PRP Records

Probable Primes Top 10000

(295148 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 ?
65015^153622-42107378Lelio R Paula02/2017
65022^356699-97305107378Lelio R Paula03/2017
650313129^26072-26072^13129107371Norbert Schneider09/2022
65042^356654+85107364Lelio R Paula11/2011
65052^356641-19921107360Enzo Doria06/2013
65065*10^107355+11107356Robert Price08/2019
65072^356623-465107355Lelio R Paula03/2017
650819^83945-92107345Lelio R Paula02/2017
650925491^16246+16246^25491107337Hans Havermann11/2020
651010^107334+28149107335Patrick De Geest03/2017
651110^107334-83107334Lelio R Paula02/2017
65122^356518+885107323Lelio R Paula03/2017
6513(59*10^107322+391)/9107323Robert Price03/2021
6514(3*2^356506-1)/467107317Lelio R Paula03/2014
6515(2^356468+1162)/2107308Stefano Morozzi09/2020
65162^356442-114713107300Enzo Doria04/2015
65172^356425+72257107295Enzo Doria04/2016
65182^356351-112237107273Enzo Doria06/2014
6520(6^137845-11)/5107264Paul Bourdelais11/2011
65192^356322+74539107264Enzo Doria04/2016
65212^356274+1874479107250Enzo Doria06/2016
652224606^22819+22819^24606107241Hans Havermann10/2020
6523(2^356243+3686)/2107240Stefano Morozzi09/2020
652420^82422-93107234Lelio R Paula02/2017
65252^356157-20365107214Enzo Doria06/2013
65268*10^107209+99107210Robert Price03/2021
65272^356129-18949107206Enzo Doria05/2013
65282^356100-109587107197Enzo Doria04/2014
65292*10^107173-37107174Robert Price11/2021
6530(2^355978+3262)/2107160Stefano Morozzi02/2021
6531(31*2^355970+1)/5107159Lelio R Paula03/2014
65322^355968-64875107158Lelio R Paula01/2017
65332^355952+1870321107153Enzo Doria05/2016
653427069^9088+9088^27069107152Hans Havermann11/2020
65352^355915-117107142Lelio R Paula11/2011
6536(16*10^107140+77)/3107141Robert Price03/2019
653724628^22369+22369^24628107124Hans Havermann11/2020
6538(19*2^355838-1)/15107119Lelio R Paula03/2014
65393^224495-8107112Lelio R Paula12/2013
65403*10^107096+23107097Robert Price03/2022
654125077^18632+18632^25077107086Hans Havermann10/2020
65427^126691-44107067Lelio R Paula03/2017
65434^177830-8243107065Mike Oakes02/2011
6544(509*10^107057+13)/9107059Robert Price05/2022
65452^355604+214051107048Enzo Doria10/2023
6546(2^355562+1702)/2107035Stefano Morozzi09/2020
654710^107028+3593037107029Paul Bourdelais10/2021
65482^355524-21237107024Enzo Doria06/2013
6549(10223*2^355515+1)/4855107022Lelio R Paula07/2014
655024843^20320+20320^24843107022Hans Havermann10/2020
65512^355494-19901107015Enzo Doria06/2013
65522^355454-869688105107003Lelio R Paula01/2017
65534*10^106997+13106998Robert Price02/2021
6554(8*10^106985-629)/9106985Robert Price01/2022
65552^355366+54615106976Lelio R Paula01/2017
6556(31*2^355346-1)/1563106969Lelio R Paula03/2014
65582^355275-19861106949Enzo Doria06/2013
655727503^7738+7738^27503106949Hans Havermann11/2020
6559(85*10^106943+77)/9106944Robert Price07/2022
6560(9179*2^355234-1)/1915106937Lelio R Paula05/2015
65614*10^106914-93106915Robert Price07/2020
65624*10^106892-3106893Robert Price10/2015
6563(66^58741+1)/67106881Paul Bourdelais08/2017
65642^354946-3106850M. Frind & P. Underwood08/2002
6565(2^354945+3134)/2106849Stefano Morozzi09/2020
6566(46^64384+1)/(46^128+1)106843Martin Hopf12/2023
65672^354873-18693106828Enzo Doria05/2013
6568(2^354831+3186)/2106815Stefano Morozzi09/2020
65702^354828+4257106814Lelio R Paula01/2017
656925216^17217+17217^25216106814Hans Havermann10/2020
6571(2^354799+1218)/2106805Stefano Morozzi09/2020
6572436^40459+40459^436106791Norbert Schneider03/2019
6573(21^80761+1)/22106783Paul Bourdelais03/2010
6574(115*10^106772-7)/9106774Robert Price02/2020
65752^354640-354640+1106758Robert Price10/2014
6576(2^354603+2606)/2106746Stefano Morozzi09/2020
65772^354585+95106741Lelio R Paula10/2011
6578(206*10^106737+1)/9106739Robert Price04/2022
65792^354553+189106732Lelio R Paula10/2011
6581(2^354546+1338)/2106729Stefano Morozzi02/2021
6580(8*10^106729-71)/9106729Serge Batalov11/2022
65822^354514-109031106720Enzo Doria04/2014
65832^354509-109465106718Enzo Doria04/2014
6584fibonacci(510628)+2106715Jon Grantham08/2023
6585(15*2^354478-1)/26983106706Lelio R Paula03/2014
6586Phi(217618,10)/899798636917106693Makoto Kamada06/2019
658715^90710+28106684Lelio R Paula04/2017
65887^126237+34106683Lelio R Paula03/2017
65892^354385-115315106681Enzo Doria06/2015
65902^354327-19305106664Enzo Doria06/2013
6591(35*10^106649+1)/9106650Serge Batalov11/2010
659210^106636+97106637Lelio R Paula02/2017
659310^106636-22923106636Patrick De Geest03/2017
65942^354220-57106631Lelio R Paula10/2011
6595(68*10^106628-329)/9106629Robert Price03/2021
6596(29*10^106620-77)/3106621Robert Price02/2020
6597(746*10^106618+1)/9106620Robert Price03/2020
65982*10^106613+29106614Robert Price02/2021
65992^354157-17041106612Enzo Doria05/2013
660012^98778+73106600Lelio R Paula02/2017
660133333^1576+1576^33333106585Hans Havermann11/2020
66022^354064+1870651106584Enzo Doria05/2016
660324568^21779+21779^24568106577Hans Havermann11/2020
66042^353992-57106563Lelio R Paula10/2011
66059*10^106559+59106560Robert Price01/2020
66067*10^106553+27106554Robert Price11/2020
660728847^4938+4938^28847106548Hans Havermann10/2020
6609NSW(139160)106535Robert Price12/2018
6608f(278321)106535Robert Price07/2023
6610(7*10^106516+113)/3106517Robert Price02/2018
66112^353832-1853849106515Enzo Doria09/2015
6612(7^126037-1)/6106513Paul Bourdelais09/2008
66132^353794-18453106503Enzo Doria05/2013
6614(2^353761+2094)/2106493Stefano Morozzi09/2020
66152^353728+7695106483Lelio R Paula01/2017
661626476^10509+10509^26476106475Hans Havermann10/2020
66172^353672-303106466Yves Minet02/2012
66186^136811+101106460Lelio R Paula02/2017
66192^353641+1871981106457Enzo Doria05/2016
6620(8*10^106454-29)/3106455Robert Price07/2018
662127845^6654+6654^27845106454Hans Havermann11/2020
662210^106449-700001106449Robert Price08/2021
662325316^16017+16017^25316106444Hans Havermann11/2020
66242^353553+54615106431Lelio R Paula01/2017
66252^353544-18897106428Enzo Doria05/2013
662628894^4823+4823^28894106426Hans Havermann11/2020
6627(19*10^106422+29)/3106423Robert Price12/2021
6628(694*10^106418+53)/9106420Robert Price02/2022
66296*10^106412-13106413Robert Price07/2022
663025696^13829+13829^25696106402Hans Havermann11/2020
66316^136729-133106396Lelio R Paula02/2017
66322^353418+1605106390Lelio R Paula01/2017
66332^353387+65106381Lelio R Paula10/2011
66342^353372+74311106376Enzo Doria04/2016
66352^353344-3693106368Yves Minet03/2017
6636(772*10^106365-7)/9106367Robert Price06/2022
6637(56*10^106351+619)/9106352Robert Price05/2021
66392^353277-20089106347Enzo Doria06/2013
66382^353275+72173106347Enzo Doria04/2016
66402^353268-17705106345Enzo Doria05/2013
66412^353267-19857106344Enzo Doria06/2013
6642(46*10^106343+143)/9106344Robert Price01/2019
6644(2^353189+3054)/2106321Stefano Morozzi09/2020
664335087^1072+1072^35087106321Hans Havermann10/2020
6645(2^353184+1290)/2106319Stefano Morozzi01/2021
664626985^8684+8684^26985106287Hans Havermann10/2020
6647(2^353051+606)/2106279Stefano Morozzi09/2020
6649222748^3+3^222748106278Anatoly F. Selevich12/2010
6648(46*10^106277+107)/9106278Robert Price06/2022
6650(9179*2^353019-1)/9106273Lelio R Paula05/2015
66512^353025+72257106272Enzo Doria04/2016
66542^352932-20345106244Enzo Doria06/2013
6652(2^353011-3)/745325861246794515484535106244Lelio R Paula12/2013
665325628^13983+13983^25628106244Hans Havermann10/2020
66552^352883-187106229Lelio R Paula10/2011
665620^81649-19^81649106228Jean-Louis Charton03/2011
6657(55*10^106222+377)/9106223Robert Price02/2019
66582^352814-131106208Lelio R Paula10/2011
66592^352752+73951106189Enzo Doria04/2016
666011876*25^75945+357106171Eric Chen10/2023
66616^136434+5106167Lelio R Paula11/2014
666225296^15737+15737^25296106166Hans Havermann09/2020
66638*10^106157-13106158Robert Price08/2019
66647*5^151872-8106155Lelio R Paula11/2014
6665105^52520-2106153Lelio R Paula10/2017
6666(23*10^106152-29)/3106153Robert Price03/2022
66672^352601-1604809106144Enzo Doria05/2015
666812^98353-43106141Lelio R Paula02/2017
66692^352585-18901106139Enzo Doria05/2013
667026363^10614+10614^26363106135Hans Havermann09/2020
6671(2^352554-3)/193106128Lelio R Paula12/2013
66722^352540+15015106126Lelio R Paula01/2017
667325068^17119+17119^25068106125Hans Havermann09/2020
66742^352524-3149106121Yves Minet10/2014
6675(7*10^106119-67)/3106120Robert Price10/2021
66762^352486-1858781106109Enzo Doria04/2016
66772^352444+12705106097Lelio R Paula01/2017
667828561^5182+5182^28561106090Hans Havermann10/2020
6679(182*10^106083+43)/9106085Robert Price02/2020
6680(266*10^106066+1)/3106068Robert Price04/2020
6681(7*10^106066-187)/9106066Tyler Busby01/2023
66822^352228-18953106032Enzo Doria05/2013
6683(2^352223+1118)/2106030Stefano Morozzi09/2020
6684(2^352212+2250)/2106027Stefano Morozzi01/2021
6685(2^352136+2638)/2106004Stefano Morozzi09/2020
66862^352107+1872533105995Enzo Doria05/2016
6687(2^352096+2086)/2105992Stefano Morozzi09/2020
66882^352066-2591105983Yves Minet07/2014
66892^352030+715105972Lelio R Paula10/2011
66909*6^136176-5105967Lelio R Paula11/2014
669117099*2^351991+58329105965Paul Vanderveen12/2017
669228582^5097+5097^28582105963Hans Havermann09/2020
6693155^48377+2105962Lelio R Paula08/2013
6694(23*10^105944-119)/3105945Robert Price07/2021
66952^351865+1869707105922Enzo Doria05/2016
669624974^17427+17427^24974105921Hans Havermann09/2020
669725163^16194+16194^25163105920Hans Havermann09/2020
66982^351831+23105912Lelio R Paula10/2011
6699(2^351818+3798)/2105908Stefano Morozzi02/2021
67009*2^351784-5105899Lelio R Paula09/2014
6701(2^351776+2766)/2105895Stefano Morozzi01/2021
6702(85*10^105881+203)/9105882Robert Price09/2020
67032^351671-112387105864Enzo Doria06/2014
67042^351669-109501105863Enzo Doria04/2014
67052^351644+74731105856Enzo Doria04/2016
670613^95025-42105853Lelio R Paula12/2016
67072^351599+15015105842Lelio R Paula01/2017
670819^82763+90105834Lelio R Paula01/2017
6709(205*10^105831-1)/3105833Robert Price11/2021
671026050^11551+11551^26050105832Hans Havermann09/2020
6711(9179*2^351540-1)/221105826Lelio R Paula05/2015
671220^81329-51105812Lelio R Paula01/2017
6713(5*10^105811+211)/9105811Robert Price02/2018
67142^351483+28425105807Lelio R Paula01/2017
671525231^15610+15610^25231105804Hans Havermann09/2020
671615^89960+86105802Lelio R Paula02/2017
67172^351460-17289105801Enzo Doria05/2013
671819^82735+22105798Lelio R Paula01/2017
67192^351435-109077105793Enzo Doria04/2014
67202^351393+1089105780Lelio R Paula01/2017
67212^351364+72631105772Enzo Doria04/2016
6722(2^351333+3626)/2105762Stefano Morozzi09/2020
672326818^8783+8783^26818105761Hans Havermann09/2020
67262^351305+1872467105754Enzo Doria05/2016
67253^221649+16105754Lelio R Paula11/2016
672432511^1790+1790^32511105754Hans Havermann09/2020
67278*3^221637-5105749Lelio R Paula09/2014
67282^351279-2780449105746Enzo Doria03/2016
6729(2^351263+3198)/2105741Stefano Morozzi09/2020
673015^89903-26105735Lelio R Paula02/2017
67322^351213-73105726Lelio R Paula10/2011
6731(2^351214+1210)/2105726Stefano Morozzi09/2020
67332^351192-4589105720Yves Minet07/2011
673420^81250-33105709Lelio R Paula12/2016
6735(2^351133+3530)/2105702Stefano Morozzi09/2020
6736(2^351103+534)/2105693Stefano Morozzi09/2020
67372^351076-113159105685Enzo Doria07/2014
673893^53688-2105684Lelio R Paula09/2013
67392^351060-4559105680Yves Minet07/2011
6740((10^52836-1)*10000/9+5927)*10^52836+(10^52836-1)/9105676Hans Havermann08/2019
674111^101473-750105674Enzo Doria11/2012
67423*5^151181-8105672Lelio R Paula11/2014
674315^89831-34105650Lelio R Paula02/2017
674511^101448-360105648Enzo Doria08/2012
67443*7^125011+4105648Lelio R Paula11/2014
67462^350943-113269105645Enzo Doria07/2014
67472*10^105636-91105637Robert Price04/2020
674824231^22880+22880^24231105634Hans Havermann09/2020
674935296^983+983^35296105626Hans Havermann09/2020
67502^350868-19725105622Enzo Doria06/2013


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Created by  Henri Lifchitz & Renaud Lifchitz : October, 26 2000, last modification: May, 20 2024 09:22 (Time in France)

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