PRP Records

Probable Primes Top 10000

(290751 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 ?
30012^451787-21805136002Enzo Doria07/2013
30022^451734-112817135986Enzo Doria06/2014
3003(11*2^451714+1)/75135979Lelio R Paula07/2015
30042^451705-21879135977Enzo Doria07/2013
30052^451560-112349135934Enzo Doria06/2014
30062^451530+45135925Lelio R Paula08/2017
300731622^19875+19875^31622135922Hans Havermann11/2020
3008(25*10^135906-73)/3135907Robert Price09/2019
30092^451450-21743135900Enzo Doria07/2013
301035218^7199+7199^35218135846Hans Havermann11/2020
301135661^6446+6446^35661135844Hans Havermann11/2020
301231869^18248+18248^31869135801Hans Havermann12/2020
3013(77*10^135789+157)/9135790Robert Price05/2022
30142^450805+65135706Lelio R Paula08/2017
301530761^25728+25728^30761135669Hans Havermann12/2020
30162*10^135663+69135664Robert Price06/2020
301733962^9867+9867^33962135651Hans Havermann11/2020
301834474^8605+8605^34474135647Hans Havermann11/2020
301934501^8508+8508^34501135583Hans Havermann12/2020
302035487^6614+6614^35487135577Hans Havermann12/2020
3021(13725^32768+1)/131074135573Lelio R Paula03/2012
3022(313007#+121876)/(2*30469*424867)135559Makoto Morimoto08/2020
3023(5^193939+1)/6135557Paul Bourdelais12/2008
3024(844*10^135527-7)/9135529Robert Price05/2021
302540387^2260+2260^40387135463Hans Havermann12/2020
30262^449944-113247135447Enzo Doria07/2014
30272^449770-113247135395Enzo Doria07/2014
30282^449637-21471135355Enzo Doria07/2013
30292^449571-75135335Lelio R Paula08/2017
3030(14*10^135301-53)/3135302Robert Price12/2018
3031(3*2^449494+1)/61340334013135301Lelio R Paula07/2015
3032(13*10^135279+437)/9135280Robert Price04/2018
30332^449330-35135262Lelio R Paula08/2017
3034(19*2^449325+1)/9135261Lelio R Paula07/2015
3035(13*10^135184-43)/3135185Robert Price11/2018
30362^449049-115309135178Enzo Doria07/2015
3037(10^135174+191)/3135174Robert Price02/2018
30382^449030-15135172Lelio R Paula08/2017
3039(157*10^135151-1)/3135153Robert Price01/2022
3040(2^448966+100280245065)135153Paul Bourdelais05/2022
3041(27*2^448936-1)/11135144Lelio R Paula07/2015
3042(37*10^135099+251)/9135100Robert Price09/2021
304332221^15586+15586^32221135095Hans Havermann12/2020
30442^448762-351401135091Enzo Doria07/2015
30452*10^135083-43135084Robert Price04/2018
304631357^20278+20278^31357135056Hans Havermann12/2020
304732242^15445+15445^32242135055Hans Havermann12/2020
3048k(198476)135054Robert Price07/2020
304932461^14470+14470^32461135053Hans Havermann12/2020
305031353^20288+20288^31353135045Hans Havermann12/2020
30515*10^135019+77135020Robert Price12/2018
3052(10^135011+719)/9135011Serge Batalov12/2014
3053(197*10^134978+7)/3134980Robert Price12/2020
30542^448386-2786261134978Enzo Doria03/2016
3055(73*10^134939+143)/9134940Robert Price07/2019
305633957^9392+9392^33957134903Hans Havermann12/2020
30572^448113-113949134896Enzo Doria11/2014
305830958^22755+22755^30958134887Hans Havermann12/2020
30592^447888-2786639134828Enzo Doria03/2016
30602^447870-396765134823Enzo Doria07/2013
30612^447766-21791134791Enzo Doria07/2013
3062(19*10^134786-49)/3134787Robert Price05/2019
3063Phi(202173,10)/10064306514895399941409134758Makoto Kamada05/2019
3064(23*2^447647+1)/155134755Lelio R Paula07/2015
30652^447552-1019134727Yves Minet02/2014
3066(2*10^134720-41)/3134720Robert Price02/2018
3067(25*10^134695-97)/9134696Robert Price01/2022
30682^447437-113569134692Enzo Doria08/2014
30692^447426-65134689Lelio R Paula08/2017
30702^447357-2797573134668Enzo Doria04/2016
30712^447278+93134645Lelio R Paula08/2017
307233193^11370+11370^33193134623Hans Havermann12/2020
307330736^23979+23979^30736134619Hans Havermann11/2020
30742^447094-113193134589Enzo Doria07/2014
30753^282041-9934134568Enzo Doria05/2014
30762^447019-109039134567Enzo Doria04/2014
307731376^19437+19437^31376134561Hans Havermann12/2020
30782^446990-22041134558Enzo Doria07/2013
3079123^64370+122134528Karsten Bonath04/2018
308030100^29461+29461^30100134525Hans Havermann11/2020
308131251^20158+20158^31251134519Hans Havermann11/2020
30822^446782-39701134495Enzo Doria09/2015
308331817^16858+16858^31817134485Hans Havermann12/2020
308432448^13937+13937^32448134471Hans Havermann12/2020
30852^446494-16485134409Enzo Doria04/2013
308630042^29785+29785^30042134408Hans Havermann12/2020
308729504^30069-30069^29504134405Norbert Schneider12/2014
30882^446441+65134393Lelio R Paula08/2017
3089(10^134385+719)/9134385Serge Batalov12/2014
309030043^29688+29688^30043134370Hans Havermann12/2020
3091(2*10^134364+529)/9134364Robert Price01/2018
309234657^7512+7512^34657134323Hans Havermann11/2020
3093(13*2^446187-1)/661134314Lelio R Paula07/2015
30945^192103+3^192103+2^192103+1134275Matthias Baur12/2019
309542035^1564+1564^42035134270Hans Havermann12/2020
3097(2^446022-7)/339134264Lelio R Paula07/2015
309630621^24248+24248^30621134264Hans Havermann12/2020
309830341^26562+26562^30341134237Hans Havermann11/2020
309910^134209+99867134210Patrick De Geest05/2021
310010^134209-80000001134209Robert Price04/2021
310110^134209-323283134209Patrick De Geest05/2021
310229976^29953+29953^29976134186Hans Havermann12/2020
310335038^6755+6755^35038134183Hans Havermann12/2020
310463^74568+2134174Lelio R Paula06/2017
31052^445671-22071134161Enzo Doria07/2013
3106532^49205+49205^532134129Norbert Schneider02/2019
310736453^4780+4780^36453134127Hans Havermann04/2021
3108(28*10^134122-1)/9134123Serge Batalov10/2014
31092^445515-113859134114Enzo Doria10/2014
3111(22*10^134111-37)/3134112Robert Price04/2019
311031083^20636+20636^31083134112Hans Havermann04/2021
311231622^17379+17379^31622134079Hans Havermann04/2021
3113(277*10^134059-7)/9134061Robert Price02/2022
31142^445328-216917134058Enzo Doria05/2014
31152^445202+1874899134020Enzo Doria06/2016
3116(35*10^134003-89)/9134004Robert Price02/2022
3117(13*2^445102+1)/17133989Lelio R Paula07/2015
3118(35*10^133979-593)/9133980Robert Price07/2018
31192*10^133955+51133956Robert Price05/2018
3120(49*10^133952+437)/9133953Robert Price09/2021
31212^444964-113639133948Enzo Doria08/2014
312231811^16240+16240^31811133943Hans Havermann04/2021
312310^133902+167841133903Patrick De Geest05/2021
312528118^30097-30097^28118133902Norbert Schneider01/2015
312410^133902-100001133902Robert Price07/2020
31262^444784-113859133894Enzo Doria10/2014
312732303^13914+13914^32303133846Hans Havermann04/2021
312830739^22458+22458^30739133757Hans Havermann04/2021
312934942^6721+6721^34942133739Hans Havermann04/2021
3130(2^444046+100280245065)133672Paul Bourdelais05/2022
313134792^6935+6935^34792133638Hans Havermann04/2021
3132(266*10^133603+1)/3133605Robert Price04/2020
313332261^13842+13842^32261133600Hans Havermann04/2021
3134(89*10^133580+1)/9133581Serge Batalov05/2010
3135(134*10^133573-11)/3133575Robert Price01/2022
313662^74521-61^74521133571Robert Price05/2013
3137(182*10^133543+1)/3133545Robert Price02/2020
3138(103*10^133535+11)/3133537Robert Price01/2021
313932589^12520+12520^32589133537Hans Havermann03/2021
314034516^7373+7373^34516133496Hans Havermann04/2021
31418*10^133487-37133488Robert Price03/2022
314230135^26882+26882^30135133482Hans Havermann04/2021
31432^443198-1867301133416Enzo Doria03/2016
3144(19*10^133390+101)/3133391Robert Price09/2019
3145(71^72043-1)/70133369Paul Bourdelais09/2017
314636117^4910+4910^36117133311Hans Havermann04/2021
31472^442799+1874633133296Enzo Doria06/2016
3148L(637751)133283Henri Lifchitz09/2008
3149109^65410-2133269Lelio R Paula10/2017
31502^442688-113489133263Enzo Doria08/2014
3151(7*2^442640-1)/783133246Lelio R Paula07/2015
3152(9*2^442463+1)/17441133192Lelio R Paula07/2015
31532^442437-1849993133187Enzo Doria08/2015
31542^442430-2791721133185Enzo Doria03/2016
3155(13*2^442428-1)/309133183Lelio R Paula07/2015
315629959^27870+27870^29959133172Hans Havermann03/2021
3157(25*2^442379-1)/71133169Lelio R Paula07/2015
315834240^7737+7737^34240133145Hans Havermann03/2021
3159452^50145+50145^452133142Norbert Schneider09/2020
316030659^21796+21796^30659133011Hans Havermann04/2021
316133276^9935+9935^33276133010Hans Havermann04/2021
316230111^26122+26122^30111133001Hans Havermann04/2021
316330790^20869+20869^30790132998Hans Havermann04/2021
3165(2^441799+78557)/5132995Lelio R Paula07/2015
31648*10^132994-27132995Robert Price10/2021
3166(109*10^132992+11)/3132994Robert Price06/2022
31672^441781-2787883132990Enzo Doria03/2016
3168(3*2^441685+1)/749132959Lelio R Paula07/2015
31692^441618+37132941Lelio R Paula08/2017
317034857^6514+6514^34857132940Hans Havermann04/2021
317134065^7988+7988^34065132937Hans Havermann04/2021
317235571^5452+5452^35571132914Hans Havermann04/2021
31732^441521-113575132912Enzo Doria08/2014
31747*10^132884-99132885Robert Price06/2019
3175(103*10^132879+17)/3132881Robert Price08/2020
31762^441396-65132874Lelio R Paula08/2017
317733350^9633+9633^33350132859Hans Havermann04/2021
31782^441330+1871959132854Enzo Doria05/2016
31792^441063+383132774Lelio R Paula06/2012
3180(10^132753+7)/17/19132751Alfred Reich06/2021
3181(22*10^132746+53)/3132747Robert Price07/2019
3182(77*10^132744-149)/9132745Robert Price03/2022
3183(22*10^132732+119)/3132733Robert Price04/2021
31842^440846+1870909132708Enzo Doria05/2016
31852^440656-113489132651Enzo Doria08/2014
3186numbpart(14180123587)132646Serge Batalov04/2017
318732950^10591+10591^32950132622Hans Havermann04/2021
318833302^9597+9597^33302132614Hans Havermann04/2021
3189(19*10^132550+191)/3132551Robert Price05/2019
3190(2^440399-1)/(16210820281161978209*31518475633*880799)132538Dario Alpern01/2015
3191(38^83891+1)/39132529Robert Price09/2013
31922*10^132493-43132494Robert Price04/2018
319331352^16809+16809^31352132480Hans Havermann04/2021
3194(418*10^132441+23)/9132443Robert Price02/2020
31952^439931-21132433Lelio R Paula08/2017
319647^79201-46^79201132432Robert Price10/2012
31972^439897-113653132423Enzo Doria08/2014
319835505^5362+5362^35505132410Hans Havermann03/2021
319930079^25222+25222^30079132402Hans Havermann04/2021
3200(5*2^439822+1)/9132400Lelio R Paula06/2015
3201(695*10^132356+7)/9132358Robert Price12/2021
3202(112*10^132337-1)/3132339Serge Batalov12/2014
32032^439576-113247132326Enzo Doria07/2014
320430059^25230+25230^30059132318Hans Havermann04/2021
32052^439497-29143132302Enzo Doria07/2015
32062^439409-114193132276Enzo Doria12/2014
3207(44*10^132233-233)/9132234Robert Price01/2019
32089*10^132148-7132149Robert Price09/2015
3209(47*10^132125-119)/9132126Robert Price05/2019
32102^438845+1870217132106Enzo Doria05/2016
32112^438789+87855132089Lelio R Paula01/2016
32122^438774-2786411132085Enzo Doria03/2016
32132^438755-1848205132079Enzo Doria07/2015
321430502^21381+21381^30502132075Hans Havermann04/2021
32152^438739-112087132074Enzo Doria06/2014
3216(2^438438+100280245065)131983Paul Bourdelais05/2022
321735872^4777+4777^35872131979Hans Havermann04/2021
321831198^16945+16945^31198131938Hans Havermann03/2021
321913907#+(318259#)/(13907#)131923Makoto Morimoto10/2017
3220L(631181)131910Henri Lifchitz09/2008
3221(47*10^131886-119)/9131887Robert Price05/2019
3222(3*2^438121+1)/4308193883131879Lelio R Paula06/2015
32232^438079-1863877131875Enzo Doria03/2016
3224(16*10^131872-37)/3131873Robert Price05/2021
3225(2^438067+5)/329131869Lelio R Paula06/2015
32262^437908-113855131824Enzo Doria09/2014
32272^437884-286349131817Enzo Doria07/2015
32285^188558+4131797Tyler NeSmith05/2021
3229(11*10^131784-17)/3131785Robert Price06/2018
32314*10^131719-93131720Robert Price07/2020
323031629^14606+14606^31629131720Hans Havermann04/2021
32323^276062-112292131716Enzo Doria07/2014
3233(7*10^131682+89)/3131683Robert Price08/2020
323429512^28969+28969^29512131681Hans Havermann03/2021
32352^437343+75953131654Enzo Doria04/2016
323635^85243-34^85243131621Robert Price05/2012
3237(28*10^131586+59)/3131587Robert Price05/2021
3238(59*10^131575+391)/9131576Robert Price03/2021
323939984^1945+1945^39984131505Hans Havermann03/2021
3240(203*10^131457+1)/3131459Robert Price03/2020
32417*10^131421-41131422Robert Price08/2021
324287309^32+32^87309131414Hans Havermann03/2021
3243(68^71713+1)/69131413Paul Bourdelais09/2017
32442^436451+1884713131385Enzo Doria03/2017
32452^436365+35131359Robert Price11/2015
32462^436300+1866871131340Enzo Doria03/2016
3247(7*10^131339+179)/3131340Robert Price09/2018
324814^114592-3131338Paul Bourdelais12/2020
324936197^4236+4236^36197131285Hans Havermann04/2021
3250(37*10^131270+341)/9131271Robert Price08/2018


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Created by  Henri Lifchitz & Renaud Lifchitz : October, 26 2000, last modification: June, 23 2022 21:24 (Time in France)

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