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 ?
4251(2^381251+3186)/2114768Stefano Morozzi09/2020
42522^381209-29323114756Enzo Doria07/2015
42532^381207-111546435114755Paul Bourdelais10/2021
4254569^41651-568^41651114754Jean-Louis Charton11/2009
42552^381201+1873205114753Enzo Doria06/2016
4256(85*10^114737+293)/9114738Robert Price12/2019
4257(265*10^114736+17)/3114738Robert Price03/2020
4258(2^381062+2170)/2114711Stefano Morozzi09/2020
42592^380974-112991114685Enzo Doria07/2014
426037097^1234+1234^37097114679Hans Havermann02/2021
426188^58949-87114626Norbert Schneider11/2015
4262(2^380773+662)/2114624Stefano Morozzi09/2020
426329913^6782+6782^29913114608Hans Havermann02/2021
42642^380700+91114603Lelio R Paula03/2013
4265(2^380632+2578)/2114582Stefano Morozzi09/2020
42667*10^114577+27114578Robert Price11/2020
426810^114575+3^114576114576Mike Oakes09/2010
426710^114575+66561114576Patrick De Geest02/2017
426910^114575-581081114575Patrick De Geest02/2017
42702^380587-115315114569Enzo Doria06/2015
427131874^3927+3927^31874114558Hans Havermann02/2021
42722^380513-216925114546Enzo Doria05/2014
42732^380451-1840087114528Enzo Doria06/2015
4274(2^380426+1510)/2114520Stefano Morozzi09/2020
4275(15*2^380388-1)/539114507Lelio R Paula04/2014
42762^380279-461347114476Enzo Doria07/2015
427727121^16590+16590^27121114447Hans Havermann01/2021
427825966^25555+25555^25966114445Hans Havermann01/2021
4279(11*10^114400+529)/9114401Robert Price09/2021
42802^380021+1871147114398Enzo Doria05/2016
42812^380005+1869707114393Enzo Doria05/2016
42822^379958-113297114379Enzo Doria07/2014
4283(2^379897+1274)/2114361Stefano Morozzi01/2021
42842^379881-109105114356Enzo Doria04/2014
4285(21*2^379857-1)/13114349Lelio R Paula03/2014
4286(4*10^114340+83)/3114341Robert Price02/2018
4287(26*10^114317-77)/3114318Robert Price11/2019
4288(4*10^114296+149)/9114296Robert Price04/2018
428988^58773-87114284Norbert Schneider11/2015
429027764^13065+13065^27764114280Hans Havermann01/2021
42912^379529-2790283114250Enzo Doria03/2016
42922^379522+1869115114248Enzo Doria05/2016
4293(145*10^114226-1)/9114228Serge Batalov12/2014
42942^379317-115033114186Enzo Doria06/2015
4295(22*10^114178+47)/3114179Robert Price06/2021
4296(17*2^379246-1)/17407114162Lelio R Paula03/2014
4297(2^379192+226)/2114148Stefano Morozzi09/2020
42986*10^114091+23114092Robert Price09/2020
4299(4*10^114076+143)/3114077Robert Price03/2018
4300(2^378820+3226)/2114036Stefano Morozzi01/2021
4301(2^378754+2058)/2114017Stefano Morozzi09/2020
4302(46*10^113969+683)/9113970Robert Price03/2019
4303(83*10^113969+133)/9113970Robert Price08/2021
430432226^3439+3439^32226113966Hans Havermann02/2021
430578*10^113954-7113956Robert Price10/2020
43062*10^113941+9113942Dmitry Domanov11/2010
430710^113933+145897113934Patrick De Geest02/2021
4310(2^378478+1642)/2113933Stefano Morozzi09/2020
430810^113933-8000000001113933Robert Price11/2020
430910^113933-66167113933Patrick De Geest02/2021
43112339662057597*10^113903+9113916Robert Price03/2021
43124*10^113905+91113906Robert Price08/2018
431310^113894+76609113895Patrick De Geest02/2021
431510^113894-10000001113894Robert Price09/2020
431410^113894-373947113894Patrick De Geest02/2021
431633933^2270+2270^33933113881Hans Havermann02/2021
43174*10^113874-21113875Robert Price09/2018
43182^378272-16565113872Enzo Doria04/2013
43192^378217-109075113855Enzo Doria04/2014
43202^378198+67113849Lelio R Paula03/2013
43212^378173-3249113842Yves Minet12/2014
4322(2^378155-5)/6597113833Lelio R Paula03/2014
432392941#+(355049#)/(92941#)113830Makoto Morimoto10/2017
432430030^6173+6173^30030113829Hans Havermann01/2021
43252^378128-262977113828Enzo Doria05/2014
43262^378123-113215113827Enzo Doria07/2014
43276^146274-18893113824Enzo Doria03/2013
432834596^1949+1949^34596113815Hans Havermann02/2021
43292^378078+75113813Lelio R Paula03/2013
4330(28*10^113810+449)/9113811Robert Price11/2021
433126273^21448+21448^26273113799Hans Havermann02/2021
43322^377966+255255113780Paul Bourdelais10/2021
43332^377940+63113772Lelio R Paula03/2013
43342^377941-2785843113772Enzo Doria04/2016
43352^377810+1875109113733Enzo Doria09/2016
43362^377803-1838635113731Enzo Doria05/2015
43372^377799+52223113729Yves Minet08/2010
4338(2^377791+3258)/2113727Stefano Morozzi02/2021
433911^109190-270113710Enzo Doria12/2012
434028206^10739+10739^28206113698Hans Havermann01/2021
43417*10^113693+9113694Robert Price09/2015
434213899^27442+27442^13899113692Norbert Schneider12/2020
4343(82*10^113681+161)/9113682Robert Price10/2019
434426121^22478+22478^26121113673Hans Havermann01/2021
43454*10^113658+49113659Robert Price01/2019
4346(10^113656+7)/40231/6439001113645Alfred Reich06/2021
4347(2*10^113631+529)/9113631Robert Price01/2018
43482^377408-2798279113612Enzo Doria04/2016
434913706^27459+27459^13706113596Norbert Schneider12/2020
43505*10^113586+57113587Robert Price12/2018
4351(2^377242+2794)/2113561Stefano Morozzi02/2021
43522^377222+93679113556Yves Minet02/2011
4354262147#+316847113552Makoto Morimoto02/2016
435327172^15101+15101^27172113552Hans Havermann01/2021
4355(2^377131+2018)/2113528Stefano Morozzi09/2020
43562^377026-458903113497Enzo Doria04/2015
4357(2^377014+2202)/2113493Stefano Morozzi09/2020
435834791^1828+1828^34791113488Hans Havermann02/2021
4359(2^376967+258)/2113479Stefano Morozzi09/2020
4360(29*10^113468-17)/3113469Robert Price09/2019
436135^73477-34^73477113454Robert Price05/2012
4362(14*10^113451-89)/3113452Robert Price05/2020
43632^376790+27113426Lelio R Paula03/2013
43642^376786-112701113424Enzo Doria06/2014
43652^376731+21113408Lelio R Paula03/2013
43669*10^113394-73113395Robert Price01/2021
436729660^6651+6651^29660113387Hans Havermann01/2021
43692^376634+1871245113379Enzo Doria05/2016
4368(4^188318+17)/3113379Robert Price02/2017
4370E(29532)/492842728006750534663978950979381235113367Thomas Ritschel01/2021
43712^376576-344369113361Enzo Doria07/2015
43722^376549-4543113353Yves Minet03/2019
4373(17*2^376526-1)/223113345Lelio R Paula03/2014
4374(27*2^376441-1)/811113319Lelio R Paula03/2014
4375(2^376350+3538)/2113293Stefano Morozzi09/2020
437627265^14272+14272^27265113273Hans Havermann02/2021
437732174^3315+3315^32174113269Hans Havermann02/2021
4378(2*10^113248+73)/3113248Robert Price09/2020
43792^376128-21237113226Enzo Doria06/2013
43805*10^113224-81113225Robert Price01/2019
438110^113220+51409113221Patrick De Geest02/2021
438310^113220-1000001113220Robert Price08/2020
438210^113220-61779113220Patrick De Geest02/2021
4384(2^376102+1578)/2113218Stefano Morozzi09/2020
4385(2^375996+3102)/2113186Stefano Morozzi09/2020
438637258^1091+1091^37258113184Hans Havermann02/2021
4387(94*10^113176+11)/3113178Robert Price04/2020
4388(46*10^113162+521)/9113163Robert Price02/2019
4389(2^375885+3614)/2113153Stefano Morozzi09/2020
4390(2^375873+2006)/2113149Stefano Morozzi09/2020
4391(8*10^113135-269)/9113135Robert Price09/2021
4392(2^375726+694)/2113105Stefano Morozzi09/2020
439326050^21959+21959^26050113100Hans Havermann02/2021
43942^375638-1787171113079Enzo Doria03/2016
4395(2^375563+2178)/2113056Stefano Morozzi09/2020
43962^375537+4847113048Yves Minet02/2011
4397(17^91837+16^91837)/33113000Robert Price08/2013
43985*F(270343)*(F(270343)+1)+1112997Serge Batalov04/2015
43992^375350-3221112992Yves Minet07/2011
4400(13*2^375306+1)/7112979Lelio R Paula03/2014
44012^375305+76757112979Enzo Doria05/2016
44022^375258+1874989112964Enzo Doria07/2016
4403(29^77237-1)/28112950Robert Price04/2012
440426620^17483+17483^26620112939Hans Havermann01/2021
44052^375154+74959112933Enzo Doria04/2016
4406(266*10^112930-17)/3112932Robert Price07/2020
4407(2^375134+778)/2112927Stefano Morozzi09/2020
4408(85*10^112919+293)/9112920Robert Price12/2019
440929412^6899+6899^29412112907Hans Havermann02/2021
4410(191*10^112903-17)/3112905Robert Price11/2021
4411(2^375022+1210)/2112893Stefano Morozzi09/2020
441225992^22039+22039^25992112889Hans Havermann02/2021
44132^374993-2787163112885Enzo Doria11/2015
4414(697*10^112869+23)/9112871Robert Price04/2021
441530420^5111+5111^30420112813Hans Havermann02/2021
441613699^27268+27268^13699112800Norbert Schneider12/2020
4417123^53970+2112793Lelio R Paula06/2013
441828942^7887+7887^28942112785Hans Havermann01/2021
44192^374640-4685112778Yves Minet05/2019
442057290^93+93^57290112775Hans Havermann01/2021
4421(2^374556+682)/2112753Stefano Morozzi09/2020
4422p(22852)#/2+512112745Robert Price05/2017
4423(11*10^112742-131)/3112743Robert Price09/2018
44242^374441-21049112718Enzo Doria06/2013
44254*10^112706-93112707Robert Price07/2020
4426(2^374321+1)/3112682H.&R. Lifchitz12/2000
4427(2^374213+1766)/2112650Stefano Morozzi09/2020
4428(2^374094+2674)/2112614Stefano Morozzi09/2020
4429(13^101089-1)/12112607Paul Bourdelais03/2010
44303^236011-8828112606Enzo Doria05/2014
443131854^3427+3427^31854112602Hans Havermann02/2021
4432(85*10^112530-373)/9112531Robert Price05/2021
4433(2^373748+1090)/2112510Stefano Morozzi09/2020
4434(2^373727+1806)/2112503Stefano Morozzi01/2021
443527618^11821+11821^27618112479Hans Havermann01/2021
443626343^18580+18580^26343112460Hans Havermann01/2021
443739^70666+2112435Lelio R Paula11/2013
4438(134*10^112400+7)/3112402Robert Price02/2020
4439(2^373365+326)/2112394Stefano Morozzi09/2020
4440(2^373350-7)/3112390Lelio R Paula03/2014
44412^373306-1840931112377Enzo Doria06/2015
4442(2^373262+270)/2112363Stefano Morozzi09/2020
444334409^1842+1842^34409112356Hans Havermann02/2021
4444(142*10^112352-7)/9112354Robert Price12/2019
444525580^24633+24633^25580112336Hans Havermann01/2021
44462^373117+1872107112320Enzo Doria05/2016
4447(2^373083+2226)/2112309Stefano Morozzi01/2021
444827963^10376+10376^27963112301Hans Havermann01/2021
44492^373040+2792761112297Enzo Doria03/2016
4450EPrime(112280)112280Eric W. Weisstein10/2010
44512^372950+7112270Lelio R Paula03/2013
44522^372945+1872167112268Enzo Doria05/2016
445336274^1243+1243^36274112249Hans Havermann02/2021
4454(55*10^112246+629)/9112247Robert Price01/2022
4455(2^372872+3798)/2112246Stefano Morozzi02/2021
445625513^25060+25060^25513112232Hans Havermann02/2021
4457(2^372754+3094)/2112210Stefano Morozzi09/2020
44586*10^112208+43112209Robert Price07/2020
4459(2^372728+3058)/2112203Stefano Morozzi09/2020
446032061^3158+3158^32061112195Hans Havermann02/2021
44612^372695+72113112193Enzo Doria04/2016
44622^372689-2563112191Yves Minet07/2014
44632^372638-1859441112176Enzo Doria03/2016
44643^235074-113056112159Enzo Doria07/2014
4465-E(29242)/489848365125303139750087112140Thomas Ritschel01/2021
4466(2^372514+1822)/2112138Stefano Morozzi02/2021
446729468^6387+6387^29468112135Hans Havermann02/2021
4468(2^372428+3742)/2112112Stefano Morozzi01/2021
446925375^25454-25454^25375112110Norbert Schneider01/2021
4470131^52949-130112108Norbert Schneider02/2019
4471(91*10^112098-1)/9112100Robert Price04/2015
44722^372310-85061112077Paul Bourdelais02/2012
4473(10^112067+53)/9112067Serge Batalov07/2015
4474(2^372237+2082)/2112055Stefano Morozzi09/2020
447575^59760+2112054Lelio R Paula08/2013
4476(2^372200+1710)/2112044Stefano Morozzi09/2020
4477(10^112048+7)/8747/373157112039Alfred Reich06/2021
4478(2^372181+2250)/2112038Stefano Morozzi01/2021
4479(2^372161+2574)/2112032Stefano Morozzi09/2020
44808*10^112018-49112019Robert Price08/2019
44822^372108+74221112016Enzo Doria04/2016
4481(2^372109+2046)/2112016Stefano Morozzi09/2020
44838*10^112011-73112012Robert Price01/2022
4484(184*10^112007-1)/3112009Robert Price02/2020
44855*10^112003+81112004Robert Price03/2019
4486215^48018+48018^215112000Norbert Schneider10/2018
448725549^24148+24148^25549111979Hans Havermann02/2021
44882^371970-459491111975Enzo Doria05/2015
448941^69427-40^69427111971Robert Price07/2012
4490(2^371782+358)/2111918Stefano Morozzi01/2021
4491(34*10^111902-547)/9111903Robert Price03/2021
4492(10^111902+71)/9111902Serge Batalov07/2015
4493(2^371625+1610)/2111870Stefano Morozzi09/2020
449429080^7027+7027^29080111865Hans Havermann01/2021
449531307^3730+3730^31307111820Hans Havermann02/2021
44962^371440-112865111815Enzo Doria06/2014
44972^371426-459161111811Enzo Doria05/2015
449825768^21771+21771^25768111779Hans Havermann02/2021
449928022^9747+9747^28022111777Hans Havermann02/2021
4500(94*10^111770+11)/3111772Robert Price04/2020


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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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