PRP Records

Probable Primes Top 10000

(271067 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 ?
22512^447552-1019134727Yves Minet02/2014
2252(2*10^134720-41)/3134720Robert Price02/2018
22532^447437-113569134692Enzo Doria08/2014
22542^447426-65134689Lelio R Paula08/2017
22552^447357-2797573134668Enzo Doria04/2016
22562^447278+93134645Lelio R Paula08/2017
22572^447094-113193134589Enzo Doria07/2014
22583^282041-9934134568Enzo Doria05/2014
22592^447019-109039134567Enzo Doria04/2014
22602^446990-22041134558Enzo Doria07/2013
2261123^64370+122134528Karsten Bonath04/2018
22622^446782-39701134495Enzo Doria09/2015
22632^446494-16485134409Enzo Doria04/2013
226429504^30069-30069^29504134405Norbert Schneider12/2014
22652^446441+65134393Lelio R Paula08/2017
2266(10^134385+719)/9134385Serge Batalov12/2014
2267(2*10^134364+529)/9134364Robert Price01/2018
2268(13*2^446187-1)/661134314Lelio R Paula07/2015
22695^192103+3^192103+2^192103+1134275Matthias Baur12/2019
2270(2^446022-7)/339134264Lelio R Paula07/2015
227163^74568+2134174Lelio R Paula06/2017
22722^445671-22071134161Enzo Doria07/2013
2273532^49205+49205^532134129Norbert Schneider02/2019
2274(28*10^134122-1)/9134123Serge Batalov10/2014
22752^445515-113859134114Enzo Doria10/2014
2276(22*10^134111-37)/3134112Robert Price04/2019
22772^445328-216917134058Enzo Doria05/2014
22782^445202+1874899134020Enzo Doria06/2016
2279(13*2^445102+1)/17133989Lelio R Paula07/2015
2280(35*10^133979-593)/9133980Robert Price07/2018
22812*10^133955+51133956Robert Price05/2018
22822^444964-113639133948Enzo Doria08/2014
228328118^30097-30097^28118133902Norbert Schneider01/2015
228410^133902-100001133902Robert Price07/2020
22852^444784-113859133894Enzo Doria10/2014
2286(266*10^133603+1)/3133605Robert Price04/2020
2287(89*10^133580+1)/9133581Serge Batalov05/2010
228862^74521-61^74521133571Robert Price05/2013
2289(182*10^133543+1)/3133545Robert Price02/2020
22902^443198-1867301133416Enzo Doria03/2016
2291(19*10^133390+101)/3133391Robert Price09/2019
2292(71^72043-1)/70133369Paul Bourdelais09/2017
22932^442799+1874633133296Enzo Doria06/2016
2294L(637751)133283Henri Lifchitz09/2008
2295109^65410-2133269Lelio R Paula10/2017
22962^442688-113489133263Enzo Doria08/2014
2297(7*2^442640-1)/783133246Lelio R Paula07/2015
2298(9*2^442463+1)/17441133192Lelio R Paula07/2015
22992^442437-1849993133187Enzo Doria08/2015
23002^442430-2791721133185Enzo Doria03/2016
2301(13*2^442428-1)/309133183Lelio R Paula07/2015
2302(25*2^442379-1)/71133169Lelio R Paula07/2015
2303(2^441799+78557)/5132995Lelio R Paula07/2015
23042^441781-2787883132990Enzo Doria03/2016
2305(3*2^441685+1)/749132959Lelio R Paula07/2015
23062^441618+37132941Lelio R Paula08/2017
23072^441521-113575132912Enzo Doria08/2014
23087*10^132884-99132885Robert Price06/2019
2309(103*10^132879+17)/3132881Robert Price08/2020
23102^441396-65132874Lelio R Paula08/2017
23112^441330+1871959132854Enzo Doria05/2016
23122^441063+383132774Lelio R Paula06/2012
2313(22*10^132746+53)/3132747Robert Price07/2019
23142^440846+1870909132708Enzo Doria05/2016
23152^440656-113489132651Enzo Doria08/2014
2316numbpart(14180123587)132646Serge Batalov04/2017
2317(19*10^132550+191)/3132551Robert Price05/2019
2318(2^440399-1)/(16210820281161978209*31518475633*880799)132538Dario Alpern01/2015
2319(38^83891+1)/39132529Robert Price09/2013
23202*10^132493-43132494Robert Price04/2018
2321(418*10^132441+23)/9132443Robert Price02/2020
23222^439931-21132433Lelio R Paula08/2017
232347^79201-46^79201132432Robert Price10/2012
23242^439897-113653132423Enzo Doria08/2014
2325(5*2^439822+1)/9132400Lelio R Paula06/2015
2326(112*10^132337-1)/3132339Serge Batalov12/2014
23272^439576-113247132326Enzo Doria07/2014
23282^439497-29143132302Enzo Doria07/2015
23292^439409-114193132276Enzo Doria12/2014
2330(44*10^132233-233)/9132234Robert Price01/2019
23319*10^132148-7132149Robert Price09/2015
2332(47*10^132125-119)/9132126Robert Price05/2019
23332^438845+1870217132106Enzo Doria05/2016
23342^438789+87855132089Lelio R Paula01/2016
23352^438774-2786411132085Enzo Doria03/2016
23362^438755-1848205132079Enzo Doria07/2015
23372^438739-112087132074Enzo Doria06/2014
233813907#+(318259#)/(13907#)131923Makoto Morimoto10/2017
2339L(631181)131910Henri Lifchitz09/2008
2340(47*10^131886-119)/9131887Robert Price05/2019
2341(3*2^438121+1)/4308193883131879Lelio R Paula06/2015
23422^438079-1863877131875Enzo Doria03/2016
2343(2^438067+5)/329131869Lelio R Paula06/2015
23442^437908-113855131824Enzo Doria09/2014
23452^437884-286349131817Enzo Doria07/2015
2346(11*10^131784-17)/3131785Robert Price06/2018
23474*10^131719-93131720Robert Price07/2020
23483^276062-112292131716Enzo Doria07/2014
2349(7*10^131682+89)/3131683Robert Price08/2020
23502^437343+75953131654Enzo Doria04/2016
235135^85243-34^85243131621Robert Price05/2012
2352(203*10^131457+1)/3131459Robert Price03/2020
2353(68^71713+1)/69131413Paul Bourdelais09/2017
23542^436451+1884713131385Enzo Doria03/2017
23552^436365+35131359Robert Price11/2015
23562^436300+1866871131340Enzo Doria03/2016
2357(7*10^131339+179)/3131340Robert Price09/2018
2358(37*10^131270+341)/9131271Robert Price08/2018
2359(5*10^131223-29)/3131224Robert Price03/2018
2360(23*2^435891-1)/699131215Lelio R Paula07/2015
2361(11*2^435879+1)/3337131211Lelio R Paula06/2015
2363(2^435808+1)/641/6700417131182Lelio R Paula02/2012
2362(2^435808+1)/4294967297131182Serge Batalov12/2016
23662^435773+1875557131181Enzo Doria06/2016
2365(16*10^131180+167)/3131181Robert Price06/2019
2364(26*10^131180-77)/3131181Robert Price11/2019
2367(25*10^131144-7)/9131145Robert Price05/2018
23682^435612-2789939131133Enzo Doria12/2015
236966^72047-65^72047131093Robert Price09/2013
2370(5*10^131090+37)/3131091Robert Price03/2018
23712^435468+75631131089Enzo Doria04/2016
237237^83588-2131083Lelio R Paula08/2015
2373(4^217720+11)/3131081Robert Price02/2017
23742^435202-113193131009Enzo Doria07/2014
23759*10^130998-19130999Robert Price07/2019
2376floor((sqrt(5)-1)/2*10^130911)130911Serge Batalov06/2017
23772^434835-111937130899Enzo Doria05/2014
23782^434685+72257130854Enzo Doria04/2016
2379(7*10^130825+113)/3130826Robert Price02/2018
23802^434539-29317130810Enzo Doria07/2015
23812^434469-114259130789Enzo Doria01/2015
23822^434246+33130722Robert Price11/2015
23839*10^130638+41130639Robert Price08/2020
23842^433911-91130621Lelio R Paula06/2017
23852^433744-114419130570Enzo Doria02/2015
23872^433708+1869451130560Enzo Doria05/2016
23862^433710+93130560Lelio R Paula06/2017
2388(29*2^433547-1)/27130511Lelio R Paula06/2015
23894*10^130480+9130481Robert Price05/2015
2390(23*2^433449-1)/75130481Lelio R Paula06/2015
2391(23*2^433334-1)/3731130445Lelio R Paula06/2015
23922^433023-113497130353Enzo Doria08/2014
23932^433002+1179379130347Enzo Doria06/2016
23942^432974+19130339Robert Price08/2015
2395(2^432457-1)/1672739247834685086279697130159Tony Prest / Never Odd Or Even09/2013
23962^432217+41130111Lelio R Paula06/2017
2397(2^216089*(2^216091-1)-339)/25130098Makoto Morimoto03/2017
2398((2^216091+1066)^2+(2^216091+1066)+41)/47/2069130095Makoto Morimoto05/2016
239997^65480-2130094Lelio R Paula05/2017
24004*10^130088-89130089Robert Price11/2018
24012^432117-113215130081Enzo Doria07/2014
24022^431804+72511129986Enzo Doria04/2016
2403(3^272141-3^136071+1)/7129844Serge Batalov03/2014
2404(47*10^129789-119)/9129790Robert Price05/2019
2405(9*2^431141+1)/17129787Lelio R Paula06/2015
2406(29*2^430881-1)/21129709Lelio R Paula06/2015
24072^430807+1869563129686Enzo Doria05/2016
24082^430721-21429129660Enzo Doria07/2013
24092^430415-276271129568Enzo Doria07/2015
2410(199*10^129487-7)/3129489Robert Price05/2020
24112^430142-2791721129486Enzo Doria03/2016
2412(7*10^129472-13)/3129473Robert Price07/2018
24132^429568-21017129313Enzo Doria07/2013
2414(11*10^129239-179)/3129240Robert Price09/2018
24152^429194-112685129201Enzo Doria06/2014
24162^429145-2780449129186Enzo Doria04/2016
24172^428892-113453129110Enzo Doria07/2014
2418(11*2^428881-7)/15129106Renaud Lifchitz03/2011
24192^428727-113959129060Enzo Doria10/2014
2420(7*2^428725-1)/13129059Lelio R Paula05/2014
2421(10^129051-31)/3129051Serge Batalov12/2014
2422(134*10^129038+7)/3129040Robert Price02/2020
24232^428564+71161129011Enzo Doria04/2016
24242^428502-113285128992Enzo Doria07/2014
24252^428421-21373128968Enzo Doria06/2013
2426L(616787)128901Henri Lifchitz09/2008
242791^65772-2128851Lelio R Paula05/2017
24282^428022+43128848Lelio R Paula05/2017
24292^427999-459397128841Enzo Doria05/2015
24302^427993+76847128839Enzo Doria05/2016
24312^427824-1851507128788Enzo Doria08/2015
24322^427807-21469128783Enzo Doria07/2013
243311^123594-240128710Enzo Doria09/2012
24342^427504-21503128692Enzo Doria07/2013
24352^427420+91128667Lelio R Paula05/2017
2436(68*10^128645-257)/9128646Robert Price07/2019
24372^427269-113635128621Enzo Doria08/2014
24382^427130+1877569128579Enzo Doria08/2016
24392^427016-115349128545Enzo Doria07/2015
2440(4*10^128510+137)/3128511Robert Price03/2018
24412^426889-112879128507Enzo Doria06/2014
24422^426804+1869931128481Enzo Doria05/2016
24432^426750+77635128465Enzo Doria05/2016
24442^426425-91128367Lelio R Paula05/2017
2445(15*2^426398-1)/11128359Lelio R Paula05/2014
24462^426352+74971128345Enzo Doria04/2016
2447(199*10^128343-7)/3128345Robert Price05/2020
24484*10^128343-21128344Robert Price09/2018
24492^426300-1863689128330Enzo Doria03/2016
24502^426293+1881017128327Enzo Doria11/2016
24512^426043+35128252Robert Price11/2015
2452(4*10^128244-19)/3128245Robert Price03/2018
2453(305*10^128198+1)/9128200Robert Price02/2020
24542^425808-459959128181Enzo Doria06/2015
24552^425627-113605128127Enzo Doria08/2014
2456(22*10^128094+53)/3128095Robert Price07/2019
2457(86*10^128086-221)/9128087Robert Price09/2019
245818565^30002-30002^18565128070Norbert Schneider01/2015
2459(2^425287-9)/2737128021Lelio R Paula05/2015
2460(3*2^425233-1)/25128007Lelio R Paula05/2014
24612^425205+4911128000Marek Hubal02/2017
24622^425118-113663127974Enzo Doria08/2014
2463(86*10^127967-329)/9127968Robert Price01/2020
24642^425061+1869761127957Enzo Doria05/2016
2465746^44541+44541^746127955Norbert Schneider07/2019
24662^424918-21141127914Enzo Doria07/2013
24672^424864-29489127897Enzo Doria08/2015
2468(97*10^127858-1)/3127860Serge Batalov12/2014
24692^424632-2786639127827Enzo Doria03/2016
24702^424577-113755127811Enzo Doria09/2014
2471(7*2^424512-1)/3127792Lelio R Paula05/2014
2472(56*10^127752+691)/9127753Robert Price05/2019
247311^122629-720127705Enzo Doria11/2012
247422*10^127645+3127647Robert Price01/2020
24754*10^127562-39127563Robert Price09/2020
24762^423696-21429127546Enzo Doria07/2013
24772^423664-1864559127536Enzo Doria03/2016
24783^267267-4127519Henri Lifchitz10/2014
2479(103*10^127491+17)/3127493Robert Price08/2020
2480(19^99689+5^99689)/24127477Robert Price09/2013
2481(21*2^423372+1)/101127447Lelio R Paula05/2014
24822^423328-21537127435Enzo Doria07/2013
2483(67*10^127413-7)/3127415Robert Price01/2020
2484(2*10^127407+73)/3127407Robert Price09/2020
2485(2^423165-7)/25127384Lelio R Paula05/2015
2486(112*10^127324+17)/3127326Robert Price03/2020
2487(F(5)^182099-F(4)^182099)/F(3)127282Wayne Halsdorf08/2013
2488(16*10^127259+197)/3127260Robert Price04/2019
2489(26*10^127240+61)/3127241Robert Price10/2019
2490(234483*27^88884-145)/26127230Curtis Bright05/2015
24912^422515-114997127190Enzo Doria06/2015
24925*10^127179-3127180Robert Price07/2015
2493(44*10^127169-233)/9127170Robert Price01/2019
24945*10^127153+77127154Robert Price12/2018
2495736^44335+44335^736127104Norbert Schneider07/2019
2496-516776642557847117490*Bern(37960)/34256837217082767928421792453127042Thomas Ritschel06/2017
2497(78^67141-1)/77127036Paul Bourdelais09/2017
24982^421860-113285126993Enzo Doria07/2014
2499(2^421827-7)/11126982Lelio R Paula05/2015
250011^121910-840126957Enzo Doria12/2012


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Created by  Henri Lifchitz & Renaud Lifchitz : October, 26 2000, last modification: September, 30 2020 10:03 (Time in France)

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