PRP Records

Probable Primes Top 10000

(294687 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 ?
62512^359454-177108207Lelio R Paula12/2011
6252(19*10^108184+191)/3108185Robert Price05/2019
62536^139022-59108181Lelio R Paula02/2017
6254(19*10^108176-43)/3108177Robert Price05/2019
62552^359352-179108176Lelio R Paula12/2011
62562^359338-1858781108172Enzo Doria04/2016
625712^100230-97108167Lelio R Paula03/2017
625827028^10043+10043^27028108163Hans Havermann11/2020
6259(25*2^359297-1)/137108159Lelio R Paula03/2014
6260(2^359262-509203)/9108148Lelio R Paula12/2013
626126583^11702+11702^26583108147Hans Havermann11/2020
6262(3^226648-8)/352715633108131Lelio R Paula12/2013
62636^138956-59108129Lelio R Paula02/2017
62642^359184+30285108126Lelio R Paula04/2017
626513^97059+10108119Lelio R Paula03/2017
62662^359137-81108112Lelio R Paula12/2011
6268(15185*2^359105-1)/567108103Lelio R Paula05/2015
62672^359110-11655108103Lelio R Paula04/2017
62692^359069-933075108091Paul Bourdelais06/2021
627026227^13222+13222^26227108090Hans Havermann10/2020
62718*6^138875+5108067Lelio R Paula11/2014
62722^358987-216919108066Enzo Doria05/2014
6273(2^358977+2714)/2108063Stefano Morozzi09/2020
627439^67918-67918^39108062Norbert Schneider02/2017
627524^78283-1*78283^24108048Dylan Delgado12/2019
627625282^18767+18767^25282108040Hans Havermann11/2020
62772^358785-16933108006Enzo Doria05/2013
6278(2^358783+5)/33383108000Lelio R Paula12/2013
62796^138770-77107985Lelio R Paula02/2017
6280(2^358727-1017)/94178479107980Lelio R Paula12/2013
628110^107976+19107977Lelio R Paula02/2017
628210^107976-202103107976Patrick De Geest03/2017
62832^358684+75781107975Enzo Doria04/2016
628424928^21411+21411^24928107955Hans Havermann10/2020
628599^54094+2107952Lelio R Paula06/2013
6286(2^358583-9)/391107942Lelio R Paula12/2013
6287(2^358562+838)/2107938Stefano Morozzi02/2021
62882^358538+55107931Lelio R Paula12/2011
62892^358517-109009107925Enzo Doria03/2014
629026395^12258+12258^26395107914Hans Havermann10/2020
62913^226159+104107906Lelio R Paula03/2017
62927*10^107870+39107871Robert Price01/2023
62932^358310-11655107863Lelio R Paula03/2017
6294(68*10^107852-329)/9107853Robert Price03/2021
62952^358275-112987107852Enzo Doria07/2014
62963^226038+4107848Tyler NeSmith01/2021
62972^358233-20005107839Enzo Doria06/2013
62982^358194+175107828Lelio R Paula12/2011
6299107^53125-106107812Norbert Schneider12/2016
6300(25*10^107804+161)/3107805Robert Price09/2019
63013^225922-2107793Lelio R Paula10/2013
630212^99874-95107783Lelio R Paula03/2017
6303(2^358042+3042)/2107782Stefano Morozzi09/2020
63042^358030-171107778Lelio R Paula12/2011
630511^103488-4170107772Enzo Doria12/2012
63062^357930-4547107748Yves Minet03/2019
63072^357911-20089107742Enzo Doria06/2013
63082^357885+12857107735Yves Minet07/2010
6309(248587#+9289)/(7*1327*111512899)107733Makoto Morimoto06/2019
63107^127473+40107728Lelio R Paula03/2017
63115*2^357850+9107725Lelio R Paula09/2014
63122^357786-291191107705Enzo Doria06/2015
631328907^5320+5320^28907107705Hans Havermann10/2020
631418^85798-23107700Lelio R Paula04/2017
63153*10^107697+61107698Robert Price09/2020
6316(14*10^107694-83)/3107695Robert Price12/2018
63172^357688-1854269107675Enzo Doria09/2015
63182^357671-112225107670Enzo Doria06/2014
631934323^1370+1370^34323107662Hans Havermann11/2020
63202^357618-21005107654Enzo Doria06/2013
63212^357615-17505107653Enzo Doria05/2013
632226350^12171+12171^26350107649Hans Havermann11/2020
6323(30^72871-1)/29107638Robert Price12/2011
632425021^20026+20026^25021107631Hans Havermann11/2020
63252^357521+1870217107625Enzo Doria05/2016
63262^357477-1203107612Lelio R Paula03/2017
632726008^13693+13693^26008107583Hans Havermann10/2020
632825432^16991+16991^25432107583Hans Havermann10/2020
6329(2^357371+3726)/2107580Stefano Morozzi09/2020
63305^153894-18107568Lelio R Paula02/2017
63312^357324-69059107566Enzo Doria11/2015
6332467^40296+40296^467107563Norbert Schneider03/2019
633329446^4495+4495^29446107559Hans Havermann10/2020
6334(8*10^107556-149)/3107557Robert Price12/2021
63352^357283-869688105107553Lelio R Paula01/2017
63362^357280-16805107552Enzo Doria05/2013
633710^107547+481719107548Patrick De Geest03/2017
633810^107547-47107547Lelio R Paula02/2017
6339(23*10^107540+37)/3107541Robert Price02/2022
634017^87396-32107537Lelio R Paula04/2017
6341(746*10^107505+1)/9107507Robert Price03/2020
6342(2^357125+1730)/2107506Stefano Morozzi09/2020
63432^357081+107107493Lelio R Paula12/2011
63442^357058-3911107486Yves Minet04/2017
63453^225274+64107484Lelio R Paula03/2017
63465*10^107482-57107483Robert Price03/2021
634718^85619-95107476Lelio R Paula04/2017
6348(2^357013+2526)/2107472Stefano Morozzi09/2020
63493^225248-130107471Lelio R Paula03/2017
6350(5*2^356961+1)/143107455Lelio R Paula03/2014
635127029^9448+9448^27029107450Hans Havermann11/2020
63522^356935-18085107449Enzo Doria05/2013
635355396^87+87^55396107442Hans Havermann10/2020
6354(14*10^107439-137)/3107440Robert Price04/2021
635510^107409+37107410Lelio R Paula02/2017
635610^107409-329633107409Patrick De Geest03/2017
6357(2^356799+3134)/2107407Stefano Morozzi09/2020
63582^356787-109027107404Enzo Doria04/2014
6359(2^356767+78557)/5107397Lelio R Paula12/2013
63603*10^107389+77107390Robert Price09/2018
6361(11*10^107385+61)/9107386Tyler Busby01/2023
63625^153622-42107378Lelio R Paula02/2017
63632^356699-97305107378Lelio R Paula03/2017
636413129^26072-26072^13129107371Norbert Schneider09/2022
63652^356654+85107364Lelio R Paula11/2011
63662^356641-19921107360Enzo Doria06/2013
63675*10^107355+11107356Robert Price08/2019
63682^356623-465107355Lelio R Paula03/2017
636919^83945-92107345Lelio R Paula02/2017
637025491^16246+16246^25491107337Hans Havermann11/2020
637110^107334+28149107335Patrick De Geest03/2017
637210^107334-83107334Lelio R Paula02/2017
63732^356518+885107323Lelio R Paula03/2017
6374(59*10^107322+391)/9107323Robert Price03/2021
6375(3*2^356506-1)/467107317Lelio R Paula03/2014
6376(2^356468+1162)/2107308Stefano Morozzi09/2020
63772^356442-114713107300Enzo Doria04/2015
63782^356425+72257107295Enzo Doria04/2016
63792^356351-112237107273Enzo Doria06/2014
6381(6^137845-11)/5107264Paul Bourdelais11/2011
63802^356322+74539107264Enzo Doria04/2016
63822^356274+1874479107250Enzo Doria06/2016
638324606^22819+22819^24606107241Hans Havermann10/2020
6384(2^356243+3686)/2107240Stefano Morozzi09/2020
638520^82422-93107234Lelio R Paula02/2017
63862^356157-20365107214Enzo Doria06/2013
63878*10^107209+99107210Robert Price03/2021
63882^356129-18949107206Enzo Doria05/2013
63892^356100-109587107197Enzo Doria04/2014
63902*10^107173-37107174Robert Price11/2021
6391(2^355978+3262)/2107160Stefano Morozzi02/2021
6392(31*2^355970+1)/5107159Lelio R Paula03/2014
63932^355968-64875107158Lelio R Paula01/2017
63942^355952+1870321107153Enzo Doria05/2016
639527069^9088+9088^27069107152Hans Havermann11/2020
63962^355915-117107142Lelio R Paula11/2011
6397(16*10^107140+77)/3107141Robert Price03/2019
639824628^22369+22369^24628107124Hans Havermann11/2020
6399(19*2^355838-1)/15107119Lelio R Paula03/2014
64003^224495-8107112Lelio R Paula12/2013
64013*10^107096+23107097Robert Price03/2022
640225077^18632+18632^25077107086Hans Havermann10/2020
64037^126691-44107067Lelio R Paula03/2017
64044^177830-8243107065Mike Oakes02/2011
6405(509*10^107057+13)/9107059Robert Price05/2022
64062^355604+214051107048Enzo Doria10/2023
6407(2^355562+1702)/2107035Stefano Morozzi09/2020
640810^107028+3593037107029Paul Bourdelais10/2021
64092^355524-21237107024Enzo Doria06/2013
6410(10223*2^355515+1)/4855107022Lelio R Paula07/2014
641124843^20320+20320^24843107022Hans Havermann10/2020
64122^355494-19901107015Enzo Doria06/2013
64132^355454-869688105107003Lelio R Paula01/2017
64144*10^106997+13106998Robert Price02/2021
6415(8*10^106985-629)/9106985Robert Price01/2022
64162^355366+54615106976Lelio R Paula01/2017
6417(31*2^355346-1)/1563106969Lelio R Paula03/2014
64192^355275-19861106949Enzo Doria06/2013
641827503^7738+7738^27503106949Hans Havermann11/2020
6420(85*10^106943+77)/9106944Robert Price07/2022
6421(9179*2^355234-1)/1915106937Lelio R Paula05/2015
64224*10^106914-93106915Robert Price07/2020
64234*10^106892-3106893Robert Price10/2015
6424(66^58741+1)/67106881Paul Bourdelais08/2017
64252^354946-3106850M. Frind & P. Underwood08/2002
6426(2^354945+3134)/2106849Stefano Morozzi09/2020
6427(46^64384+1)/(46^128+1)106843Martin Hopf12/2023
64282^354873-18693106828Enzo Doria05/2013
6429(2^354831+3186)/2106815Stefano Morozzi09/2020
64312^354828+4257106814Lelio R Paula01/2017
643025216^17217+17217^25216106814Hans Havermann10/2020
6432(2^354799+1218)/2106805Stefano Morozzi09/2020
6433436^40459+40459^436106791Norbert Schneider03/2019
6434(21^80761+1)/22106783Paul Bourdelais03/2010
6435(115*10^106772-7)/9106774Robert Price02/2020
64362^354640-354640+1106758Robert Price10/2014
6437(2^354603+2606)/2106746Stefano Morozzi09/2020
64382^354585+95106741Lelio R Paula10/2011
6439(206*10^106737+1)/9106739Robert Price04/2022
64402^354553+189106732Lelio R Paula10/2011
6442(2^354546+1338)/2106729Stefano Morozzi02/2021
6441(8*10^106729-71)/9106729Serge Batalov11/2022
64432^354514-109031106720Enzo Doria04/2014
64442^354509-109465106718Enzo Doria04/2014
6445fibonacci(510628)+2106715Jon Grantham08/2023
6446(15*2^354478-1)/26983106706Lelio R Paula03/2014
6447Phi(217618,10)/899798636917106693Makoto Kamada06/2019
644815^90710+28106684Lelio R Paula04/2017
64497^126237+34106683Lelio R Paula03/2017
64502^354385-115315106681Enzo Doria06/2015
64512^354327-19305106664Enzo Doria06/2013
6452(35*10^106649+1)/9106650Serge Batalov11/2010
645310^106636+97106637Lelio R Paula02/2017
645410^106636-22923106636Patrick De Geest03/2017
64552^354220-57106631Lelio R Paula10/2011
6456(68*10^106628-329)/9106629Robert Price03/2021
6457(29*10^106620-77)/3106621Robert Price02/2020
6458(746*10^106618+1)/9106620Robert Price03/2020
64592*10^106613+29106614Robert Price02/2021
64602^354157-17041106612Enzo Doria05/2013
646112^98778+73106600Lelio R Paula02/2017
646233333^1576+1576^33333106585Hans Havermann11/2020
64632^354064+1870651106584Enzo Doria05/2016
646424568^21779+21779^24568106577Hans Havermann11/2020
64652^353992-57106563Lelio R Paula10/2011
64669*10^106559+59106560Robert Price01/2020
64677*10^106553+27106554Robert Price11/2020
646828847^4938+4938^28847106548Hans Havermann10/2020
6469NSW(139160)106535Robert Price12/2018
6470f(278321)106535Robert Price07/2023
6471(7*10^106516+113)/3106517Robert Price02/2018
64722^353832-1853849106515Enzo Doria09/2015
6473(7^126037-1)/6106513Paul Bourdelais09/2008
64742^353794-18453106503Enzo Doria05/2013
6475(2^353761+2094)/2106493Stefano Morozzi09/2020
64762^353728+7695106483Lelio R Paula01/2017
647726476^10509+10509^26476106475Hans Havermann10/2020
64782^353672-303106466Yves Minet02/2012
64796^136811+101106460Lelio R Paula02/2017
64802^353641+1871981106457Enzo Doria05/2016
6481(8*10^106454-29)/3106455Robert Price07/2018
648227845^6654+6654^27845106454Hans Havermann11/2020
648310^106449-700001106449Robert Price08/2021
648425316^16017+16017^25316106444Hans Havermann11/2020
64852^353553+54615106431Lelio R Paula01/2017
64862^353544-18897106428Enzo Doria05/2013
648728894^4823+4823^28894106426Hans Havermann11/2020
6488(19*10^106422+29)/3106423Robert Price12/2021
6489(694*10^106418+53)/9106420Robert Price02/2022
64906*10^106412-13106413Robert Price07/2022
649125696^13829+13829^25696106402Hans Havermann11/2020
64926^136729-133106396Lelio R Paula02/2017
64932^353418+1605106390Lelio R Paula01/2017
64942^353387+65106381Lelio R Paula10/2011
64952^353372+74311106376Enzo Doria04/2016
64962^353344-3693106368Yves Minet03/2017
6497(772*10^106365-7)/9106367Robert Price06/2022
6498(56*10^106351+619)/9106352Robert Price05/2021
65002^353277-20089106347Enzo Doria06/2013
64992^353275+72173106347Enzo Doria04/2016


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Created by  Henri Lifchitz & Renaud Lifchitz : October, 26 2000, last modification: March, 27 2024 11:51 (Time in France)

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