PRP Records

Probable Primes Top 10000

(301238 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 ?
7001(2^358562+838)/2107938Stefano Morozzi02/2021
70022^358538+55107931Lelio R Paula12/2011
70032^358517-109009107925Enzo Doria03/2014
700426395^12258+12258^26395107914Hans Havermann10/2020
70053^226159+104107906Lelio R Paula03/2017
70067*10^107870+39107871Robert Price01/2023
70072^358310-11655107863Lelio R Paula03/2017
7008(68*10^107852-329)/9107853Robert Price03/2021
70092^358275-112987107852Enzo Doria07/2014
70103^226038+4107848Tyler NeSmith01/2021
70112^358233-20005107839Enzo Doria06/2013
70122^358194+175107828Lelio R Paula12/2011
7013107^53125-106107812Norbert Schneider12/2016
7014(25*10^107804+161)/3107805Robert Price09/2019
70153^225922-2107793Lelio R Paula10/2013
701612^99874-95107783Lelio R Paula03/2017
7017(2^358042+3042)/2107782Stefano Morozzi09/2020
70182^358030-171107778Lelio R Paula12/2011
701911^103488-4170107772Enzo Doria12/2012
70202^357930-4547107748Yves Minet03/2019
70212^357911-20089107742Enzo Doria06/2013
70222^357885+12857107735Yves Minet07/2010
7023(248587#+9289)/(7*1327*111512899)107733Makoto Morimoto06/2019
70247^127473+40107728Lelio R Paula03/2017
70255*2^357850+9107725Lelio R Paula09/2014
70262^357786-291191107705Enzo Doria06/2015
702728907^5320+5320^28907107705Hans Havermann10/2020
702818^85798-23107700Lelio R Paula04/2017
70293*10^107697+61107698Robert Price09/2020
7030(14*10^107694-83)/3107695Robert Price12/2018
70312^357688-1854269107675Enzo Doria09/2015
70322^357671-112225107670Enzo Doria06/2014
703334323^1370+1370^34323107662Hans Havermann11/2020
70342^357618-21005107654Enzo Doria06/2013
70352^357615-17505107653Enzo Doria05/2013
703626350^12171+12171^26350107649Hans Havermann11/2020
7037(30^72871-1)/29107638Robert Price12/2011
703825021^20026+20026^25021107631Hans Havermann11/2020
70392^357521+1870217107625Enzo Doria05/2016
70402^357477-1203107612Lelio R Paula03/2017
704126008^13693+13693^26008107583Hans Havermann10/2020
704225432^16991+16991^25432107583Hans Havermann10/2020
7043(2^357371+3726)/2107580Stefano Morozzi09/2020
70445^153894-18107568Lelio R Paula02/2017
70452^357324-69059107566Enzo Doria11/2015
7046467^40296+40296^467107563Norbert Schneider03/2019
704729446^4495+4495^29446107559Hans Havermann10/2020
7048(8*10^107556-149)/3107557Robert Price12/2021
70492^357283-869688105107553Lelio R Paula01/2017
70502^357280-16805107552Enzo Doria05/2013
705110^107547+481719107548Patrick De Geest03/2017
705210^107547-47107547Lelio R Paula02/2017
7053(23*10^107540+37)/3107541Robert Price02/2022
705417^87396-32107537Lelio R Paula04/2017
7055(746*10^107505+1)/9107507Robert Price03/2020
7056(2^357125+1730)/2107506Stefano Morozzi09/2020
70572^357081+107107493Lelio R Paula12/2011
70582^357058-3911107486Yves Minet04/2017
70593^225274+64107484Lelio R Paula03/2017
70605*10^107482-57107483Robert Price03/2021
706118^85619-95107476Lelio R Paula04/2017
7062(2^357013+2526)/2107472Stefano Morozzi09/2020
70633^225248-130107471Lelio R Paula03/2017
7064(5*2^356961+1)/143107455Lelio R Paula03/2014
706527029^9448+9448^27029107450Hans Havermann11/2020
70662^356935-18085107449Enzo Doria05/2013
706755396^87+87^55396107442Hans Havermann10/2020
7068(14*10^107439-137)/3107440Robert Price04/2021
7069164^48505-48505^164107432Norman Luhn09/2024
707010^107409+37107410Lelio R Paula02/2017
707110^107409-329633107409Patrick De Geest03/2017
7072(2^356799+3134)/2107407Stefano Morozzi09/2020
70732^356787-109027107404Enzo Doria04/2014
7074(2^356767+78557)/5107397Lelio R Paula12/2013
70753*10^107389+77107390Robert Price09/2018
7076(11*10^107385+61)/9107386Tyler Busby01/2023
70775^153622-42107378Lelio R Paula02/2017
70782^356699-97305107378Lelio R Paula03/2017
707913129^26072-26072^13129107371Norbert Schneider09/2022
70802^356654+85107364Lelio R Paula11/2011
70812^356641-19921107360Enzo Doria06/2013
70825*10^107355+11107356Robert Price08/2019
70832^356623-465107355Lelio R Paula03/2017
708419^83945-92107345Lelio R Paula02/2017
708525491^16246+16246^25491107337Hans Havermann11/2020
708610^107334+28149107335Patrick De Geest03/2017
708710^107334-83107334Lelio R Paula02/2017
70882^356518+885107323Lelio R Paula03/2017
7089(59*10^107322+391)/9107323Robert Price03/2021
7090(3*2^356506-1)/467107317Lelio R Paula03/2014
7091(2^356468+1162)/2107308Stefano Morozzi09/2020
70922^356442-114713107300Enzo Doria04/2015
70932^356425+72257107295Enzo Doria04/2016
70942^356351-112237107273Enzo Doria06/2014
7096(6^137845-11)/5107264Paul Bourdelais11/2011
70952^356322+74539107264Enzo Doria04/2016
70972^356274+1874479107250Enzo Doria06/2016
709824606^22819+22819^24606107241Hans Havermann10/2020
7099(2^356243+3686)/2107240Stefano Morozzi09/2020
710020^82422-93107234Lelio R Paula02/2017
71012^356157-20365107214Enzo Doria06/2013
71028*10^107209+99107210Robert Price03/2021
71032^356129-18949107206Enzo Doria05/2013
71042^356100-109587107197Enzo Doria04/2014
71052*10^107173-37107174Robert Price11/2021
7106(2^355978+3262)/2107160Stefano Morozzi02/2021
7107(31*2^355970+1)/5107159Lelio R Paula03/2014
71082^355968-64875107158Lelio R Paula01/2017
71092^355952+1870321107153Enzo Doria05/2016
711027069^9088+9088^27069107152Hans Havermann11/2020
71112^355915-117107142Lelio R Paula11/2011
7112(16*10^107140+77)/3107141Robert Price03/2019
711324628^22369+22369^24628107124Hans Havermann11/2020
7114(19*2^355838-1)/15107119Lelio R Paula03/2014
71153^224495-8107112Lelio R Paula12/2013
71163*10^107096+23107097Robert Price03/2022
711725077^18632+18632^25077107086Hans Havermann10/2020
71187^126691-44107067Lelio R Paula03/2017
71194^177830-8243107065Mike Oakes02/2011
7120(509*10^107057+13)/9107059Robert Price05/2022
71212^355604+214051107048Enzo Doria10/2023
7122(2^355562+1702)/2107035Stefano Morozzi09/2020
712310^107028+3593037107029Paul Bourdelais10/2021
712410^107028-43301107028Alfred Reich08/2024
71252^355524-21237107024Enzo Doria06/2013
7127(10223*2^355515+1)/4855107022Lelio R Paula07/2014
712624843^20320+20320^24843107022Hans Havermann10/2020
71282^355494-19901107015Enzo Doria06/2013
71292^355454-869688105107003Lelio R Paula01/2017
71304*10^106997+13106998Robert Price02/2021
7131(8*10^106985-629)/9106985Robert Price01/2022
71322^355366+54615106976Lelio R Paula01/2017
7133(31*2^355346-1)/1563106969Lelio R Paula03/2014
71342^355275-19861106949Enzo Doria06/2013
713527503^7738+7738^27503106949Hans Havermann11/2020
7136(85*10^106943+77)/9106944Robert Price07/2022
7137(9179*2^355234-1)/1915106937Lelio R Paula05/2015
71384*10^106914-93106915Robert Price07/2020
71394*10^106892-3106893Robert Price10/2015
7140(66^58741+1)/67106881Paul Bourdelais08/2017
71412^355001+335931106866Enzo Doria08/2024
71422^354946-3106850M. Frind & P. Underwood08/2002
7143(2^354945+3134)/2106849Stefano Morozzi09/2020
7144(46^64384+1)/(46^128+1)106843Martin Hopf12/2023
71452^354873-18693106828Enzo Doria05/2013
7146(2^354831+3186)/2106815Stefano Morozzi09/2020
71482^354828+4257106814Lelio R Paula01/2017
714725216^17217+17217^25216106814Hans Havermann10/2020
7149(2^354799+1218)/2106805Stefano Morozzi09/2020
7150436^40459+40459^436106791Norbert Schneider03/2019
7151(21^80761+1)/22106783Paul Bourdelais03/2010
7152(115*10^106772-7)/9106774Robert Price02/2020
71532^354640-354640+1106758Robert Price10/2014
7154(2^354603+2606)/2106746Stefano Morozzi09/2020
71552^354585+95106741Lelio R Paula10/2011
7156(206*10^106737+1)/9106739Robert Price04/2022
71572^354553+189106732Lelio R Paula10/2011
7159(2^354546+1338)/2106729Stefano Morozzi02/2021
7158(8*10^106729-71)/9106729Serge Batalov11/2022
71602^354514-109031106720Enzo Doria04/2014
71612^354509-109465106718Enzo Doria04/2014
7162fibonacci(510628)+2106715Jon Grantham08/2023
7163(15*2^354478-1)/26983106706Lelio R Paula03/2014
7164Phi(217618,10)/899798636917106693Makoto Kamada06/2019
716515^90710+28106684Lelio R Paula04/2017
71667^126237+34106683Lelio R Paula03/2017
71672^354385-115315106681Enzo Doria06/2015
71682^354327-19305106664Enzo Doria06/2013
7169(35*10^106649+1)/9106650Serge Batalov11/2010
717010^106636+97106637Lelio R Paula02/2017
717110^106636-22923106636Patrick De Geest03/2017
71722^354220-57106631Lelio R Paula10/2011
7173(68*10^106628-329)/9106629Robert Price03/2021
7174(29*10^106620-77)/3106621Robert Price02/2020
7175(746*10^106618+1)/9106620Robert Price03/2020
71762*10^106613+29106614Robert Price02/2021
71772^354157-17041106612Enzo Doria05/2013
717812^98778+73106600Lelio R Paula02/2017
717933333^1576+1576^33333106585Hans Havermann11/2020
71802^354064+1870651106584Enzo Doria05/2016
718124568^21779+21779^24568106577Hans Havermann11/2020
71822^353992-57106563Lelio R Paula10/2011
71839*10^106559+59106560Robert Price01/2020
71847*10^106553+27106554Robert Price11/2020
718528847^4938+4938^28847106548Hans Havermann10/2020
7186NSW(139160)106535Robert Price12/2018
7187f(278321)106535Robert Price07/2023
7188(7*10^106516+113)/3106517Robert Price02/2018
71892^353832-1853849106515Enzo Doria09/2015
7190(7^126037-1)/6106513Paul Bourdelais09/2008
71912^353794-18453106503Enzo Doria05/2013
7192(2^353761+2094)/2106493Stefano Morozzi09/2020
71932^353728+7695106483Lelio R Paula01/2017
719426476^10509+10509^26476106475Hans Havermann10/2020
71952^353672-303106466Yves Minet02/2012
71966^136811+101106460Lelio R Paula02/2017
71972^353641+1871981106457Enzo Doria05/2016
7198(8*10^106454-29)/3106455Robert Price07/2018
719927845^6654+6654^27845106454Hans Havermann11/2020
720010^106449-700001106449Robert Price08/2021
720125316^16017+16017^25316106444Hans Havermann11/2020
72022^353553+54615106431Lelio R Paula01/2017
72032^353544-18897106428Enzo Doria05/2013
720428894^4823+4823^28894106426Hans Havermann11/2020
7205(19*10^106422+29)/3106423Robert Price12/2021
7206(694*10^106418+53)/9106420Robert Price02/2022
72076*10^106412-13106413Robert Price07/2022
720825696^13829+13829^25696106402Hans Havermann11/2020
72096^136729-133106396Lelio R Paula02/2017
72102^353418+1605106390Lelio R Paula01/2017
72112^353387+65106381Lelio R Paula10/2011
72122^353372+74311106376Enzo Doria04/2016
72132^353344-3693106368Yves Minet03/2017
7214(772*10^106365-7)/9106367Robert Price06/2022
7215(56*10^106351+619)/9106352Robert Price05/2021
72162^353277-20089106347Enzo Doria06/2013
72172^353275+72173106347Enzo Doria04/2016
72182^353268-17705106345Enzo Doria05/2013
72192^353267-19857106344Enzo Doria06/2013
7220(46*10^106343+143)/9106344Robert Price01/2019
7221(2^353189+3054)/2106321Stefano Morozzi09/2020
722235087^1072+1072^35087106321Hans Havermann10/2020
7223(2^353184+1290)/2106319Stefano Morozzi01/2021
7224F(508799)/24738824977/1990778864897106310Serge Batalov07/2024
722526985^8684+8684^26985106287Hans Havermann10/2020
7226(2^353051+606)/2106279Stefano Morozzi09/2020
7228222748^3+3^222748106278Anatoly F. Selevich12/2010
7227(46*10^106277+107)/9106278Robert Price06/2022
7229(9179*2^353019-1)/9106273Lelio R Paula05/2015
72302^353025+72257106272Enzo Doria04/2016
72332^352932-20345106244Enzo Doria06/2013
7231(2^353011-3)/745325861246794515484535106244Lelio R Paula12/2013
723225628^13983+13983^25628106244Hans Havermann10/2020
72342^352883-187106229Lelio R Paula10/2011
723520^81649-19^81649106228Jean-Louis Charton03/2011
7236(55*10^106222+377)/9106223Robert Price02/2019
72372^352814-131106208Lelio R Paula10/2011
72382^352752+73951106189Enzo Doria04/2016
723911876*25^75945+357106171Eric Chen10/2023
72406^136434+5106167Lelio R Paula11/2014
724125296^15737+15737^25296106166Hans Havermann09/2020
72428*10^106157-13106158Robert Price08/2019
72432^352641+225677106156Enzo Doria08/2024
72447*5^151872-8106155Lelio R Paula11/2014
7245105^52520-2106153Lelio R Paula10/2017
7246(23*10^106152-29)/3106153Robert Price03/2022
72472^352601-1604809106144Enzo Doria05/2015
724812^98353-43106141Lelio R Paula02/2017
72492^352585-18901106139Enzo Doria05/2013
725026363^10614+10614^26363106135Hans Havermann09/2020


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Created by  Henri Lifchitz & Renaud Lifchitz : October, 26 2000, last modification: April, 03 2025 20:11 (Time in France)

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