PRP Records

Probable Primes Top 10000

(294627 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 ?
625199^54094+2107952Lelio R Paula06/2013
6252(2^358583-9)/391107942Lelio R Paula12/2013
6253(2^358562+838)/2107938Stefano Morozzi02/2021
62542^358538+55107931Lelio R Paula12/2011
62552^358517-109009107925Enzo Doria03/2014
625626395^12258+12258^26395107914Hans Havermann10/2020
62573^226159+104107906Lelio R Paula03/2017
62587*10^107870+39107871Robert Price01/2023
62592^358310-11655107863Lelio R Paula03/2017
6260(68*10^107852-329)/9107853Robert Price03/2021
62612^358275-112987107852Enzo Doria07/2014
62623^226038+4107848Tyler NeSmith01/2021
62632^358233-20005107839Enzo Doria06/2013
62642^358194+175107828Lelio R Paula12/2011
6265107^53125-106107812Norbert Schneider12/2016
6266(25*10^107804+161)/3107805Robert Price09/2019
62673^225922-2107793Lelio R Paula10/2013
626812^99874-95107783Lelio R Paula03/2017
6269(2^358042+3042)/2107782Stefano Morozzi09/2020
62702^358030-171107778Lelio R Paula12/2011
627111^103488-4170107772Enzo Doria12/2012
62722^357930-4547107748Yves Minet03/2019
62732^357911-20089107742Enzo Doria06/2013
62742^357885+12857107735Yves Minet07/2010
6275(248587#+9289)/(7*1327*111512899)107733Makoto Morimoto06/2019
62767^127473+40107728Lelio R Paula03/2017
62775*2^357850+9107725Lelio R Paula09/2014
62782^357786-291191107705Enzo Doria06/2015
627928907^5320+5320^28907107705Hans Havermann10/2020
628018^85798-23107700Lelio R Paula04/2017
62813*10^107697+61107698Robert Price09/2020
6282(14*10^107694-83)/3107695Robert Price12/2018
62832^357688-1854269107675Enzo Doria09/2015
62842^357671-112225107670Enzo Doria06/2014
628534323^1370+1370^34323107662Hans Havermann11/2020
62862^357618-21005107654Enzo Doria06/2013
62872^357615-17505107653Enzo Doria05/2013
628826350^12171+12171^26350107649Hans Havermann11/2020
6289(30^72871-1)/29107638Robert Price12/2011
629025021^20026+20026^25021107631Hans Havermann11/2020
62912^357521+1870217107625Enzo Doria05/2016
62922^357477-1203107612Lelio R Paula03/2017
629326008^13693+13693^26008107583Hans Havermann10/2020
629425432^16991+16991^25432107583Hans Havermann10/2020
6295(2^357371+3726)/2107580Stefano Morozzi09/2020
62965^153894-18107568Lelio R Paula02/2017
62972^357324-69059107566Enzo Doria11/2015
6298467^40296+40296^467107563Norbert Schneider03/2019
629929446^4495+4495^29446107559Hans Havermann10/2020
6300(8*10^107556-149)/3107557Robert Price12/2021
63012^357283-869688105107553Lelio R Paula01/2017
63022^357280-16805107552Enzo Doria05/2013
630310^107547+481719107548Patrick De Geest03/2017
630410^107547-47107547Lelio R Paula02/2017
6305(23*10^107540+37)/3107541Robert Price02/2022
630617^87396-32107537Lelio R Paula04/2017
6307(746*10^107505+1)/9107507Robert Price03/2020
6308(2^357125+1730)/2107506Stefano Morozzi09/2020
63092^357081+107107493Lelio R Paula12/2011
63102^357058-3911107486Yves Minet04/2017
63113^225274+64107484Lelio R Paula03/2017
63125*10^107482-57107483Robert Price03/2021
631318^85619-95107476Lelio R Paula04/2017
6314(2^357013+2526)/2107472Stefano Morozzi09/2020
63153^225248-130107471Lelio R Paula03/2017
6316(5*2^356961+1)/143107455Lelio R Paula03/2014
631727029^9448+9448^27029107450Hans Havermann11/2020
63182^356935-18085107449Enzo Doria05/2013
631955396^87+87^55396107442Hans Havermann10/2020
6320(14*10^107439-137)/3107440Robert Price04/2021
632110^107409+37107410Lelio R Paula02/2017
632210^107409-329633107409Patrick De Geest03/2017
6323(2^356799+3134)/2107407Stefano Morozzi09/2020
63242^356787-109027107404Enzo Doria04/2014
6325(2^356767+78557)/5107397Lelio R Paula12/2013
63263*10^107389+77107390Robert Price09/2018
6327(11*10^107385+61)/9107386Tyler Busby01/2023
63285^153622-42107378Lelio R Paula02/2017
63292^356699-97305107378Lelio R Paula03/2017
633013129^26072-26072^13129107371Norbert Schneider09/2022
63312^356654+85107364Lelio R Paula11/2011
63322^356641-19921107360Enzo Doria06/2013
63335*10^107355+11107356Robert Price08/2019
63342^356623-465107355Lelio R Paula03/2017
633519^83945-92107345Lelio R Paula02/2017
633625491^16246+16246^25491107337Hans Havermann11/2020
633710^107334+28149107335Patrick De Geest03/2017
633810^107334-83107334Lelio R Paula02/2017
63392^356518+885107323Lelio R Paula03/2017
6340(59*10^107322+391)/9107323Robert Price03/2021
6341(3*2^356506-1)/467107317Lelio R Paula03/2014
6342(2^356468+1162)/2107308Stefano Morozzi09/2020
63432^356442-114713107300Enzo Doria04/2015
63442^356425+72257107295Enzo Doria04/2016
63452^356351-112237107273Enzo Doria06/2014
6347(6^137845-11)/5107264Paul Bourdelais11/2011
63462^356322+74539107264Enzo Doria04/2016
63482^356274+1874479107250Enzo Doria06/2016
634924606^22819+22819^24606107241Hans Havermann10/2020
6350(2^356243+3686)/2107240Stefano Morozzi09/2020
635120^82422-93107234Lelio R Paula02/2017
63522^356157-20365107214Enzo Doria06/2013
63538*10^107209+99107210Robert Price03/2021
63542^356129-18949107206Enzo Doria05/2013
63552^356100-109587107197Enzo Doria04/2014
63562*10^107173-37107174Robert Price11/2021
6357(2^355978+3262)/2107160Stefano Morozzi02/2021
6358(31*2^355970+1)/5107159Lelio R Paula03/2014
63592^355968-64875107158Lelio R Paula01/2017
63602^355952+1870321107153Enzo Doria05/2016
636127069^9088+9088^27069107152Hans Havermann11/2020
63622^355915-117107142Lelio R Paula11/2011
6363(16*10^107140+77)/3107141Robert Price03/2019
636424628^22369+22369^24628107124Hans Havermann11/2020
6365(19*2^355838-1)/15107119Lelio R Paula03/2014
63663^224495-8107112Lelio R Paula12/2013
63673*10^107096+23107097Robert Price03/2022
636825077^18632+18632^25077107086Hans Havermann10/2020
63697^126691-44107067Lelio R Paula03/2017
63704^177830-8243107065Mike Oakes02/2011
6371(509*10^107057+13)/9107059Robert Price05/2022
63722^355604+214051107048Enzo Doria10/2023
6373(2^355562+1702)/2107035Stefano Morozzi09/2020
637410^107028+3593037107029Paul Bourdelais10/2021
63752^355524-21237107024Enzo Doria06/2013
6376(10223*2^355515+1)/4855107022Lelio R Paula07/2014
637724843^20320+20320^24843107022Hans Havermann10/2020
63782^355494-19901107015Enzo Doria06/2013
63792^355454-869688105107003Lelio R Paula01/2017
63804*10^106997+13106998Robert Price02/2021
6381(8*10^106985-629)/9106985Robert Price01/2022
63822^355366+54615106976Lelio R Paula01/2017
6383(31*2^355346-1)/1563106969Lelio R Paula03/2014
63852^355275-19861106949Enzo Doria06/2013
638427503^7738+7738^27503106949Hans Havermann11/2020
6386(85*10^106943+77)/9106944Robert Price07/2022
6387(9179*2^355234-1)/1915106937Lelio R Paula05/2015
63884*10^106914-93106915Robert Price07/2020
63894*10^106892-3106893Robert Price10/2015
6390(66^58741+1)/67106881Paul Bourdelais08/2017
63912^354946-3106850M. Frind & P. Underwood08/2002
6392(2^354945+3134)/2106849Stefano Morozzi09/2020
6393(46^64384+1)/(46^128+1)106843Martin Hopf12/2023
63942^354873-18693106828Enzo Doria05/2013
6395(2^354831+3186)/2106815Stefano Morozzi09/2020
63972^354828+4257106814Lelio R Paula01/2017
639625216^17217+17217^25216106814Hans Havermann10/2020
6398(2^354799+1218)/2106805Stefano Morozzi09/2020
6399436^40459+40459^436106791Norbert Schneider03/2019
6400(21^80761+1)/22106783Paul Bourdelais03/2010
6401(115*10^106772-7)/9106774Robert Price02/2020
64022^354640-354640+1106758Robert Price10/2014
6403(2^354603+2606)/2106746Stefano Morozzi09/2020
64042^354585+95106741Lelio R Paula10/2011
6405(206*10^106737+1)/9106739Robert Price04/2022
64062^354553+189106732Lelio R Paula10/2011
6408(2^354546+1338)/2106729Stefano Morozzi02/2021
6407(8*10^106729-71)/9106729Serge Batalov11/2022
64092^354514-109031106720Enzo Doria04/2014
64102^354509-109465106718Enzo Doria04/2014
6411fibonacci(510628)+2106715Jon Grantham08/2023
6412(15*2^354478-1)/26983106706Lelio R Paula03/2014
6413Phi(217618,10)/899798636917106693Makoto Kamada06/2019
641415^90710+28106684Lelio R Paula04/2017
64157^126237+34106683Lelio R Paula03/2017
64162^354385-115315106681Enzo Doria06/2015
64172^354327-19305106664Enzo Doria06/2013
6418(35*10^106649+1)/9106650Serge Batalov11/2010
641910^106636+97106637Lelio R Paula02/2017
642010^106636-22923106636Patrick De Geest03/2017
64212^354220-57106631Lelio R Paula10/2011
6422(68*10^106628-329)/9106629Robert Price03/2021
6423(29*10^106620-77)/3106621Robert Price02/2020
6424(746*10^106618+1)/9106620Robert Price03/2020
64252*10^106613+29106614Robert Price02/2021
64262^354157-17041106612Enzo Doria05/2013
642712^98778+73106600Lelio R Paula02/2017
642833333^1576+1576^33333106585Hans Havermann11/2020
64292^354064+1870651106584Enzo Doria05/2016
643024568^21779+21779^24568106577Hans Havermann11/2020
64312^353992-57106563Lelio R Paula10/2011
64329*10^106559+59106560Robert Price01/2020
64337*10^106553+27106554Robert Price11/2020
643428847^4938+4938^28847106548Hans Havermann10/2020
6436NSW(139160)106535Robert Price12/2018
6435f(278321)106535Robert Price07/2023
6437(7*10^106516+113)/3106517Robert Price02/2018
64382^353832-1853849106515Enzo Doria09/2015
6439(7^126037-1)/6106513Paul Bourdelais09/2008
64402^353794-18453106503Enzo Doria05/2013
6441(2^353761+2094)/2106493Stefano Morozzi09/2020
64422^353728+7695106483Lelio R Paula01/2017
644326476^10509+10509^26476106475Hans Havermann10/2020
64442^353672-303106466Yves Minet02/2012
64456^136811+101106460Lelio R Paula02/2017
64462^353641+1871981106457Enzo Doria05/2016
6447(8*10^106454-29)/3106455Robert Price07/2018
644827845^6654+6654^27845106454Hans Havermann11/2020
644910^106449-700001106449Robert Price08/2021
645025316^16017+16017^25316106444Hans Havermann11/2020
64512^353553+54615106431Lelio R Paula01/2017
64522^353544-18897106428Enzo Doria05/2013
645328894^4823+4823^28894106426Hans Havermann11/2020
6454(19*10^106422+29)/3106423Robert Price12/2021
6455(694*10^106418+53)/9106420Robert Price02/2022
64566*10^106412-13106413Robert Price07/2022
645725696^13829+13829^25696106402Hans Havermann11/2020
64586^136729-133106396Lelio R Paula02/2017
64592^353418+1605106390Lelio R Paula01/2017
64602^353387+65106381Lelio R Paula10/2011
64612^353372+74311106376Enzo Doria04/2016
64622^353344-3693106368Yves Minet03/2017
6463(772*10^106365-7)/9106367Robert Price06/2022
6464(56*10^106351+619)/9106352Robert Price05/2021
64662^353277-20089106347Enzo Doria06/2013
64652^353275+72173106347Enzo Doria04/2016
64672^353268-17705106345Enzo Doria05/2013
64682^353267-19857106344Enzo Doria06/2013
6469(46*10^106343+143)/9106344Robert Price01/2019
6471(2^353189+3054)/2106321Stefano Morozzi09/2020
647035087^1072+1072^35087106321Hans Havermann10/2020
6472(2^353184+1290)/2106319Stefano Morozzi01/2021
647326985^8684+8684^26985106287Hans Havermann10/2020
6474(2^353051+606)/2106279Stefano Morozzi09/2020
6476222748^3+3^222748106278Anatoly F. Selevich12/2010
6475(46*10^106277+107)/9106278Robert Price06/2022
6477(9179*2^353019-1)/9106273Lelio R Paula05/2015
64782^353025+72257106272Enzo Doria04/2016
64812^352932-20345106244Enzo Doria06/2013
6479(2^353011-3)/745325861246794515484535106244Lelio R Paula12/2013
648025628^13983+13983^25628106244Hans Havermann10/2020
64822^352883-187106229Lelio R Paula10/2011
648320^81649-19^81649106228Jean-Louis Charton03/2011
6484(55*10^106222+377)/9106223Robert Price02/2019
64852^352814-131106208Lelio R Paula10/2011
64862^352752+73951106189Enzo Doria04/2016
648711876*25^75945+357106171Eric Chen10/2023
64886^136434+5106167Lelio R Paula11/2014
648925296^15737+15737^25296106166Hans Havermann09/2020
64908*10^106157-13106158Robert Price08/2019
64917*5^151872-8106155Lelio R Paula11/2014
6492105^52520-2106153Lelio R Paula10/2017
6493(23*10^106152-29)/3106153Robert Price03/2022
64942^352601-1604809106144Enzo Doria05/2015
649512^98353-43106141Lelio R Paula02/2017
64962^352585-18901106139Enzo Doria05/2013
649726363^10614+10614^26363106135Hans Havermann09/2020
6498(2^352554-3)/193106128Lelio R Paula12/2013
64992^352540+15015106126Lelio R Paula01/2017
650025068^17119+17119^25068106125Hans Havermann09/2020


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Created by  Henri Lifchitz & Renaud Lifchitz : October, 26 2000, last modification: March, 12 2024 13:37 (Time in France)

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