PRP Records

Probable Primes Top 10000

(295149 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 ?
4252(22*10^134111-37)/3134112Robert Price04/2019
425131083^20636+20636^31083134112Hans Havermann04/2021
42533*2^445478+5134103Jon Grantham07/2023
425431622^17379+17379^31622134079Hans Havermann04/2021
42555*2^445380-3134074Jon Grantham07/2023
4256(6*32^89076+4241)/31134073Eric Chen11/2023
4257(277*10^134059-7)/9134061Robert Price02/2022
42582^445328-216917134058Enzo Doria05/2014
42592^445202+1874899134020Enzo Doria06/2016
42605^191739-3^191739-1134020Jon Grantham08/2023
4261(35*10^134003-89)/9134004Robert Price02/2022
4262(13*2^445102+1)/17133989Lelio R Paula07/2015
4263(35*10^133979-593)/9133980Robert Price07/2018
42642*10^133955+51133956Robert Price05/2018
4265(49*10^133952+437)/9133953Robert Price09/2021
42662^444964-113639133948Enzo Doria08/2014
426731811^16240+16240^31811133943Hans Havermann04/2021
426810^133902+167841133903Patrick De Geest05/2021
427028118^30097-30097^28118133902Norbert Schneider01/2015
426910^133902-100001133902Robert Price07/2020
42712^444784-113859133894Enzo Doria10/2014
427232303^13914+13914^32303133846Hans Havermann04/2021
4273(2276213*2^444444+1)/3133797Alex_soldier11/2022
4274(1403559*2^444444+1)/5133797Alex_soldier11/2022
4275(1209887*2^444444+1)/9133797Alex_soldier11/2022
4276(608239*2^444444+1)/25133796Alex_soldier11/2022
4277(1824587*2^444444+1)/27133796Alex_soldier11/2022
4278(40795*2^444444+1)/7133795Alex_soldier11/2022
427930739^22458+22458^30739133757Hans Havermann04/2021
428034942^6721+6721^34942133739Hans Havermann04/2021
4281(2^444046+100280245065)133672Paul Bourdelais05/2022
428234792^6935+6935^34792133638Hans Havermann04/2021
4283(266*10^133603+1)/3133605Robert Price04/2020
428432261^13842+13842^32261133600Hans Havermann04/2021
4285(89*10^133580+1)/9133581Serge Batalov05/2010
4286(134*10^133573-11)/3133575Robert Price01/2022
428726726^30173-30173^26726133574Frank Doornink03/2024
428862^74521-61^74521133571Robert Price05/2013
4289(182*10^133543+1)/3133545Robert Price02/2020
4290(103*10^133535+11)/3133537Robert Price01/2021
429132589^12520+12520^32589133537Hans Havermann03/2021
429234516^7373+7373^34516133496Hans Havermann04/2021
42938*10^133487-37133488Robert Price03/2022
429430135^26882+26882^30135133482Hans Havermann04/2021
42952^443198-1867301133416Enzo Doria03/2016
4296(19*10^133390+101)/3133391Robert Price09/2019
4297(71^72043-1)/70133369Paul Bourdelais09/2017
429836117^4910+4910^36117133311Hans Havermann04/2021
42992^442799+1874633133296Enzo Doria06/2016
4300L(637751)133283Henri Lifchitz09/2008
4301109^65410-2133269Lelio R Paula10/2017
43022^442688-113489133263Enzo Doria08/2014
4303(7*2^442640-1)/783133246Lelio R Paula07/2015
4304(9*2^442463+1)/17441133192Lelio R Paula07/2015
43052^442437-1849993133187Enzo Doria08/2015
43062^442430-2791721133185Enzo Doria03/2016
4307(13*2^442428-1)/309133183Lelio R Paula07/2015
430829959^27870+27870^29959133172Hans Havermann03/2021
4309(25*2^442379-1)/71133169Lelio R Paula07/2015
43102^442368+213691133167Enzo Doria09/2023
431134240^7737+7737^34240133145Hans Havermann03/2021
4312452^50145+50145^452133142Norbert Schneider09/2020
431330659^21796+21796^30659133011Hans Havermann04/2021
431433276^9935+9935^33276133010Hans Havermann04/2021
431530111^26122+26122^30111133001Hans Havermann04/2021
431630790^20869+20869^30790132998Hans Havermann04/2021
4318(2^441799+78557)/5132995Lelio R Paula07/2015
43178*10^132994-27132995Robert Price10/2021
4319(109*10^132992+11)/3132994Robert Price06/2022
43202^441781-2787883132990Enzo Doria03/2016
4321fibonacci(636232)+4132965Jon Grantham08/2023
4322(3*2^441685+1)/749132959Lelio R Paula07/2015
43232^441618+37132941Lelio R Paula08/2017
432434857^6514+6514^34857132940Hans Havermann04/2021
432534065^7988+7988^34065132937Hans Havermann04/2021
432635571^5452+5452^35571132914Hans Havermann04/2021
43272^441521-113575132912Enzo Doria08/2014
43287*10^132884-99132885Robert Price06/2019
432926987^29988-29988^26987132882Frank Doornink03/2024
4330(103*10^132879+17)/3132881Robert Price08/2020
43312^441396-65132874Lelio R Paula08/2017
433233350^9633+9633^33350132859Hans Havermann04/2021
43332^441330+1871959132854Enzo Doria05/2016
433425772^30111-30111^25772132825Frank Doornink02/2024
43352^441063+383132774Lelio R Paula06/2012
4336(10^132753+7)/17/19132751Alfred Reich06/2021
4337(22*10^132746+53)/3132747Robert Price07/2019
4338(77*10^132744-149)/9132745Robert Price03/2022
4339(22*10^132732+119)/3132733Robert Price04/2021
43402^440846+1870909132708Enzo Doria05/2016
4341(948^44579-1)/947132701Jinyuan Wang04/2023
43422^440656-113489132651Enzo Doria08/2014
4343numbpart(14180123587)132646Serge Batalov04/2017
434432950^10591+10591^32950132622Hans Havermann04/2021
434533302^9597+9597^33302132614Hans Havermann04/2021
4346(19*10^132550+191)/3132551Robert Price05/2019
4347(2^440399-1)/(16210820281161978209*31518475633*880799)132538Dario Alpern01/2015
4348(38^83891+1)/39132529Robert Price09/2013
43492*10^132493-43132494Robert Price04/2018
435031352^16809+16809^31352132480Hans Havermann04/2021
4351(418*10^132441+23)/9132443Robert Price02/2020
43522^439931-21132433Lelio R Paula08/2017
435347^79201-46^79201132432Robert Price10/2012
43542^439897-113653132423Enzo Doria08/2014
435535505^5362+5362^35505132410Hans Havermann03/2021
435630079^25222+25222^30079132402Hans Havermann04/2021
4357(5*2^439822+1)/9132400Lelio R Paula06/2015
4358(695*10^132356+7)/9132358Robert Price12/2021
4359(112*10^132337-1)/3132339Serge Batalov12/2014
43602^439576-113247132326Enzo Doria07/2014
436130059^25230+25230^30059132318Hans Havermann04/2021
43622^439497-29143132302Enzo Doria07/2015
43632^439409-114193132276Enzo Doria12/2014
4364(44*10^132233-233)/9132234Robert Price01/2019
436525507^30000-30000^25507132200Frank Doornink02/2024
43669*10^132148-7132149Robert Price09/2015
4367(47*10^132125-119)/9132126Robert Price05/2019
43682^438900+214051132123Enzo Doria10/2023
43692^438845+1870217132106Enzo Doria05/2016
43702^438789+87855132089Lelio R Paula01/2016
43712^438774-2786411132085Enzo Doria03/2016
43722^438755-1848205132079Enzo Doria07/2015
437330502^21381+21381^30502132075Hans Havermann04/2021
43742^438739-112087132074Enzo Doria06/2014
4375(2^438438+100280245065)131983Paul Bourdelais05/2022
437635872^4777+4777^35872131979Hans Havermann04/2021
437731198^16945+16945^31198131938Hans Havermann03/2021
437813907#+(318259#)/(13907#)131923Makoto Morimoto10/2017
4379L(631181)131910Henri Lifchitz09/2008
4380(47*10^131886-119)/9131887Robert Price05/2019
43815*2^438096-3131881Jon Grantham07/2023
4382(3*2^438121+1)/4308193883131879Lelio R Paula06/2015
43832^438079-1863877131875Enzo Doria03/2016
4384(16*10^131872-37)/3131873Robert Price05/2021
4385(2^438067+5)/329131869Lelio R Paula06/2015
43862^437908-113855131824Enzo Doria09/2014
43872^437884-286349131817Enzo Doria07/2015
438815^112072+14131807Alfred Reich10/2023
43895^188558+4131797Tyler NeSmith05/2021
4390(11*10^131784-17)/3131785Robert Price06/2018
43924*10^131719-93131720Robert Price07/2020
439131629^14606+14606^31629131720Hans Havermann04/2021
43933^276062-112292131716Enzo Doria07/2014
439411*31^88313+322688131708Eric Chen05/2024
4395(7*10^131682+89)/3131683Robert Price08/2020
439629512^28969+28969^29512131681Hans Havermann03/2021
43972^437343+75953131654Enzo Doria04/2016
439835^85243-34^85243131621Robert Price05/2012
4399(28*10^131586+59)/3131587Robert Price05/2021
4400(59*10^131575+391)/9131576Robert Price03/2021
440139984^1945+1945^39984131505Hans Havermann03/2021
440225842^29801-29801^25842131492Frank Doornink03/2024
440328592^29505-29505^28592131482Frank Doornink05/2024
440425647^29818-29818^25647131469Frank Doornink02/2024
4405(203*10^131457+1)/3131459Robert Price03/2020
44067*10^131421-41131422Robert Price08/2021
440787309^32+32^87309131414Hans Havermann03/2021
4408(68^71713+1)/69131413Paul Bourdelais09/2017
4409(650*10^131391+43)/9131393Tyler Busby01/2023
44102^436451+1884713131385Enzo Doria03/2017
44112^436365+35131359Robert Price11/2015
44132^436300+1866871131340Enzo Doria03/2016
4412(7*10^131339+179)/3131340Robert Price09/2018
441414^114592-3131338Paul Bourdelais12/2020
441536197^4236+4236^36197131285Hans Havermann04/2021
4416(37*10^131270+341)/9131271Robert Price08/2018
441729863^24790+24790^29863131227Hans Havermann03/2021
4418(5*10^131223-29)/3131224Robert Price03/2018
441929524^27825+27825^29524131218Hans Havermann03/2021
4420(23*2^435891-1)/699131215Lelio R Paula07/2015
4421(11*2^435879+1)/3337131211Lelio R Paula06/2015
442230639^19136+19136^30639131192Hans Havermann04/2021
4423(2^435808+1)/641/6700417131182Lelio R Paula02/2012
4424(2^435808+1)/4294967297131182Serge Batalov12/2016
44252^435773+1875557131181Enzo Doria06/2016
4426(16*10^131180+167)/3131181Robert Price06/2019
4427(26*10^131180-77)/3131181Robert Price11/2019
4428(25*10^131144-7)/9131145Robert Price05/2018
442929299^29358-29358^29299131138Norbert Schneider03/2022
44302^435612-2789939131133Enzo Doria12/2015
443133976^7231+7231^33976131121Hans Havermann03/2021
443233715^7746+7746^33715131121Hans Havermann03/2021
443366^72047-65^72047131093Robert Price09/2013
4434(5*10^131090+37)/3131091Robert Price03/2018
44352^435468+75631131089Enzo Doria04/2016
443637^83588-2131083Lelio R Paula08/2015
4437(4^217720+11)/3131081Robert Price02/2017
443830407^20448+20448^30407131074Hans Havermann04/2021
4439(22*10^131070+179)/3131071Robert Price02/2022
444028831^29388-29388^28831131067Frank Doornink05/2024
444129487^27836+27836^29487131059Hans Havermann04/2021
444229962^23615+23615^29962131030Hans Havermann03/2021
44432^435202-113193131009Enzo Doria07/2014
444441705^1384+1384^41705131002Hans Havermann04/2021
44459*10^130998-19130999Robert Price07/2019
444636243^4108+4108^36243130969Hans Havermann04/2021
4447(445^49433+1)/446130914Jinyuan Wang05/2024
4448floor((sqrt(5)-1)/2*10^130911)130911Serge Batalov06/2017
44492^434835-111937130899Enzo Doria05/2014
4450(62*10^130895-629)/9130896Robert Price07/2021
44512^434685+72257130854Enzo Doria04/2016
4452(7*10^130825+113)/3130826Robert Price02/2018
44532^434539-29317130810Enzo Doria07/2015
4454(74*10^130791+637)/9130792Robert Price01/2022
44552^434469-114259130789Enzo Doria01/2015
4456(5*10^130763+103)/9130763Robert Price04/2022
44572^434246+33130722Robert Price11/2015
445830156^21599+21599^30156130710Hans Havermann04/2021
4459(17*10^130695-161)/9130696Robert Price02/2021
446030513^19148+19148^30513130661Hans Havermann03/2021
446129736^24761+24761^29736130654Hans Havermann04/2021
44629*10^130638+41130639Robert Price08/2020
44632^433911-91130621Lelio R Paula06/2017
446430786^17449+17449^30786130588Hans Havermann03/2021
44652^433744-114419130570Enzo Doria02/2015
44672^433708+1869451130560Enzo Doria05/2016
44662^433710+93130560Lelio R Paula06/2017
44687*10^130535-27130536Robert Price11/2022
4469(9629^32768+1)/120501441265666130520Kellen Shenton05/2021
4470804*34^85220+713130516Eric Chen08/2023
4471(29*2^433547-1)/27130511Lelio R Paula06/2015
44723^273521+10130503Tyler NeSmith01/2021
447341659^1356+1356^41659130487Hans Havermann03/2021
44744*10^130480+9130481Robert Price05/2015
4475(23*2^433449-1)/75130481Lelio R Paula06/2015
44763*2^433422+5130474Jon Grantham07/2023
4477(23*2^433334-1)/3731130445Lelio R Paula06/2015
4478(31*10^130414-49)/9130415Robert Price11/2021
447926462^29485-29485^26462130402Frank Doornink03/2024
448033481^7848+7848^33481130401Hans Havermann03/2021
4481(17*10^130393+7)/3130394Robert Price06/2023
4482(22*10^130392+203)/9130393Robert Price10/2021
448329773^23950+23950^29773130386Hans Havermann04/2021
44842^433023-113497130353Enzo Doria08/2014
448531175^15178+15178^31175130350Hans Havermann04/2021
44862^433002+1179379130347Enzo Doria06/2016
44872^432974+19130339Robert Price08/2015
448831903^12168+12168^31903130331Hans Havermann04/2021
44892^432917+22217130322Enzo Doria09/2023
449029387^27112+27112^29387130278Hans Havermann04/2021
44912^432768+213181130277Enzo Doria09/2023
449229577^25370+25370^29577130267Hans Havermann04/2021
449331738^12685+12685^31738130231Hans Havermann03/2021
449444235^878+878^44235130206Hans Havermann04/2021
449532160^11171+11171^32160130187Hans Havermann04/2021
449629489^25956+25956^29489130172Hans Havermann04/2021
4497(2^432457-1)/1672739247834685086279697130159Tony Prest / Never Odd Or Even09/2013
449833005^8766+8766^33005130133Hans Havermann04/2021
4499(35*10^130132-611)/9130133Robert Price02/2022
4500(444^49408+1)/(444^256+1)130125Martin Hopf12/2023


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Created by  Henri Lifchitz & Renaud Lifchitz : October, 26 2000, last modification: May, 22 2024 21:19 (Time in France)

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