PRP Records

Probable Primes Top 10000

(280932 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 ?
250133193^11370+11370^33193134623Hans Havermann12/2020
250230736^23979+23979^30736134619Hans Havermann11/2020
25032^447094-113193134589Enzo Doria07/2014
25043^282041-9934134568Enzo Doria05/2014
25052^447019-109039134567Enzo Doria04/2014
250631376^19437+19437^31376134561Hans Havermann12/2020
25072^446990-22041134558Enzo Doria07/2013
2508123^64370+122134528Karsten Bonath04/2018
250930100^29461+29461^30100134525Hans Havermann11/2020
251031251^20158+20158^31251134519Hans Havermann11/2020
25112^446782-39701134495Enzo Doria09/2015
251231817^16858+16858^31817134485Hans Havermann12/2020
251332448^13937+13937^32448134471Hans Havermann12/2020
25142^446494-16485134409Enzo Doria04/2013
251530042^29785+29785^30042134408Hans Havermann12/2020
251629504^30069-30069^29504134405Norbert Schneider12/2014
25172^446441+65134393Lelio R Paula08/2017
2518(10^134385+719)/9134385Serge Batalov12/2014
251930043^29688+29688^30043134370Hans Havermann12/2020
2520(2*10^134364+529)/9134364Robert Price01/2018
252134657^7512+7512^34657134323Hans Havermann11/2020
2522(13*2^446187-1)/661134314Lelio R Paula07/2015
25235^192103+3^192103+2^192103+1134275Matthias Baur12/2019
252442035^1564+1564^42035134270Hans Havermann12/2020
2526(2^446022-7)/339134264Lelio R Paula07/2015
252530621^24248+24248^30621134264Hans Havermann12/2020
252730341^26562+26562^30341134237Hans Havermann11/2020
252810^134209-80000001134209Robert Price04/2021
252929976^29953+29953^29976134186Hans Havermann12/2020
253035038^6755+6755^35038134183Hans Havermann12/2020
253163^74568+2134174Lelio R Paula06/2017
25322^445671-22071134161Enzo Doria07/2013
2533532^49205+49205^532134129Norbert Schneider02/2019
2534(28*10^134122-1)/9134123Serge Batalov10/2014
25352^445515-113859134114Enzo Doria10/2014
2536(22*10^134111-37)/3134112Robert Price04/2019
253731622^17379+17379^31622134079Hans Havermann04/2021
25382^445328-216917134058Enzo Doria05/2014
25392^445202+1874899134020Enzo Doria06/2016
2540(13*2^445102+1)/17133989Lelio R Paula07/2015
2541(35*10^133979-593)/9133980Robert Price07/2018
25422*10^133955+51133956Robert Price05/2018
25432^444964-113639133948Enzo Doria08/2014
254528118^30097-30097^28118133902Norbert Schneider01/2015
254410^133902-100001133902Robert Price07/2020
25462^444784-113859133894Enzo Doria10/2014
254734942^6721+6721^34942133739Hans Havermann04/2021
254834792^6935+6935^34792133638Hans Havermann04/2021
2549(266*10^133603+1)/3133605Robert Price04/2020
2550(89*10^133580+1)/9133581Serge Batalov05/2010
255162^74521-61^74521133571Robert Price05/2013
2552(182*10^133543+1)/3133545Robert Price02/2020
2553(103*10^133535+11)/3133537Robert Price01/2021
255432589^12520+12520^32589133537Hans Havermann03/2021
255530135^26882+26882^30135133482Hans Havermann04/2021
25562^443198-1867301133416Enzo Doria03/2016
2557(19*10^133390+101)/3133391Robert Price09/2019
2558(71^72043-1)/70133369Paul Bourdelais09/2017
25592^442799+1874633133296Enzo Doria06/2016
2560L(637751)133283Henri Lifchitz09/2008
2561109^65410-2133269Lelio R Paula10/2017
25622^442688-113489133263Enzo Doria08/2014
2563(7*2^442640-1)/783133246Lelio R Paula07/2015
2564(9*2^442463+1)/17441133192Lelio R Paula07/2015
25652^442437-1849993133187Enzo Doria08/2015
25662^442430-2791721133185Enzo Doria03/2016
2567(13*2^442428-1)/309133183Lelio R Paula07/2015
256829959^27870+27870^29959133172Hans Havermann03/2021
2569(25*2^442379-1)/71133169Lelio R Paula07/2015
257034240^7737+7737^34240133145Hans Havermann03/2021
2571452^50145+50145^452133142Norbert Schneider09/2020
257230659^21796+21796^30659133011Hans Havermann04/2021
257333276^9935+9935^33276133010Hans Havermann04/2021
257430111^26122+26122^30111133001Hans Havermann04/2021
257530790^20869+20869^30790132998Hans Havermann04/2021
2576(2^441799+78557)/5132995Lelio R Paula07/2015
25772^441781-2787883132990Enzo Doria03/2016
2578(3*2^441685+1)/749132959Lelio R Paula07/2015
25792^441618+37132941Lelio R Paula08/2017
258035571^5452+5452^35571132914Hans Havermann04/2021
25812^441521-113575132912Enzo Doria08/2014
25827*10^132884-99132885Robert Price06/2019
2583(103*10^132879+17)/3132881Robert Price08/2020
25842^441396-65132874Lelio R Paula08/2017
25852^441330+1871959132854Enzo Doria05/2016
25862^441063+383132774Lelio R Paula06/2012
2587(22*10^132746+53)/3132747Robert Price07/2019
25882^440846+1870909132708Enzo Doria05/2016
25892^440656-113489132651Enzo Doria08/2014
2590numbpart(14180123587)132646Serge Batalov04/2017
259132950^10591+10591^32950132622Hans Havermann04/2021
259233302^9597+9597^33302132614Hans Havermann04/2021
2593(19*10^132550+191)/3132551Robert Price05/2019
2594(2^440399-1)/(16210820281161978209*31518475633*880799)132538Dario Alpern01/2015
2595(38^83891+1)/39132529Robert Price09/2013
25962*10^132493-43132494Robert Price04/2018
2597(418*10^132441+23)/9132443Robert Price02/2020
25982^439931-21132433Lelio R Paula08/2017
259947^79201-46^79201132432Robert Price10/2012
26002^439897-113653132423Enzo Doria08/2014
260135505^5362+5362^35505132410Hans Havermann03/2021
2602(5*2^439822+1)/9132400Lelio R Paula06/2015
2603(112*10^132337-1)/3132339Serge Batalov12/2014
26042^439576-113247132326Enzo Doria07/2014
26052^439497-29143132302Enzo Doria07/2015
26062^439409-114193132276Enzo Doria12/2014
2607(44*10^132233-233)/9132234Robert Price01/2019
26089*10^132148-7132149Robert Price09/2015
2609(47*10^132125-119)/9132126Robert Price05/2019
26102^438845+1870217132106Enzo Doria05/2016
26112^438789+87855132089Lelio R Paula01/2016
26122^438774-2786411132085Enzo Doria03/2016
26132^438755-1848205132079Enzo Doria07/2015
26142^438739-112087132074Enzo Doria06/2014
261535872^4777+4777^35872131979Hans Havermann04/2021
261631198^16945+16945^31198131938Hans Havermann03/2021
261713907#+(318259#)/(13907#)131923Makoto Morimoto10/2017
2618L(631181)131910Henri Lifchitz09/2008
2619(47*10^131886-119)/9131887Robert Price05/2019
2620(3*2^438121+1)/4308193883131879Lelio R Paula06/2015
26212^438079-1863877131875Enzo Doria03/2016
2622(2^438067+5)/329131869Lelio R Paula06/2015
26232^437908-113855131824Enzo Doria09/2014
26242^437884-286349131817Enzo Doria07/2015
2625(11*10^131784-17)/3131785Robert Price06/2018
26264*10^131719-93131720Robert Price07/2020
26273^276062-112292131716Enzo Doria07/2014
2628(7*10^131682+89)/3131683Robert Price08/2020
262929512^28969+28969^29512131681Hans Havermann03/2021
26302^437343+75953131654Enzo Doria04/2016
263135^85243-34^85243131621Robert Price05/2012
2632(59*10^131575+391)/9131576Robert Price03/2021
263339984^1945+1945^39984131505Hans Havermann03/2021
2634(203*10^131457+1)/3131459Robert Price03/2020
263587309^32+32^87309131414Hans Havermann03/2021
2636(68^71713+1)/69131413Paul Bourdelais09/2017
26372^436451+1884713131385Enzo Doria03/2017
26382^436365+35131359Robert Price11/2015
26402^436300+1866871131340Enzo Doria03/2016
2639(7*10^131339+179)/3131340Robert Price09/2018
264114^114592-3131338Paul Bourdelais12/2020
2642(37*10^131270+341)/9131271Robert Price08/2018
264329863^24790+24790^29863131227Hans Havermann03/2021
2644(5*10^131223-29)/3131224Robert Price03/2018
264529524^27825+27825^29524131218Hans Havermann03/2021
2646(23*2^435891-1)/699131215Lelio R Paula07/2015
2647(11*2^435879+1)/3337131211Lelio R Paula06/2015
2649(2^435808+1)/641/6700417131182Lelio R Paula02/2012
2648(2^435808+1)/4294967297131182Serge Batalov12/2016
26512^435773+1875557131181Enzo Doria06/2016
2652(16*10^131180+167)/3131181Robert Price06/2019
2650(26*10^131180-77)/3131181Robert Price11/2019
2653(25*10^131144-7)/9131145Robert Price05/2018
26542^435612-2789939131133Enzo Doria12/2015
265533976^7231+7231^33976131121Hans Havermann03/2021
265633715^7746+7746^33715131121Hans Havermann03/2021
265766^72047-65^72047131093Robert Price09/2013
2658(5*10^131090+37)/3131091Robert Price03/2018
26592^435468+75631131089Enzo Doria04/2016
266037^83588-2131083Lelio R Paula08/2015
2661(4^217720+11)/3131081Robert Price02/2017
266230407^20448+20448^30407131074Hans Havermann04/2021
266329487^27836+27836^29487131059Hans Havermann04/2021
266429962^23615+23615^29962131030Hans Havermann03/2021
26652^435202-113193131009Enzo Doria07/2014
26669*10^130998-19130999Robert Price07/2019
266736243^4108+4108^36243130969Hans Havermann04/2021
2668floor((sqrt(5)-1)/2*10^130911)130911Serge Batalov06/2017
26692^434835-111937130899Enzo Doria05/2014
26702^434685+72257130854Enzo Doria04/2016
2671(7*10^130825+113)/3130826Robert Price02/2018
26722^434539-29317130810Enzo Doria07/2015
26732^434469-114259130789Enzo Doria01/2015
26742^434246+33130722Robert Price11/2015
267530156^21599+21599^30156130710Hans Havermann04/2021
2676(17*10^130695-161)/9130695Robert Price02/2021
267730513^19148+19148^30513130661Hans Havermann03/2021
26789*10^130638+41130639Robert Price08/2020
26792^433911-91130621Lelio R Paula06/2017
268030786^17449+17449^30786130588Hans Havermann03/2021
26812^433744-114419130570Enzo Doria02/2015
26832^433708+1869451130560Enzo Doria05/2016
26822^433710+93130560Lelio R Paula06/2017
2684(29*2^433547-1)/27130511Lelio R Paula06/2015
26853^273521+10130503Tyler NeSmith01/2021
268641659^1356+1356^41659130487Hans Havermann03/2021
26874*10^130480+9130481Robert Price05/2015
2688(23*2^433449-1)/75130481Lelio R Paula06/2015
2689(23*2^433334-1)/3731130445Lelio R Paula06/2015
269033481^7848+7848^33481130401Hans Havermann03/2021
26912^433023-113497130353Enzo Doria08/2014
269231175^15178+15178^31175130350Hans Havermann04/2021
26932^433002+1179379130347Enzo Doria06/2016
26942^432974+19130339Robert Price08/2015
269531903^12168+12168^31903130331Hans Havermann04/2021
269629577^25370+25370^29577130267Hans Havermann04/2021
269731738^12685+12685^31738130231Hans Havermann03/2021
269829489^25956+25956^29489130172Hans Havermann04/2021
2699(2^432457-1)/1672739247834685086279697130159Tony Prest / Never Odd Or Even09/2013
27002^432217+41130111Lelio R Paula06/2017
2701(2^216089*(2^216091-1)-339)/25130098Makoto Morimoto03/2017
2702((2^216091+1066)^2+(2^216091+1066)+41)/47/2069130095Makoto Morimoto05/2016
270397^65480-2130094Lelio R Paula05/2017
270436007^4102+4102^36007130094Hans Havermann04/2021
27054*10^130088-89130089Robert Price11/2018
27062^432117-113215130081Enzo Doria07/2014
27072^431804+72511129986Enzo Doria04/2016
2708(3^272141-3^136071+1)/7129844Serge Batalov03/2014
270931385^13702+13702^31385129833Hans Havermann04/2021
2710(47*10^129789-119)/9129790Robert Price05/2019
2711(9*2^431141+1)/17129787Lelio R Paula06/2015
2712(29*2^430881-1)/21129709Lelio R Paula06/2015
27132^430807+1869563129686Enzo Doria05/2016
27142^430721-21429129660Enzo Doria07/2013
27152^430415-276271129568Enzo Doria07/2015
271637095^3104+3104^37095129533Hans Havermann04/2021
271731132^14459+14459^31132129514Hans Havermann04/2021
271832582^9435+9435^32582129506Hans Havermann03/2021
271930442^17953+17953^30442129505Hans Havermann03/2021
2720(199*10^129487-7)/3129489Robert Price05/2020
27212^430142-2791721129486Enzo Doria03/2016
2722(7*10^129472-13)/3129473Robert Price07/2018
2723(8*10^129469+79)/3129470Robert Price10/2020
272431678^12213+12213^31678129463Hans Havermann04/2021
272531100^14439+14439^31100129362Hans Havermann04/2021
27262^429568-21017129313Enzo Doria07/2013
2727(11*10^129239-179)/3129240Robert Price09/2018
272828659^28988+28988^28659129208Norbert Schneider02/2021
272929423^24616+24616^29423129203Hans Havermann03/2021
27302^429194-112685129201Enzo Doria06/2014
27312^429145-2780449129186Enzo Doria04/2016
273233577^7014+7014^33577129136Hans Havermann03/2021
27332^428892-113453129110Enzo Doria07/2014
2734(11*2^428881-7)/15129106Renaud Lifchitz03/2011
27352^428727-113959129060Enzo Doria10/2014
2736(7*2^428725-1)/13129059Lelio R Paula05/2014
2737(10^129051-31)/3129051Serge Batalov12/2014
2738(134*10^129038+7)/3129040Robert Price02/2020
27392^428564+71161129011Enzo Doria04/2016
274028781^28930+28930^28781129002Norbert Schneider02/2021
274129065^27424+27424^29065128995Hans Havermann04/2021
27422^428502-113285128992Enzo Doria07/2014
27432^428421-21373128968Enzo Doria06/2013
2744L(616787)128901Henri Lifchitz09/2008
274520^99055-3128874Paul Bourdelais12/2020
274691^65772-2128851Lelio R Paula05/2017
27472^428022+43128848Lelio R Paula05/2017
27482^427999-459397128841Enzo Doria05/2015
27492^427993+76847128839Enzo Doria05/2016
275031059^14060+14060^31059128833Hans Havermann03/2021


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Created by  Henri Lifchitz & Renaud Lifchitz : October, 26 2000, last modification: April, 13 2021 12:02 (Time in France)

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