391518David Broadhurst06/2002
8966(7*2^303963+1)/391503Lelio R Paula09/2013
8967(2^303945-9)/361791494Lelio R Paula06/2013
8968(384007^16384+1)/291494Richard Fischer05/2020
89692^303930+188052791493Enzo Doria10/2016
897024810^4859+4859^2481091464Hans Havermann08/2020
89712*10^91457+2991458Robert Price02/2021
89723^191684-6891457Lelio R Paula04/2016
8973(21*2^303813-1)/16991456Lelio R Paula02/2014
8974(298*10^91446+11)/391448Robert Price11/2020
897511^87797-12091432Enzo Doria07/2012
89762^303698-184723191423Enzo Doria07/2015
8977(38^28933-1)^2-291416Norbert Schneider06/2016
897825660^3643+3643^2566091388Hans Havermann08/2020
89792^303554+7729991379Enzo Doria05/2016
89802^303542+1270591376Lelio R Paula02/2016
898131^61269-291375Lelio R Paula09/2013
8982(2^303525+2774)/291370Stefano Morozzi01/2021
89832^303516-6487591368Lelio R Paula02/2016
8984(2^303497+1266)/291362Stefano Morozzi09/2020
8985(2^303497+3710)/291362Stefano Morozzi09/2020
8986(31*10^91352+257)/991353Robert Price12/2021
898721856^15121+15121^2185691349Hans Havermann09/2020
8988(24737*2^303428+1)/391345Lelio R Paula06/2014
8989(21181*2^303357+1)/3236191320Lelio R Paula06/2014
899023081^9046+9046^2308191319Hans Havermann09/2020
89912^303344-278696991316Enzo Doria03/2016
89926^117346+6591313Lelio R Paula05/2016
89932^303321+85591309Lelio R Paula02/2016
8994(2^303315+3746)/291307Stefano Morozzi01/2021
899512^84606+4791306Lelio R Paula06/2016
89962^303288+187431191299Enzo Doria06/2016
8997197^39788-291293Lelio R Paula10/2017
899811^87663-171091292Enzo Doria12/2012
8999(4*10^91284-61)/391285Robert Price12/2021
9000(2^303226+1830)/291280Stefano Morozzi02/2021


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Created by  Henri Lifchitz & Renaud Lifchitz : October, 26 2000, last modification: September, 22 2022 18:03 (Time in France)

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