PRP Records

Probable Primes Top 10000

(295503 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) !!!


Submit your PRPs


See the Top discoverers
See the Latest PRPs
Search by form



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 ?
65016^138956-59108129Lelio R Paula02/2017
65022^359184+30285108126Lelio R Paula04/2017
650313^97059+10108119Lelio R Paula03/2017
65042^359137-81108112Lelio R Paula12/2011
6506(15185*2^359105-1)/567108103Lelio R Paula05/2015
65052^359110-11655108103Lelio R Paula04/2017
65072^359069-933075108091Paul Bourdelais06/2021
650826227^13222+13222^26227108090Hans Havermann10/2020
65098*6^138875+5108067Lelio R Paula11/2014
65102^358987-216919108066Enzo Doria05/2014
6511(2^358977+2714)/2108063Stefano Morozzi09/2020
651239^67918-67918^39108062Norbert Schneider02/2017
651324^78283-1*78283^24108048Dylan Delgado12/2019
651425282^18767+18767^25282108040Hans Havermann11/2020
65152^358785-16933108006Enzo Doria05/2013
6516(2^358783+5)/33383108000Lelio R Paula12/2013
65176^138770-77107985Lelio R Paula02/2017
6518(2^358727-1017)/94178479107980Lelio R Paula12/2013
651910^107976+19107977Lelio R Paula02/2017
652010^107976-202103107976Patrick De Geest03/2017
65212^358684+75781107975Enzo Doria04/2016
652224928^21411+21411^24928107955Hans Havermann10/2020
652399^54094+2107952Lelio R Paula06/2013
6524(2^358583-9)/391107942Lelio R Paula12/2013
6525(2^358562+838)/2107938Stefano Morozzi02/2021
65262^358538+55107931Lelio R Paula12/2011
65272^358517-109009107925Enzo Doria03/2014
652826395^12258+12258^26395107914Hans Havermann10/2020
65293^226159+104107906Lelio R Paula03/2017
65307*10^107870+39107871Robert Price01/2023
65312^358310-11655107863Lelio R Paula03/2017
6532(68*10^107852-329)/9107853Robert Price03/2021
65332^358275-112987107852Enzo Doria07/2014
65343^226038+4107848Tyler NeSmith01/2021
65352^358233-20005107839Enzo Doria06/2013
65362^358194+175107828Lelio R Paula12/2011
6537107^53125-106107812Norbert Schneider12/2016
6538(25*10^107804+161)/3107805Robert Price09/2019
65393^225922-2107793Lelio R Paula10/2013
654012^99874-95107783Lelio R Paula03/2017
6541(2^358042+3042)/2107782Stefano Morozzi09/2020
65422^358030-171107778Lelio R Paula12/2011
654311^103488-4170107772Enzo Doria12/2012
65442^357930-4547107748Yves Minet03/2019
65452^357911-20089107742Enzo Doria06/2013
65462^357885+12857107735Yves Minet07/2010
6547(248587#+9289)/(7*1327*111512899)107733Makoto Morimoto06/2019
65487^127473+40107728Lelio R Paula03/2017
65495*2^357850+9107725Lelio R Paula09/2014
65502^357786-291191107705Enzo Doria06/2015
655128907^5320+5320^28907107705Hans Havermann10/2020
655218^85798-23107700Lelio R Paula04/2017
65533*10^107697+61107698Robert Price09/2020
6554(14*10^107694-83)/3107695Robert Price12/2018
65552^357688-1854269107675Enzo Doria09/2015
65562^357671-112225107670Enzo Doria06/2014
655734323^1370+1370^34323107662Hans Havermann11/2020
65582^357618-21005107654Enzo Doria06/2013
65592^357615-17505107653Enzo Doria05/2013
656026350^12171+12171^26350107649Hans Havermann11/2020
6561(30^72871-1)/29107638Robert Price12/2011
656225021^20026+20026^25021107631Hans Havermann11/2020
65632^357521+1870217107625Enzo Doria05/2016
65642^357477-1203107612Lelio R Paula03/2017
656526008^13693+13693^26008107583Hans Havermann10/2020
656625432^16991+16991^25432107583Hans Havermann10/2020
6567(2^357371+3726)/2107580Stefano Morozzi09/2020
65685^153894-18107568Lelio R Paula02/2017
65692^357324-69059107566Enzo Doria11/2015
6570467^40296+40296^467107563Norbert Schneider03/2019
657129446^4495+4495^29446107559Hans Havermann10/2020
6572(8*10^107556-149)/3107557Robert Price12/2021
65732^357283-869688105107553Lelio R Paula01/2017
65742^357280-16805107552Enzo Doria05/2013
657510^107547+481719107548Patrick De Geest03/2017
657610^107547-47107547Lelio R Paula02/2017
6577(23*10^107540+37)/3107541Robert Price02/2022
657817^87396-32107537Lelio R Paula04/2017
6579(746*10^107505+1)/9107507Robert Price03/2020
6580(2^357125+1730)/2107506Stefano Morozzi09/2020
65812^357081+107107493Lelio R Paula12/2011
65822^357058-3911107486Yves Minet04/2017
65833^225274+64107484Lelio R Paula03/2017
65845*10^107482-57107483Robert Price03/2021
658518^85619-95107476Lelio R Paula04/2017
6586(2^357013+2526)/2107472Stefano Morozzi09/2020
65873^225248-130107471Lelio R Paula03/2017
6588(5*2^356961+1)/143107455Lelio R Paula03/2014
658927029^9448+9448^27029107450Hans Havermann11/2020
65902^356935-18085107449Enzo Doria05/2013
659155396^87+87^55396107442Hans Havermann10/2020
6592(14*10^107439-137)/3107440Robert Price04/2021
659310^107409+37107410Lelio R Paula02/2017
659410^107409-329633107409Patrick De Geest03/2017
6595(2^356799+3134)/2107407Stefano Morozzi09/2020
65962^356787-109027107404Enzo Doria04/2014
6597(2^356767+78557)/5107397Lelio R Paula12/2013
65983*10^107389+77107390Robert Price09/2018
6599(11*10^107385+61)/9107386Tyler Busby01/2023
66005^153622-42107378Lelio R Paula02/2017
66012^356699-97305107378Lelio R Paula03/2017
660213129^26072-26072^13129107371Norbert Schneider09/2022
66032^356654+85107364Lelio R Paula11/2011
66042^356641-19921107360Enzo Doria06/2013
66055*10^107355+11107356Robert Price08/2019
66062^356623-465107355Lelio R Paula03/2017
660719^83945-92107345Lelio R Paula02/2017
660825491^16246+16246^25491107337Hans Havermann11/2020
660910^107334+28149107335Patrick De Geest03/2017
661010^107334-83107334Lelio R Paula02/2017
66112^356518+885107323Lelio R Paula03/2017
6612(59*10^107322+391)/9107323Robert Price03/2021
6613(3*2^356506-1)/467107317Lelio R Paula03/2014
6614(2^356468+1162)/2107308Stefano Morozzi09/2020
66152^356442-114713107300Enzo Doria04/2015
66162^356425+72257107295Enzo Doria04/2016
66172^356351-112237107273Enzo Doria06/2014
6619(6^137845-11)/5107264Paul Bourdelais11/2011
66182^356322+74539107264Enzo Doria04/2016
66202^356274+1874479107250Enzo Doria06/2016
662124606^22819+22819^24606107241Hans Havermann10/2020
6622(2^356243+3686)/2107240Stefano Morozzi09/2020
662320^82422-93107234Lelio R Paula02/2017
66242^356157-20365107214Enzo Doria06/2013
66258*10^107209+99107210Robert Price03/2021
66262^356129-18949107206Enzo Doria05/2013
66272^356100-109587107197Enzo Doria04/2014
66282*10^107173-37107174Robert Price11/2021
6629(2^355978+3262)/2107160Stefano Morozzi02/2021
6630(31*2^355970+1)/5107159Lelio R Paula03/2014
66312^355968-64875107158Lelio R Paula01/2017
66322^355952+1870321107153Enzo Doria05/2016
663327069^9088+9088^27069107152Hans Havermann11/2020
66342^355915-117107142Lelio R Paula11/2011
6635(16*10^107140+77)/3107141Robert Price03/2019
663624628^22369+22369^24628107124Hans Havermann11/2020
6637(19*2^355838-1)/15107119Lelio R Paula03/2014
66383^224495-8107112Lelio R Paula12/2013
66393*10^107096+23107097Robert Price03/2022
664025077^18632+18632^25077107086Hans Havermann10/2020
66417^126691-44107067Lelio R Paula03/2017
66424^177830-8243107065Mike Oakes02/2011
6643(509*10^107057+13)/9107059Robert Price05/2022
66442^355604+214051107048Enzo Doria10/2023
6645(2^355562+1702)/2107035Stefano Morozzi09/2020
664610^107028+3593037107029Paul Bourdelais10/2021
66472^355524-21237107024Enzo Doria06/2013
6648(10223*2^355515+1)/4855107022Lelio R Paula07/2014
664924843^20320+20320^24843107022Hans Havermann10/2020
66502^355494-19901107015Enzo Doria06/2013
66512^355454-869688105107003Lelio R Paula01/2017
66524*10^106997+13106998Robert Price02/2021
6653(8*10^106985-629)/9106985Robert Price01/2022
66542^355366+54615106976Lelio R Paula01/2017
6655(31*2^355346-1)/1563106969Lelio R Paula03/2014
66572^355275-19861106949Enzo Doria06/2013
665627503^7738+7738^27503106949Hans Havermann11/2020
6658(85*10^106943+77)/9106944Robert Price07/2022
6659(9179*2^355234-1)/1915106937Lelio R Paula05/2015
66604*10^106914-93106915Robert Price07/2020
66614*10^106892-3106893Robert Price10/2015
6662(66^58741+1)/67106881Paul Bourdelais08/2017
66632^354946-3106850M. Frind & P. Underwood08/2002
6664(2^354945+3134)/2106849Stefano Morozzi09/2020
6665(46^64384+1)/(46^128+1)106843Martin Hopf12/2023
66662^354873-18693106828Enzo Doria05/2013
6667(2^354831+3186)/2106815Stefano Morozzi09/2020
66692^354828+4257106814Lelio R Paula01/2017
666825216^17217+17217^25216106814Hans Havermann10/2020
6670(2^354799+1218)/2106805Stefano Morozzi09/2020
6671436^40459+40459^436106791Norbert Schneider03/2019
6672(21^80761+1)/22106783Paul Bourdelais03/2010
6673(115*10^106772-7)/9106774Robert Price02/2020
66742^354640-354640+1106758Robert Price10/2014
6675(2^354603+2606)/2106746Stefano Morozzi09/2020
66762^354585+95106741Lelio R Paula10/2011
6677(206*10^106737+1)/9106739Robert Price04/2022
66782^354553+189106732Lelio R Paula10/2011
6680(2^354546+1338)/2106729Stefano Morozzi02/2021
6679(8*10^106729-71)/9106729Serge Batalov11/2022
66812^354514-109031106720Enzo Doria04/2014
66822^354509-109465106718Enzo Doria04/2014
6683fibonacci(510628)+2106715Jon Grantham08/2023
6684(15*2^354478-1)/26983106706Lelio R Paula03/2014
6685Phi(217618,10)/899798636917106693Makoto Kamada06/2019
668615^90710+28106684Lelio R Paula04/2017
66877^126237+34106683Lelio R Paula03/2017
66882^354385-115315106681Enzo Doria06/2015
66892^354327-19305106664Enzo Doria06/2013
6690(35*10^106649+1)/9106650Serge Batalov11/2010
669110^106636+97106637Lelio R Paula02/2017
669210^106636-22923106636Patrick De Geest03/2017
66932^354220-57106631Lelio R Paula10/2011
6694(68*10^106628-329)/9106629Robert Price03/2021
6695(29*10^106620-77)/3106621Robert Price02/2020
6696(746*10^106618+1)/9106620Robert Price03/2020
66972*10^106613+29106614Robert Price02/2021
66982^354157-17041106612Enzo Doria05/2013
669912^98778+73106600Lelio R Paula02/2017
670033333^1576+1576^33333106585Hans Havermann11/2020
67012^354064+1870651106584Enzo Doria05/2016
670224568^21779+21779^24568106577Hans Havermann11/2020
67032^353992-57106563Lelio R Paula10/2011
67049*10^106559+59106560Robert Price01/2020
67057*10^106553+27106554Robert Price11/2020
670628847^4938+4938^28847106548Hans Havermann10/2020
6707NSW(139160)106535Robert Price12/2018
6708f(278321)106535Robert Price07/2023
6709(7*10^106516+113)/3106517Robert Price02/2018
67102^353832-1853849106515Enzo Doria09/2015
6711(7^126037-1)/6106513Paul Bourdelais09/2008
67122^353794-18453106503Enzo Doria05/2013
6713(2^353761+2094)/2106493Stefano Morozzi09/2020
67142^353728+7695106483Lelio R Paula01/2017
671526476^10509+10509^26476106475Hans Havermann10/2020
67162^353672-303106466Yves Minet02/2012
67176^136811+101106460Lelio R Paula02/2017
67182^353641+1871981106457Enzo Doria05/2016
6719(8*10^106454-29)/3106455Robert Price07/2018
672027845^6654+6654^27845106454Hans Havermann11/2020
672110^106449-700001106449Robert Price08/2021
672225316^16017+16017^25316106444Hans Havermann11/2020
67232^353553+54615106431Lelio R Paula01/2017
67242^353544-18897106428Enzo Doria05/2013
672528894^4823+4823^28894106426Hans Havermann11/2020
6726(19*10^106422+29)/3106423Robert Price12/2021
6727(694*10^106418+53)/9106420Robert Price02/2022
67286*10^106412-13106413Robert Price07/2022
672925696^13829+13829^25696106402Hans Havermann11/2020
67306^136729-133106396Lelio R Paula02/2017
67312^353418+1605106390Lelio R Paula01/2017
67322^353387+65106381Lelio R Paula10/2011
67332^353372+74311106376Enzo Doria04/2016
67342^353344-3693106368Yves Minet03/2017
6735(772*10^106365-7)/9106367Robert Price06/2022
6736(56*10^106351+619)/9106352Robert Price05/2021
67382^353277-20089106347Enzo Doria06/2013
67372^353275+72173106347Enzo Doria04/2016
67392^353268-17705106345Enzo Doria05/2013
67402^353267-19857106344Enzo Doria06/2013
6741(46*10^106343+143)/9106344Robert Price01/2019
6742(2^353189+3054)/2106321Stefano Morozzi09/2020
674335087^1072+1072^35087106321Hans Havermann10/2020
6744(2^353184+1290)/2106319Stefano Morozzi01/2021
6745F(508799)/24738824977/1990778864897106310Serge Batalov07/2024
674626985^8684+8684^26985106287Hans Havermann10/2020
6747(2^353051+606)/2106279Stefano Morozzi09/2020
6749222748^3+3^222748106278Anatoly F. Selevich12/2010
6748(46*10^106277+107)/9106278Robert Price06/2022
6750(9179*2^353019-1)/9106273Lelio R Paula05/2015


Find by discoverer :


Created by  Henri Lifchitz & Renaud Lifchitz : October, 26 2000, last modification: July, 22 2024 13:34 (Time in France)

Go back
Valid XHTML 1.0!    Valid CSS!