PRP Records

Probable Primes Top 10000

(288949 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 ?
500119^83945-92107345Lelio R Paula02/2017
500225491^16246+16246^25491107337Hans Havermann11/2020
500310^107334+28149107335Patrick De Geest03/2017
500410^107334-83107334Lelio R Paula02/2017
50052^356518+885107323Lelio R Paula03/2017
5006(59*10^107322+391)/9107323Robert Price03/2021
5007(3*2^356506-1)/467107317Lelio R Paula03/2014
5008(2^356468+1162)/2107308Stefano Morozzi09/2020
50092^356442-114713107300Enzo Doria04/2015
50102^356425+72257107295Enzo Doria04/2016
50112^356351-112237107273Enzo Doria06/2014
5013(6^137845-11)/5107264Paul Bourdelais11/2011
50122^356322+74539107264Enzo Doria04/2016
50142^356274+1874479107250Enzo Doria06/2016
501524606^22819+22819^24606107241Hans Havermann10/2020
5016(2^356243+3686)/2107240Stefano Morozzi09/2020
501720^82422-93107234Lelio R Paula02/2017
50182^356157-20365107214Enzo Doria06/2013
50198*10^107209+99107210Robert Price03/2021
50202^356129-18949107206Enzo Doria05/2013
50212^356100-109587107197Enzo Doria04/2014
50222*10^107173-37107174Robert Price11/2021
5023(2^355978+3262)/2107160Stefano Morozzi02/2021
5024(31*2^355970+1)/5107159Lelio R Paula03/2014
50252^355968-64875107158Lelio R Paula01/2017
50262^355952+1870321107153Enzo Doria05/2016
502727069^9088+9088^27069107152Hans Havermann11/2020
50282^355915-117107142Lelio R Paula11/2011
5029(16*10^107140+77)/3107141Robert Price03/2019
503024628^22369+22369^24628107124Hans Havermann11/2020
5031(19*2^355838-1)/15107119Lelio R Paula03/2014
50323^224495-8107112Lelio R Paula12/2013
503325077^18632+18632^25077107086Hans Havermann10/2020
50347^126691-44107067Lelio R Paula03/2017
50354^177830-8243107065Mike Oakes02/2011
5036(2^355562+1702)/2107035Stefano Morozzi09/2020
503710^107028+3593037107029Paul Bourdelais10/2021
50382^355524-21237107024Enzo Doria06/2013
5040(10223*2^355515+1)/4855107022Lelio R Paula07/2014
503924843^20320+20320^24843107022Hans Havermann10/2020
50412^355494-19901107015Enzo Doria06/2013
50422^355454-869688105107003Lelio R Paula01/2017
50434*10^106997+13106998Robert Price02/2021
50442^355366+54615106976Lelio R Paula01/2017
5045(31*2^355346-1)/1563106969Lelio R Paula03/2014
50462^355275-19861106949Enzo Doria06/2013
504727503^7738+7738^27503106949Hans Havermann11/2020
5048(9179*2^355234-1)/1915106937Lelio R Paula05/2015
50494*10^106914-93106915Robert Price07/2020
50504*10^106892-3106893Robert Price10/2015
5051(66^58741+1)/67106881Paul Bourdelais08/2017
50522^354946-3106850M. Frind & P. Underwood08/2002
5053(2^354945+3134)/2106849Stefano Morozzi09/2020
50542^354873-18693106828Enzo Doria05/2013
5055(2^354831+3186)/2106815Stefano Morozzi09/2020
50572^354828+4257106814Lelio R Paula01/2017
505625216^17217+17217^25216106814Hans Havermann10/2020
5058(2^354799+1218)/2106805Stefano Morozzi09/2020
5059436^40459+40459^436106791Norbert Schneider03/2019
5060(21^80761+1)/22106783Paul Bourdelais03/2010
5061(115*10^106772-7)/9106774Robert Price02/2020
50622^354640-354640+1106758Robert Price10/2014
5063(2^354603+2606)/2106746Stefano Morozzi09/2020
50642^354585+95106741Lelio R Paula10/2011
50652^354553+189106732Lelio R Paula10/2011
5066(2^354546+1338)/2106729Stefano Morozzi02/2021
50672^354514-109031106720Enzo Doria04/2014
50682^354509-109465106718Enzo Doria04/2014
5069(15*2^354478-1)/26983106706Lelio R Paula03/2014
5070Phi(217618,10)/899798636917106693Makoto Kamada06/2019
507115^90710+28106684Lelio R Paula04/2017
50727^126237+34106683Lelio R Paula03/2017
50732^354385-115315106681Enzo Doria06/2015
50742^354327-19305106664Enzo Doria06/2013
5075(35*10^106649+1)/9106650Serge Batalov11/2010
507610^106636+97106637Lelio R Paula02/2017
507710^106636-22923106636Patrick De Geest03/2017
50782^354220-57106631Lelio R Paula10/2011
5079(68*10^106628-329)/9106629Robert Price03/2021
5080(29*10^106620-77)/3106621Robert Price02/2020
5081(746*10^106618+1)/9106620Robert Price03/2020
50822*10^106613+29106614Robert Price02/2021
50832^354157-17041106612Enzo Doria05/2013
508412^98778+73106600Lelio R Paula02/2017
508533333^1576+1576^33333106585Hans Havermann11/2020
50862^354064+1870651106584Enzo Doria05/2016
508724568^21779+21779^24568106577Hans Havermann11/2020
50882^353992-57106563Lelio R Paula10/2011
50899*10^106559+59106560Robert Price01/2020
50907*10^106553+27106554Robert Price11/2020
509128847^4938+4938^28847106548Hans Havermann10/2020
5092NSW(139160)106535Robert Price12/2018
5093(7*10^106516+113)/3106517Robert Price02/2018
50942^353832-1853849106515Enzo Doria09/2015
5095(7^126037-1)/6106513Paul Bourdelais09/2008
50962^353794-18453106503Enzo Doria05/2013
5097(2^353761+2094)/2106493Stefano Morozzi09/2020
50982^353728+7695106483Lelio R Paula01/2017
509926476^10509+10509^26476106475Hans Havermann10/2020
51002^353672-303106466Yves Minet02/2012
51016^136811+101106460Lelio R Paula02/2017
51022^353641+1871981106457Enzo Doria05/2016
5103(8*10^106454-29)/3106455Robert Price07/2018
510427845^6654+6654^27845106454Hans Havermann11/2020
510510^106449-700001106449Robert Price08/2021
510625316^16017+16017^25316106444Hans Havermann11/2020
51072^353553+54615106431Lelio R Paula01/2017
51082^353544-18897106428Enzo Doria05/2013
510928894^4823+4823^28894106426Hans Havermann11/2020
5110(19*10^106422+29)/3106423Robert Price12/2021
511125696^13829+13829^25696106402Hans Havermann11/2020
51126^136729-133106396Lelio R Paula02/2017
51132^353418+1605106390Lelio R Paula01/2017
51142^353387+65106381Lelio R Paula10/2011
51152^353372+74311106376Enzo Doria04/2016
51162^353344-3693106368Yves Minet03/2017
5117(56*10^106351+619)/9106352Robert Price05/2021
51192^353277-20089106347Enzo Doria06/2013
51182^353275+72173106347Enzo Doria04/2016
51202^353268-17705106345Enzo Doria05/2013
51212^353267-19857106344Enzo Doria06/2013
5122(46*10^106343+143)/9106344Robert Price01/2019
5124(2^353189+3054)/2106321Stefano Morozzi09/2020
512335087^1072+1072^35087106321Hans Havermann10/2020
5125(2^353184+1290)/2106319Stefano Morozzi01/2021
512626985^8684+8684^26985106287Hans Havermann10/2020
5127(2^353051+606)/2106279Stefano Morozzi09/2020
5128222748^3+3^222748106278Anatoly F. Selevich12/2010
5129(9179*2^353019-1)/9106273Lelio R Paula05/2015
51302^353025+72257106272Enzo Doria04/2016
51332^352932-20345106244Enzo Doria06/2013
5131(2^353011-3)/745325861246794515484535106244Lelio R Paula12/2013
513225628^13983+13983^25628106244Hans Havermann10/2020
51342^352883-187106229Lelio R Paula10/2011
513520^81649-19^81649106228Jean-Louis Charton03/2011
5136(55*10^106222+377)/9106223Robert Price02/2019
51372^352814-131106208Lelio R Paula10/2011
51382^352752+73951106189Enzo Doria04/2016
51396^136434+5106167Lelio R Paula11/2014
514025296^15737+15737^25296106166Hans Havermann09/2020
51418*10^106157-13106158Robert Price08/2019
51427*5^151872-8106155Lelio R Paula11/2014
5143105^52520-2106153Lelio R Paula10/2017
51442^352601-1604809106144Enzo Doria05/2015
514512^98353-43106141Lelio R Paula02/2017
51462^352585-18901106139Enzo Doria05/2013
514726363^10614+10614^26363106135Hans Havermann09/2020
5148(2^352554-3)/193106128Lelio R Paula12/2013
51492^352540+15015106126Lelio R Paula01/2017
515025068^17119+17119^25068106125Hans Havermann09/2020
51512^352524-3149106121Yves Minet10/2014
5152(7*10^106119-67)/3106120Robert Price10/2021
51532^352486-1858781106109Enzo Doria04/2016
51542^352444+12705106097Lelio R Paula01/2017
515528561^5182+5182^28561106090Hans Havermann10/2020
5156(182*10^106083+43)/9106085Robert Price02/2020
5157(266*10^106066+1)/3106068Robert Price04/2020
51582^352228-18953106032Enzo Doria05/2013
5159(2^352223+1118)/2106030Stefano Morozzi09/2020
5160(2^352212+2250)/2106027Stefano Morozzi01/2021
5161(2^352136+2638)/2106004Stefano Morozzi09/2020
51622^352107+1872533105995Enzo Doria05/2016
5163(2^352096+2086)/2105992Stefano Morozzi09/2020
51642^352066-2591105983Yves Minet07/2014
51652^352030+715105972Lelio R Paula10/2011
51669*6^136176-5105967Lelio R Paula11/2014
516717099*2^351991+58329105965Paul Vanderveen12/2017
516828582^5097+5097^28582105963Hans Havermann09/2020
5169155^48377+2105962Lelio R Paula08/2013
5170(23*10^105944-119)/3105945Robert Price07/2021
51712^351865+1869707105922Enzo Doria05/2016
517224974^17427+17427^24974105921Hans Havermann09/2020
517325163^16194+16194^25163105920Hans Havermann09/2020
51742^351831+23105912Lelio R Paula10/2011
5175(2^351818+3798)/2105908Stefano Morozzi02/2021
51769*2^351784-5105899Lelio R Paula09/2014
5177(2^351776+2766)/2105895Stefano Morozzi01/2021
5178(85*10^105881+203)/9105882Robert Price09/2020
51792^351671-112387105864Enzo Doria06/2014
51802^351669-109501105863Enzo Doria04/2014
51812^351644+74731105856Enzo Doria04/2016
518213^95025-42105853Lelio R Paula12/2016
51832^351599+15015105842Lelio R Paula01/2017
518419^82763+90105834Lelio R Paula01/2017
5185(205*10^105831-1)/3105833Robert Price11/2021
518626050^11551+11551^26050105832Hans Havermann09/2020
5187(9179*2^351540-1)/221105826Lelio R Paula05/2015
518820^81329-51105812Lelio R Paula01/2017
5189(5*10^105811+211)/9105811Robert Price02/2018
51902^351483+28425105807Lelio R Paula01/2017
519125231^15610+15610^25231105804Hans Havermann09/2020
519215^89960+86105802Lelio R Paula02/2017
51932^351460-17289105801Enzo Doria05/2013
519419^82735+22105798Lelio R Paula01/2017
51952^351435-109077105793Enzo Doria04/2014
51962^351393+1089105780Lelio R Paula01/2017
51972^351364+72631105772Enzo Doria04/2016
5198(2^351333+3626)/2105762Stefano Morozzi09/2020
519926818^8783+8783^26818105761Hans Havermann09/2020
52022^351305+1872467105754Enzo Doria05/2016
52013^221649+16105754Lelio R Paula11/2016
520032511^1790+1790^32511105754Hans Havermann09/2020
52038*3^221637-5105749Lelio R Paula09/2014
52042^351279-2780449105746Enzo Doria03/2016
5205(2^351263+3198)/2105741Stefano Morozzi09/2020
520615^89903-26105735Lelio R Paula02/2017
52082^351213-73105726Lelio R Paula10/2011
5207(2^351214+1210)/2105726Stefano Morozzi09/2020
52092^351192-4589105720Yves Minet07/2011
521020^81250-33105709Lelio R Paula12/2016
5211(2^351133+3530)/2105702Stefano Morozzi09/2020
5212(2^351103+534)/2105693Stefano Morozzi09/2020
52132^351076-113159105685Enzo Doria07/2014
521493^53688-2105684Lelio R Paula09/2013
52152^351060-4559105680Yves Minet07/2011
5216((10^52836-1)*10000/9+5927)*10^52836+(10^52836-1)/9105676Hans Havermann08/2019
521711^101473-750105674Enzo Doria11/2012
52183*5^151181-8105672Lelio R Paula11/2014
521915^89831-34105650Lelio R Paula02/2017
522111^101448-360105648Enzo Doria08/2012
52203*7^125011+4105648Lelio R Paula11/2014
52222^350943-113269105645Enzo Doria07/2014
52232*10^105636-91105637Robert Price04/2020
522424231^22880+22880^24231105634Hans Havermann09/2020
522535296^983+983^35296105626Hans Havermann09/2020
52262^350868-19725105622Enzo Doria06/2013
52272^350858-59291105619Enzo Doria10/2015
52282^350851+135105617Lelio R Paula10/2011
52292^350841-741105614Lelio R Paula01/2017
52303*10^105582+77105583Robert Price09/2018
523124915^17284+17284^24915105581Hans Havermann09/2020
5232(5*10^105576-53)/3105577Robert Price09/2020
52338*10^105571+3105572Robert Price08/2015
52342^350674-78557105564Jorge Menendez03/2018
52352*5^151026-3105563Lelio R Paula11/2014
5236(2^350702+5)/34264674063105562Lelio R Paula12/2013
52376^135647-5^135647105554Jean-Louis Charton02/2009
52383^221211+236105545Lelio R Paula11/2016
5239(32*10^105530-77)/9105531Robert Price06/2018
524010^105515+33105516Lelio R Paula11/2016
524124644^19125+19125^24644105516Hans Havermann10/2020
524210^105515-41033105515Patrick De Geest12/2016
5243(29*2^350473-1)/267927105499Lelio R Paula03/2014
524417^85732-72105489Lelio R Paula01/2017
5245(2^350399+3618)/2105481Stefano Morozzi09/2020
5246(2^350379+1010)/2105475Stefano Morozzi09/2020
524725233^15118+15118^25233105462Hans Havermann09/2020
524826261^10366+10366^26261105454Hans Havermann09/2020
52492^350307-110329105453Enzo Doria05/2014
52502^350253-20365105437Enzo Doria06/2013


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Created by  Henri Lifchitz & Renaud Lifchitz : October, 26 2000, last modification: January, 19 2022 17:15 (Time in France)

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