PRP Records

Probable Primes Top 10000

(280932 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 ?
425191^55259-90^55259108255Robert Price07/2015
425210^108251+85749108252Patrick De Geest02/2021
425310^108251-50000000001108251Robert Price12/2020
425410^108251-252081108251Patrick De Geest02/2021
42554*10^108238-71108239Robert Price12/2018
42563^226845+68108233Lelio R Paula03/2017
425731836^2509+2509^31836108227Hans Havermann10/2020
42585^154822-12866108216Enzo Doria05/2014
4259(9*2^359480+1)/5108215Lelio R Paula03/2014
42602^359454-177108207Lelio R Paula12/2011
4261(19*10^108184+191)/3108185Robert Price05/2019
42626^139022-59108181Lelio R Paula02/2017
4263(19*10^108176-43)/3108177Robert Price05/2019
42642^359352-179108176Lelio R Paula12/2011
42652^359338-1858781108172Enzo Doria04/2016
426612^100230-97108167Lelio R Paula03/2017
426727028^10043+10043^27028108163Hans Havermann11/2020
4268(25*2^359297-1)/137108159Lelio R Paula03/2014
4269(2^359262-509203)/9108148Lelio R Paula12/2013
427026583^11702+11702^26583108147Hans Havermann11/2020
4271(3^226648-8)/352715633108131Lelio R Paula12/2013
42726^138956-59108129Lelio R Paula02/2017
42732^359184+30285108126Lelio R Paula04/2017
427413^97059+10108119Lelio R Paula03/2017
42752^359137-81108112Lelio R Paula12/2011
4277(15185*2^359105-1)/567108103Lelio R Paula05/2015
42762^359110-11655108103Lelio R Paula04/2017
427826227^13222+13222^26227108090Hans Havermann10/2020
42798*6^138875+5108067Lelio R Paula11/2014
42802^358987-216919108066Enzo Doria05/2014
4281(2^358977+2714)/2108063Stefano Morozzi09/2020
428239^67918-67918^39108062Norbert Schneider02/2017
428324^78283-1*78283^24108048Dylan Delgado12/2019
428425282^18767+18767^25282108040Hans Havermann11/2020
42852^358785-16933108006Enzo Doria05/2013
4286(2^358783+5)/33383108000Lelio R Paula12/2013
42876^138770-77107985Lelio R Paula02/2017
4288(2^358727-1017)/94178479107980Lelio R Paula12/2013
428910^107976+19107977Lelio R Paula02/2017
429010^107976-202103107976Patrick De Geest03/2017
42912^358684+75781107975Enzo Doria04/2016
429224928^21411+21411^24928107955Hans Havermann10/2020
429399^54094+2107952Lelio R Paula06/2013
4294(2^358583-9)/391107942Lelio R Paula12/2013
4295(2^358562+838)/2107938Stefano Morozzi02/2021
42962^358538+55107931Lelio R Paula12/2011
42972^358517-109009107925Enzo Doria03/2014
429826395^12258+12258^26395107914Hans Havermann10/2020
42993^226159+104107906Lelio R Paula03/2017
43002^358310-11655107863Lelio R Paula03/2017
4301(68*10^107852-329)/9107853Robert Price03/2021
43022^358275-112987107852Enzo Doria07/2014
43033^226038+4107848Tyler NeSmith01/2021
43042^358233-20005107839Enzo Doria06/2013
43052^358194+175107828Lelio R Paula12/2011
4306107^53125-106107812Norbert Schneider12/2016
4307(25*10^107804+161)/3107805Robert Price09/2019
43083^225922-2107793Lelio R Paula10/2013
430912^99874-95107783Lelio R Paula03/2017
4310(2^358042+3042)/2107782Stefano Morozzi09/2020
43112^358030-171107778Lelio R Paula12/2011
431211^103488-4170107772Enzo Doria12/2012
43132^357930-4547107748Yves Minet03/2019
43142^357911-20089107742Enzo Doria06/2013
43152^357885+12857107735Yves Minet07/2010
4316(248587#+9289)/(7*1327*111512899)107733Makoto Morimoto06/2019
43177^127473+40107728Lelio R Paula03/2017
43185*2^357850+9107725Lelio R Paula09/2014
43192^357786-291191107705Enzo Doria06/2015
432028907^5320+5320^28907107705Hans Havermann10/2020
432118^85798-23107700Lelio R Paula04/2017
43223*10^107697+61107698Robert Price09/2020
4323(14*10^107694-83)/3107695Robert Price12/2018
43242^357688-1854269107675Enzo Doria09/2015
43252^357671-112225107670Enzo Doria06/2014
432634323^1370+1370^34323107662Hans Havermann11/2020
43272^357618-21005107654Enzo Doria06/2013
43282^357615-17505107653Enzo Doria05/2013
432926350^12171+12171^26350107649Hans Havermann11/2020
4330(30^72871-1)/29107638Robert Price12/2011
433125021^20026+20026^25021107631Hans Havermann11/2020
43322^357521+1870217107625Enzo Doria05/2016
43332^357477-1203107612Lelio R Paula03/2017
433426008^13693+13693^26008107583Hans Havermann10/2020
433525432^16991+16991^25432107583Hans Havermann10/2020
4336(2^357371+3726)/2107580Stefano Morozzi09/2020
43375^153894-18107568Lelio R Paula02/2017
43382^357324-69059107566Enzo Doria11/2015
4339467^40296+40296^467107563Norbert Schneider03/2019
434029446^4495+4495^29446107559Hans Havermann10/2020
43412^357283-869688105107553Lelio R Paula01/2017
43422^357280-16805107552Enzo Doria05/2013
434310^107547+481719107548Patrick De Geest03/2017
434410^107547-47107547Lelio R Paula02/2017
434517^87396-32107537Lelio R Paula04/2017
4346(746*10^107505+1)/9107507Robert Price03/2020
4347(2^357125+1730)/2107506Stefano Morozzi09/2020
43482^357081+107107493Lelio R Paula12/2011
43492^357058-3911107486Yves Minet04/2017
43503^225274+64107484Lelio R Paula03/2017
43515*10^107482-57107483Robert Price03/2021
435218^85619-95107476Lelio R Paula04/2017
4353(2^357013+2526)/2107472Stefano Morozzi09/2020
43543^225248-130107471Lelio R Paula03/2017
4355(5*2^356961+1)/143107455Lelio R Paula03/2014
435627029^9448+9448^27029107450Hans Havermann11/2020
43572^356935-18085107449Enzo Doria05/2013
435855396^87+87^55396107442Hans Havermann10/2020
435910^107409+37107410Lelio R Paula02/2017
436010^107409-329633107409Patrick De Geest03/2017
4361(2^356799+3134)/2107407Stefano Morozzi09/2020
43622^356787-109027107404Enzo Doria04/2014
4363(2^356767+78557)/5107397Lelio R Paula12/2013
43643*10^107389+77107390Robert Price09/2018
43655^153622-42107378Lelio R Paula02/2017
43662^356699-97305107378Lelio R Paula03/2017
43672^356654+85107364Lelio R Paula11/2011
43682^356641-19921107360Enzo Doria06/2013
43695*10^107355+11107356Robert Price08/2019
43702^356623-465107355Lelio R Paula03/2017
437119^83945-92107345Lelio R Paula02/2017
437225491^16246+16246^25491107337Hans Havermann11/2020
437310^107334+28149107335Patrick De Geest03/2017
437410^107334-83107334Lelio R Paula02/2017
43752^356518+885107323Lelio R Paula03/2017
4376(59*10^107322+391)/9107323Robert Price03/2021
4377(3*2^356506-1)/467107317Lelio R Paula03/2014
4378(2^356468+1162)/2107308Stefano Morozzi09/2020
43792^356442-114713107300Enzo Doria04/2015
43802^356425+72257107295Enzo Doria04/2016
43812^356351-112237107273Enzo Doria06/2014
4383(6^137845-11)/5107264Paul Bourdelais11/2011
43822^356322+74539107264Enzo Doria04/2016
43842^356274+1874479107250Enzo Doria06/2016
438524606^22819+22819^24606107241Hans Havermann10/2020
4386(2^356243+3686)/2107240Stefano Morozzi09/2020
438720^82422-93107234Lelio R Paula02/2017
43882^356157-20365107214Enzo Doria06/2013
43898*10^107209+99107210Robert Price03/2021
43902^356129-18949107206Enzo Doria05/2013
43912^356100-109587107197Enzo Doria04/2014
4392(2^355978+3262)/2107160Stefano Morozzi02/2021
4393(31*2^355970+1)/5107159Lelio R Paula03/2014
43942^355968-64875107158Lelio R Paula01/2017
43952^355952+1870321107153Enzo Doria05/2016
439627069^9088+9088^27069107152Hans Havermann11/2020
43972^355915-117107142Lelio R Paula11/2011
4398(16*10^107140+77)/3107141Robert Price03/2019
439924628^22369+22369^24628107124Hans Havermann11/2020
4400(19*2^355838-1)/15107119Lelio R Paula03/2014
44013^224495-8107112Lelio R Paula12/2013
440225077^18632+18632^25077107086Hans Havermann10/2020
44037^126691-44107067Lelio R Paula03/2017
44044^177830-8243107065Mike Oakes02/2011
4405(2^355562+1702)/2107035Stefano Morozzi09/2020
44062^355524-21237107024Enzo Doria06/2013
4408(10223*2^355515+1)/4855107022Lelio R Paula07/2014
440724843^20320+20320^24843107022Hans Havermann10/2020
44092^355494-19901107015Enzo Doria06/2013
44102^355454-869688105107003Lelio R Paula01/2017
44114*10^106997+13106998Robert Price02/2021
44122^355366+54615106976Lelio R Paula01/2017
4413(31*2^355346-1)/1563106969Lelio R Paula03/2014
44152^355275-19861106949Enzo Doria06/2013
441427503^7738+7738^27503106949Hans Havermann11/2020
4416(9179*2^355234-1)/1915106937Lelio R Paula05/2015
44174*10^106914-93106915Robert Price07/2020
44184*10^106892-3106893Robert Price10/2015
4419(66^58741+1)/67106881Paul Bourdelais08/2017
44202^354946-3106850M. Frind & P. Underwood08/2002
4421(2^354945+3134)/2106849Stefano Morozzi09/2020
44222^354873-18693106828Enzo Doria05/2013
4423(2^354831+3186)/2106815Stefano Morozzi09/2020
44242^354828+4257106814Lelio R Paula01/2017
442525216^17217+17217^25216106814Hans Havermann10/2020
4426(2^354799+1218)/2106805Stefano Morozzi09/2020
4427436^40459+40459^436106791Norbert Schneider03/2019
4428(21^80761+1)/22106783Paul Bourdelais03/2010
4429(115*10^106772-7)/9106774Robert Price02/2020
44302^354640-354640+1106758Robert Price10/2014
4431(2^354603+2606)/2106746Stefano Morozzi09/2020
44322^354585+95106741Lelio R Paula10/2011
44332^354553+189106732Lelio R Paula10/2011
4434(2^354546+1338)/2106729Stefano Morozzi02/2021
44352^354514-109031106720Enzo Doria04/2014
44362^354509-109465106718Enzo Doria04/2014
4437(15*2^354478-1)/26983106706Lelio R Paula03/2014
4438Phi(217618,10)/899798636917106693Makoto Kamada06/2019
443915^90710+28106684Lelio R Paula04/2017
44407^126237+34106683Lelio R Paula03/2017
44412^354385-115315106681Enzo Doria06/2015
44422^354327-19305106664Enzo Doria06/2013
4443(35*10^106649+1)/9106650Serge Batalov11/2010
444410^106636+97106637Lelio R Paula02/2017
444510^106636-22923106636Patrick De Geest03/2017
44462^354220-57106631Lelio R Paula10/2011
4447(68*10^106628-329)/9106629Robert Price03/2021
4448(29*10^106620-77)/3106621Robert Price02/2020
4449(746*10^106618+1)/9106620Robert Price03/2020
44502*10^106613+29106614Robert Price02/2021
44512^354157-17041106612Enzo Doria05/2013
445212^98778+73106600Lelio R Paula02/2017
445333333^1576+1576^33333106585Hans Havermann11/2020
44542^354064+1870651106584Enzo Doria05/2016
445524568^21779+21779^24568106577Hans Havermann11/2020
44562^353992-57106563Lelio R Paula10/2011
44579*10^106559+59106560Robert Price01/2020
44587*10^106553+27106554Robert Price11/2020
445928847^4938+4938^28847106548Hans Havermann10/2020
4460NSW(139160)106535Robert Price12/2018
4461(7*10^106516+113)/3106517Robert Price02/2018
44622^353832-1853849106515Enzo Doria09/2015
4463(7^126037-1)/6106513Paul Bourdelais09/2008
44642^353794-18453106503Enzo Doria05/2013
4465(2^353761+2094)/2106493Stefano Morozzi09/2020
44662^353728+7695106483Lelio R Paula01/2017
446726476^10509+10509^26476106475Hans Havermann10/2020
44682^353672-303106466Yves Minet02/2012
44696^136811+101106460Lelio R Paula02/2017
44702^353641+1871981106457Enzo Doria05/2016
4471(8*10^106454-29)/3106455Robert Price07/2018
447227845^6654+6654^27845106454Hans Havermann11/2020
447325316^16017+16017^25316106444Hans Havermann11/2020
44742^353553+54615106431Lelio R Paula01/2017
44752^353544-18897106428Enzo Doria05/2013
447628894^4823+4823^28894106426Hans Havermann11/2020
447725696^13829+13829^25696106402Hans Havermann11/2020
44786^136729-133106396Lelio R Paula02/2017
44792^353418+1605106390Lelio R Paula01/2017
44802^353387+65106381Lelio R Paula10/2011
44812^353372+74311106376Enzo Doria04/2016
44822^353344-3693106368Yves Minet03/2017
44842^353277-20089106347Enzo Doria06/2013
44832^353275+72173106347Enzo Doria04/2016
44852^353268-17705106345Enzo Doria05/2013
44862^353267-19857106344Enzo Doria06/2013
4487(46*10^106343+143)/9106344Robert Price01/2019
4488(2^353189+3054)/2106321Stefano Morozzi09/2020
448935087^1072+1072^35087106321Hans Havermann10/2020
4490(2^353184+1290)/2106319Stefano Morozzi01/2021
449126985^8684+8684^26985106287Hans Havermann10/2020
4492(2^353051+606)/2106279Stefano Morozzi09/2020
4493222748^3+3^222748106278Anatoly F. Selevich12/2010
4494(9179*2^353019-1)/9106273Lelio R Paula05/2015
44952^353025+72257106272Enzo Doria04/2016
44982^352932-20345106244Enzo Doria06/2013
4496(2^353011-3)/745325861246794515484535106244Lelio R Paula12/2013
449725628^13983+13983^25628106244Hans Havermann10/2020
44992^352883-187106229Lelio R Paula10/2011
450020^81649-19^81649106228Jean-Louis Charton03/2011


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Created by  Henri Lifchitz & Renaud Lifchitz : October, 26 2000, last modification: April, 13 2021 12:02 (Time in France)

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