PRP Records

Probable Primes Top 10000

(294627 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 ?
425115^112072+14131807Alfred Reich10/2023
42525^188558+4131797Tyler NeSmith05/2021
4253(11*10^131784-17)/3131785Robert Price06/2018
42554*10^131719-93131720Robert Price07/2020
425431629^14606+14606^31629131720Hans Havermann04/2021
42563^276062-112292131716Enzo Doria07/2014
4257(7*10^131682+89)/3131683Robert Price08/2020
425829512^28969+28969^29512131681Hans Havermann03/2021
42592^437343+75953131654Enzo Doria04/2016
426035^85243-34^85243131621Robert Price05/2012
4261(28*10^131586+59)/3131587Robert Price05/2021
4262(59*10^131575+391)/9131576Robert Price03/2021
426339984^1945+1945^39984131505Hans Havermann03/2021
426425647^29818-29818^25647131469Frank Doornink02/2024
4265(203*10^131457+1)/3131459Robert Price03/2020
42667*10^131421-41131422Robert Price08/2021
426787309^32+32^87309131414Hans Havermann03/2021
4268(68^71713+1)/69131413Paul Bourdelais09/2017
4269(650*10^131391+43)/9131393Tyler Busby01/2023
42702^436451+1884713131385Enzo Doria03/2017
42712^436365+35131359Robert Price11/2015
42732^436300+1866871131340Enzo Doria03/2016
4272(7*10^131339+179)/3131340Robert Price09/2018
427414^114592-3131338Paul Bourdelais12/2020
427536197^4236+4236^36197131285Hans Havermann04/2021
4276(37*10^131270+341)/9131271Robert Price08/2018
427729863^24790+24790^29863131227Hans Havermann03/2021
4278(5*10^131223-29)/3131224Robert Price03/2018
427929524^27825+27825^29524131218Hans Havermann03/2021
4280(23*2^435891-1)/699131215Lelio R Paula07/2015
4281(11*2^435879+1)/3337131211Lelio R Paula06/2015
428230639^19136+19136^30639131192Hans Havermann04/2021
4284(2^435808+1)/641/6700417131182Lelio R Paula02/2012
4283(2^435808+1)/4294967297131182Serge Batalov12/2016
42872^435773+1875557131181Enzo Doria06/2016
4286(16*10^131180+167)/3131181Robert Price06/2019
4285(26*10^131180-77)/3131181Robert Price11/2019
4288(25*10^131144-7)/9131145Robert Price05/2018
428929299^29358-29358^29299131138Norbert Schneider03/2022
42902^435612-2789939131133Enzo Doria12/2015
429133976^7231+7231^33976131121Hans Havermann03/2021
429233715^7746+7746^33715131121Hans Havermann03/2021
429366^72047-65^72047131093Robert Price09/2013
4294(5*10^131090+37)/3131091Robert Price03/2018
42952^435468+75631131089Enzo Doria04/2016
429637^83588-2131083Lelio R Paula08/2015
4297(4^217720+11)/3131081Robert Price02/2017
429830407^20448+20448^30407131074Hans Havermann04/2021
4299(22*10^131070+179)/3131071Robert Price02/2022
430029487^27836+27836^29487131059Hans Havermann04/2021
430129962^23615+23615^29962131030Hans Havermann03/2021
43022^435202-113193131009Enzo Doria07/2014
430341705^1384+1384^41705131002Hans Havermann04/2021
43049*10^130998-19130999Robert Price07/2019
430536243^4108+4108^36243130969Hans Havermann04/2021
4306floor((sqrt(5)-1)/2*10^130911)130911Serge Batalov06/2017
43072^434835-111937130899Enzo Doria05/2014
4308(62*10^130895-629)/9130896Robert Price07/2021
43092^434685+72257130854Enzo Doria04/2016
4310(7*10^130825+113)/3130826Robert Price02/2018
43112^434539-29317130810Enzo Doria07/2015
4312(74*10^130791+637)/9130792Robert Price01/2022
43132^434469-114259130789Enzo Doria01/2015
4314(5*10^130763+103)/9130763Robert Price04/2022
43152^434246+33130722Robert Price11/2015
431630156^21599+21599^30156130710Hans Havermann04/2021
4317(17*10^130695-161)/9130695Robert Price02/2021
431830513^19148+19148^30513130661Hans Havermann03/2021
431929736^24761+24761^29736130654Hans Havermann04/2021
43209*10^130638+41130639Robert Price08/2020
43212^433911-91130621Lelio R Paula06/2017
432230786^17449+17449^30786130588Hans Havermann03/2021
43232^433744-114419130570Enzo Doria02/2015
43252^433708+1869451130560Enzo Doria05/2016
43242^433710+93130560Lelio R Paula06/2017
43267*10^130535-27130536Robert Price11/2022
4327(9629^32768+1)/120501441265666130520Kellen Shenton05/2021
4328804*34^85220+713130516Eric Chen08/2023
4329(29*2^433547-1)/27130511Lelio R Paula06/2015
43303^273521+10130503Tyler NeSmith01/2021
433141659^1356+1356^41659130487Hans Havermann03/2021
43324*10^130480+9130481Robert Price05/2015
4333(23*2^433449-1)/75130481Lelio R Paula06/2015
43343*2^433422+5130474Jon Grantham07/2023
4335(23*2^433334-1)/3731130445Lelio R Paula06/2015
4336(31*10^130414-49)/9130415Robert Price11/2021
433733481^7848+7848^33481130401Hans Havermann03/2021
4338(17*10^130393+7)/3130394Robert Price06/2023
4339(22*10^130392+203)/9130393Robert Price10/2021
434029773^23950+23950^29773130386Hans Havermann04/2021
43412^433023-113497130353Enzo Doria08/2014
434231175^15178+15178^31175130350Hans Havermann04/2021
43432^433002+1179379130347Enzo Doria06/2016
43442^432974+19130339Robert Price08/2015
434531903^12168+12168^31903130331Hans Havermann04/2021
43462^432917+22217130322Enzo Doria09/2023
434729387^27112+27112^29387130278Hans Havermann04/2021
43482^432768+213181130277Enzo Doria09/2023
434929577^25370+25370^29577130267Hans Havermann04/2021
435031738^12685+12685^31738130231Hans Havermann03/2021
435144235^878+878^44235130206Hans Havermann04/2021
435232160^11171+11171^32160130187Hans Havermann04/2021
435329489^25956+25956^29489130172Hans Havermann04/2021
4354(2^432457-1)/1672739247834685086279697130159Tony Prest / Never Odd Or Even09/2013
435533005^8766+8766^33005130133Hans Havermann04/2021
4356(35*10^130132-611)/9130133Robert Price02/2022
4357(444^49408+1)/(444^256+1)130125Martin Hopf12/2023
43582^432217+41130111Lelio R Paula06/2017
4359(2^216089*(2^216091-1)-339)/25130098Makoto Morimoto03/2017
4360((2^216091+1066)^2+(2^216091+1066)+41)/47/2069130095Makoto Morimoto05/2016
436197^65480-2130094Lelio R Paula05/2017
436236007^4102+4102^36007130094Hans Havermann04/2021
43634*10^130088-89130089Robert Price11/2018
43642^432117-113215130081Enzo Doria07/2014
4365(4*10^130080+41)/9130080Serge Batalov11/2022
43662^431804+72511129986Enzo Doria04/2016
4367(2313^38809-1)/(2313^197-1)129898Ryan Propper11/2023
4368(13*10^129896+137)/3129897Robert Price06/2021
4369(13*10^129890+71)/3129891Robert Price06/2021
437029048^29101-29101^29048129882Norbert Schneider03/2022
437137832^2709+2709^37832129871Hans Havermann04/2021
437231055^15184+15184^31055129853Hans Havermann04/2021
4373(3^272141-3^136071+1)/7129844Serge Batalov03/2014
437431385^13702+13702^31385129833Hans Havermann04/2021
4375(13*10^129826+41)/9129827Tyler Busby02/2023
437628901^29102-29102^28901129822Norbert Schneider03/2022
4377(47*10^129789-119)/9129790Robert Price05/2019
4378(9*2^431141+1)/17129787Lelio R Paula06/2015
437925771^29408-29408^25771129723Frank Doornink02/2024
4380(166*10^129712+17)/3129714Robert Price07/2022
4381(29*2^430881-1)/21129709Lelio R Paula06/2015
43822^430807+1869563129686Enzo Doria05/2016
43832^430721-21429129660Enzo Doria07/2013
4384(4*10^129618+89)/3129619Robert Price08/2021
4385(10^129587-7^129587)/3129587Jon Grantham07/2023
43862^430415-276271129568Enzo Doria07/2015
438732282^10311+10311^32282129558Hans Havermann04/2021
438829486^24741+24741^29486129545Hans Havermann04/2021
4389(29*10^129543+313)/9129544Robert Price04/2021
439037095^3104+3104^37095129533Hans Havermann04/2021
439131132^14459+14459^31132129514Hans Havermann04/2021
439232582^9435+9435^32582129506Hans Havermann03/2021
439330442^17953+17953^30442129505Hans Havermann03/2021
4394(199*10^129487-7)/3129489Robert Price05/2020
43952^430142-2791721129486Enzo Doria03/2016
4396(7*10^129472-13)/3129473Robert Price07/2018
4397(8*10^129469+79)/3129470Robert Price10/2020
439831678^12213+12213^31678129463Hans Havermann04/2021
439910620^32143-10619^32143129412Norbert Schneider08/2023
4400(772*10^129406-7)/9129408Robert Price06/2022
440131100^14439+14439^31100129362Hans Havermann04/2021
440233009^8288+8288^33009129345Hans Havermann04/2021
4403(44^78697+43^78697)/87129333Aurel Gibier11/2023
440429675^22804+22804^29675129324Hans Havermann04/2021
440529068^28099+28099^29068129315Hans Havermann04/2021
44062^429568-21017129313Enzo Doria07/2013
4407(10^129295+83)/3129295Robert Price08/2021
4408(853*10^129274-7)/9129276Robert Price07/2021
440930958^14961+14961^30958129249Hans Havermann04/2021
4410(11*10^129239-179)/3129240Robert Price09/2018
441128659^28988+28988^28659129208Norbert Schneider02/2021
441229423^24616+24616^29423129203Hans Havermann03/2021
44132^429194-112685129201Enzo Doria06/2014
44142^429145-2780449129186Enzo Doria04/2016
441532500^9427+9427^32500129168Hans Havermann04/2021
441633577^7014+7014^33577129136Hans Havermann03/2021
44172^428892-113453129110Enzo Doria07/2014
4418(11*2^428881-7)/15129106Renaud Lifchitz03/2011
44192^428727-113959129060Enzo Doria10/2014
4420(7*2^428725-1)/13129059Lelio R Paula05/2014
4421(10^129051-31)/3129051Serge Batalov12/2014
4422(134*10^129038+7)/3129040Robert Price02/2020
44232^428564+71161129011Enzo Doria04/2016
442428781^28930+28930^28781129002Norbert Schneider02/2021
442529065^27424+27424^29065128995Hans Havermann04/2021
44262^428502-113285128992Enzo Doria07/2014
44272^428421-21373128968Enzo Doria06/2013
4428L(616787)128901Henri Lifchitz09/2008
442920^99055-3128874Paul Bourdelais12/2020
443091^65772-2128851Lelio R Paula05/2017
44312^428022+43128848Lelio R Paula05/2017
44322^427999-459397128841Enzo Doria05/2015
44332^427993+76847128839Enzo Doria05/2016
443431059^14060+14060^31059128833Hans Havermann03/2021
443510^128805+152871128806Patrick De Geest05/2021
443610^128805-10001128805Robert Price02/2021
44372^427824-1851507128788Enzo Doria08/2015
44382^427807-21469128783Enzo Doria07/2013
443929082^26783+26783^29082128772Hans Havermann04/2021
444040055^1638+1638^40055128750Hans Havermann04/2021
444111^123594-240128710Enzo Doria09/2012
44422^427504-21503128692Enzo Doria07/2013
444337727^2574+2574^37727128673Hans Havermann04/2021
444429686^21591+21591^29686128668Hans Havermann04/2021
444510^128668-70000000001128668Robert Price08/2021
44462^427420+91128667Lelio R Paula05/2017
44478*10^128651-37128652Robert Price03/2022
4448(68*10^128645-257)/9128646Robert Price07/2019
44492^427269-113635128621Enzo Doria08/2014
44502^427130+1877569128579Enzo Doria08/2016
44512^427068+20011128561Enzo Doria06/2023
44522^427016-115349128545Enzo Doria07/2015
4453(4*10^128510+137)/3128511Robert Price03/2018
44542^426889-112879128507Enzo Doria06/2014
44552^426804+1869931128481Enzo Doria05/2016
44562^426750+77635128465Enzo Doria05/2016
445736988^2969+2969^36988128445Hans Havermann03/2021
445836664^3185+3185^36664128439Hans Havermann03/2021
445932618^8649+8649^32618128416Hans Havermann04/2021
446028883^27874+27874^28883128391Hans Havermann04/2021
44612^426425-91128367Lelio R Paula05/2017
4462(15*2^426398-1)/11128359Lelio R Paula05/2014
44632^426352+74971128345Enzo Doria04/2016
4464(199*10^128343-7)/3128345Robert Price05/2020
44654*10^128343-21128344Robert Price09/2018
4466(65*10^128338+493)/9128339Robert Price08/2021
446735632^3997+3997^35632128337Hans Havermann04/2021
44682^426300-1863689128330Enzo Doria03/2016
44692^426293+1881017128327Enzo Doria11/2016
4470(88*10^128324-637)/9128325Robert Price11/2020
4471(491*10^128285+31)/9128287Robert Price04/2022
447239103^1908+1908^39103128281Hans Havermann04/2021
44732^426043+35128252Robert Price11/2015
4474(4*10^128244-19)/3128245Robert Price03/2018
447535489^4102+4102^35489128222Hans Havermann04/2021
447634721^4926+4926^34721128208Hans Havermann04/2021
4477(305*10^128198+1)/9128200Robert Price02/2020
44782^425808-459959128181Enzo Doria06/2015
447930632^15291+15291^30632128178Hans Havermann04/2021
448035981^3648+3648^35981128167Hans Havermann04/2021
44812^425627-113605128127Enzo Doria08/2014
4482(4*10^128109+119)/3128110Robert Price12/2021
4483(22*10^128094+53)/3128095Robert Price07/2019
4484(86*10^128086-221)/9128087Robert Price09/2019
448518565^30002-30002^18565128070Norbert Schneider01/2015
4486(2^425287-9)/2737128021Lelio R Paula05/2015
4487(3*2^425233-1)/25128007Lelio R Paula05/2014
4488Phi(149401,10)/30037901719561128003Makoto Kamada07/2022
44892^425205+4911128000Marek Hubal02/2017
449029241^23836+23836^29241127995Hans Havermann04/2021
44912^425118-113663127974Enzo Doria08/2014
4492(86*10^127967-329)/9127968Robert Price01/2020
44932^425061+1869761127957Enzo Doria05/2016
4494746^44541+44541^746127955Norbert Schneider07/2019
449530236^17043+17043^30236127946Hans Havermann03/2021
44962^424938+212419127920Enzo Doria08/2023
44972^424918-21141127914Enzo Doria07/2013
4498(62*10^127903+91)/9127904Robert Price07/2021
44992^424864-29489127897Enzo Doria08/2015
450030438^15893+15893^30438127877Hans Havermann02/2021


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Created by  Henri Lifchitz & Renaud Lifchitz : October, 26 2000, last modification: March, 12 2024 13:37 (Time in France)

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