PRP Records

Probable Primes Top 10000

(292102 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 ?
55012^356442-114713107300Enzo Doria04/2015
55022^356425+72257107295Enzo Doria04/2016
55032^356351-112237107273Enzo Doria06/2014
5505(6^137845-11)/5107264Paul Bourdelais11/2011
55042^356322+74539107264Enzo Doria04/2016
55062^356274+1874479107250Enzo Doria06/2016
550724606^22819+22819^24606107241Hans Havermann10/2020
5508(2^356243+3686)/2107240Stefano Morozzi09/2020
550920^82422-93107234Lelio R Paula02/2017
55102^356157-20365107214Enzo Doria06/2013
55118*10^107209+99107210Robert Price03/2021
55122^356129-18949107206Enzo Doria05/2013
55132^356100-109587107197Enzo Doria04/2014
55142*10^107173-37107174Robert Price11/2021
5515(2^355978+3262)/2107160Stefano Morozzi02/2021
5516(31*2^355970+1)/5107159Lelio R Paula03/2014
55172^355968-64875107158Lelio R Paula01/2017
55182^355952+1870321107153Enzo Doria05/2016
551927069^9088+9088^27069107152Hans Havermann11/2020
55202^355915-117107142Lelio R Paula11/2011
5521(16*10^107140+77)/3107141Robert Price03/2019
552224628^22369+22369^24628107124Hans Havermann11/2020
5523(19*2^355838-1)/15107119Lelio R Paula03/2014
55243^224495-8107112Lelio R Paula12/2013
55253*10^107096+23107097Robert Price03/2022
552625077^18632+18632^25077107086Hans Havermann10/2020
55277^126691-44107067Lelio R Paula03/2017
55284^177830-8243107065Mike Oakes02/2011
5529(509*10^107057+13)/9107059Robert Price05/2022
5530(2^355562+1702)/2107035Stefano Morozzi09/2020
553110^107028+3593037107029Paul Bourdelais10/2021
55322^355524-21237107024Enzo Doria06/2013
5533(10223*2^355515+1)/4855107022Lelio R Paula07/2014
553424843^20320+20320^24843107022Hans Havermann10/2020
55352^355494-19901107015Enzo Doria06/2013
55362^355454-869688105107003Lelio R Paula01/2017
55374*10^106997+13106998Robert Price02/2021
5538(8*10^106985-629)/9106985Robert Price01/2022
55392^355366+54615106976Lelio R Paula01/2017
5540(31*2^355346-1)/1563106969Lelio R Paula03/2014
55422^355275-19861106949Enzo Doria06/2013
554127503^7738+7738^27503106949Hans Havermann11/2020
5543(85*10^106943+77)/9106944Robert Price07/2022
5544(9179*2^355234-1)/1915106937Lelio R Paula05/2015
55454*10^106914-93106915Robert Price07/2020
55464*10^106892-3106893Robert Price10/2015
5547(66^58741+1)/67106881Paul Bourdelais08/2017
55482^354946-3106850M. Frind & P. Underwood08/2002
5549(2^354945+3134)/2106849Stefano Morozzi09/2020
55502^354873-18693106828Enzo Doria05/2013
5551(2^354831+3186)/2106815Stefano Morozzi09/2020
55532^354828+4257106814Lelio R Paula01/2017
555225216^17217+17217^25216106814Hans Havermann10/2020
5554(2^354799+1218)/2106805Stefano Morozzi09/2020
5555436^40459+40459^436106791Norbert Schneider03/2019
5556(21^80761+1)/22106783Paul Bourdelais03/2010
5557(115*10^106772-7)/9106774Robert Price02/2020
55582^354640-354640+1106758Robert Price10/2014
5559(2^354603+2606)/2106746Stefano Morozzi09/2020
55602^354585+95106741Lelio R Paula10/2011
5561(206*10^106737+1)/9106739Robert Price04/2022
55622^354553+189106732Lelio R Paula10/2011
5564(2^354546+1338)/2106729Stefano Morozzi02/2021
5563(8*10^106729-71)/9106729Serge Batalov11/2022
55652^354514-109031106720Enzo Doria04/2014
55662^354509-109465106718Enzo Doria04/2014
5567(15*2^354478-1)/26983106706Lelio R Paula03/2014
5568Phi(217618,10)/899798636917106693Makoto Kamada06/2019
556915^90710+28106684Lelio R Paula04/2017
55707^126237+34106683Lelio R Paula03/2017
55712^354385-115315106681Enzo Doria06/2015
55722^354327-19305106664Enzo Doria06/2013
5573(35*10^106649+1)/9106650Serge Batalov11/2010
557410^106636+97106637Lelio R Paula02/2017
557510^106636-22923106636Patrick De Geest03/2017
55762^354220-57106631Lelio R Paula10/2011
5577(68*10^106628-329)/9106629Robert Price03/2021
5578(29*10^106620-77)/3106621Robert Price02/2020
5579(746*10^106618+1)/9106620Robert Price03/2020
55802*10^106613+29106614Robert Price02/2021
55812^354157-17041106612Enzo Doria05/2013
558212^98778+73106600Lelio R Paula02/2017
558333333^1576+1576^33333106585Hans Havermann11/2020
55842^354064+1870651106584Enzo Doria05/2016
558524568^21779+21779^24568106577Hans Havermann11/2020
55862^353992-57106563Lelio R Paula10/2011
55879*10^106559+59106560Robert Price01/2020
55887*10^106553+27106554Robert Price11/2020
558928847^4938+4938^28847106548Hans Havermann10/2020
5590NSW(139160)106535Robert Price12/2018
5591(7*10^106516+113)/3106517Robert Price02/2018
55922^353832-1853849106515Enzo Doria09/2015
5593(7^126037-1)/6106513Paul Bourdelais09/2008
55942^353794-18453106503Enzo Doria05/2013
5595(2^353761+2094)/2106493Stefano Morozzi09/2020
55962^353728+7695106483Lelio R Paula01/2017
559726476^10509+10509^26476106475Hans Havermann10/2020
55982^353672-303106466Yves Minet02/2012
55996^136811+101106460Lelio R Paula02/2017
56002^353641+1871981106457Enzo Doria05/2016
5601(8*10^106454-29)/3106455Robert Price07/2018
560227845^6654+6654^27845106454Hans Havermann11/2020
560310^106449-700001106449Robert Price08/2021
560425316^16017+16017^25316106444Hans Havermann11/2020
56052^353553+54615106431Lelio R Paula01/2017
56062^353544-18897106428Enzo Doria05/2013
560728894^4823+4823^28894106426Hans Havermann11/2020
5608(19*10^106422+29)/3106423Robert Price12/2021
5609(694*10^106418+53)/9106420Robert Price02/2022
56106*10^106412-13106413Robert Price07/2022
561125696^13829+13829^25696106402Hans Havermann11/2020
56126^136729-133106396Lelio R Paula02/2017
56132^353418+1605106390Lelio R Paula01/2017
56142^353387+65106381Lelio R Paula10/2011
56152^353372+74311106376Enzo Doria04/2016
56162^353344-3693106368Yves Minet03/2017
5617(772*10^106365-7)/9106367Robert Price06/2022
5618(56*10^106351+619)/9106352Robert Price05/2021
56202^353277-20089106347Enzo Doria06/2013
56192^353275+72173106347Enzo Doria04/2016
56212^353268-17705106345Enzo Doria05/2013
56222^353267-19857106344Enzo Doria06/2013
5623(46*10^106343+143)/9106344Robert Price01/2019
5625(2^353189+3054)/2106321Stefano Morozzi09/2020
562435087^1072+1072^35087106321Hans Havermann10/2020
5626(2^353184+1290)/2106319Stefano Morozzi01/2021
562726985^8684+8684^26985106287Hans Havermann10/2020
5628(2^353051+606)/2106279Stefano Morozzi09/2020
5630222748^3+3^222748106278Anatoly F. Selevich12/2010
5629(46*10^106277+107)/9106278Robert Price06/2022
5631(9179*2^353019-1)/9106273Lelio R Paula05/2015
56322^353025+72257106272Enzo Doria04/2016
56352^352932-20345106244Enzo Doria06/2013
5633(2^353011-3)/745325861246794515484535106244Lelio R Paula12/2013
563425628^13983+13983^25628106244Hans Havermann10/2020
56362^352883-187106229Lelio R Paula10/2011
563720^81649-19^81649106228Jean-Louis Charton03/2011
5638(55*10^106222+377)/9106223Robert Price02/2019
56392^352814-131106208Lelio R Paula10/2011
56402^352752+73951106189Enzo Doria04/2016
56416^136434+5106167Lelio R Paula11/2014
564225296^15737+15737^25296106166Hans Havermann09/2020
56438*10^106157-13106158Robert Price08/2019
56447*5^151872-8106155Lelio R Paula11/2014
5645105^52520-2106153Lelio R Paula10/2017
5646(23*10^106152-29)/3106153Robert Price03/2022
56472^352601-1604809106144Enzo Doria05/2015
564812^98353-43106141Lelio R Paula02/2017
56492^352585-18901106139Enzo Doria05/2013
565026363^10614+10614^26363106135Hans Havermann09/2020
5651(2^352554-3)/193106128Lelio R Paula12/2013
56522^352540+15015106126Lelio R Paula01/2017
565325068^17119+17119^25068106125Hans Havermann09/2020
56542^352524-3149106121Yves Minet10/2014
5655(7*10^106119-67)/3106120Robert Price10/2021
56562^352486-1858781106109Enzo Doria04/2016
56572^352444+12705106097Lelio R Paula01/2017
565828561^5182+5182^28561106090Hans Havermann10/2020
5659(182*10^106083+43)/9106085Robert Price02/2020
5660(266*10^106066+1)/3106068Robert Price04/2020
5661(7*10^106066-187)/9106066Tyler Busby01/2023
56622^352228-18953106032Enzo Doria05/2013
5663(2^352223+1118)/2106030Stefano Morozzi09/2020
5664(2^352212+2250)/2106027Stefano Morozzi01/2021
5665(2^352136+2638)/2106004Stefano Morozzi09/2020
56662^352107+1872533105995Enzo Doria05/2016
5667(2^352096+2086)/2105992Stefano Morozzi09/2020
56682^352066-2591105983Yves Minet07/2014
56692^352030+715105972Lelio R Paula10/2011
56709*6^136176-5105967Lelio R Paula11/2014
567117099*2^351991+58329105965Paul Vanderveen12/2017
567228582^5097+5097^28582105963Hans Havermann09/2020
5673155^48377+2105962Lelio R Paula08/2013
5674(23*10^105944-119)/3105945Robert Price07/2021
56752^351865+1869707105922Enzo Doria05/2016
567624974^17427+17427^24974105921Hans Havermann09/2020
567725163^16194+16194^25163105920Hans Havermann09/2020
56782^351831+23105912Lelio R Paula10/2011
5679(2^351818+3798)/2105908Stefano Morozzi02/2021
56809*2^351784-5105899Lelio R Paula09/2014
5681(2^351776+2766)/2105895Stefano Morozzi01/2021
5682(85*10^105881+203)/9105882Robert Price09/2020
56832^351671-112387105864Enzo Doria06/2014
56842^351669-109501105863Enzo Doria04/2014
56852^351644+74731105856Enzo Doria04/2016
568613^95025-42105853Lelio R Paula12/2016
56872^351599+15015105842Lelio R Paula01/2017
568819^82763+90105834Lelio R Paula01/2017
5689(205*10^105831-1)/3105833Robert Price11/2021
569026050^11551+11551^26050105832Hans Havermann09/2020
5691(9179*2^351540-1)/221105826Lelio R Paula05/2015
569220^81329-51105812Lelio R Paula01/2017
5693(5*10^105811+211)/9105811Robert Price02/2018
56942^351483+28425105807Lelio R Paula01/2017
569525231^15610+15610^25231105804Hans Havermann09/2020
569615^89960+86105802Lelio R Paula02/2017
56972^351460-17289105801Enzo Doria05/2013
569819^82735+22105798Lelio R Paula01/2017
56992^351435-109077105793Enzo Doria04/2014
57002^351393+1089105780Lelio R Paula01/2017
57012^351364+72631105772Enzo Doria04/2016
5702(2^351333+3626)/2105762Stefano Morozzi09/2020
570326818^8783+8783^26818105761Hans Havermann09/2020
57062^351305+1872467105754Enzo Doria05/2016
57053^221649+16105754Lelio R Paula11/2016
570432511^1790+1790^32511105754Hans Havermann09/2020
57078*3^221637-5105749Lelio R Paula09/2014
57082^351279-2780449105746Enzo Doria03/2016
5709(2^351263+3198)/2105741Stefano Morozzi09/2020
571015^89903-26105735Lelio R Paula02/2017
57122^351213-73105726Lelio R Paula10/2011
5711(2^351214+1210)/2105726Stefano Morozzi09/2020
57132^351192-4589105720Yves Minet07/2011
571420^81250-33105709Lelio R Paula12/2016
5715(2^351133+3530)/2105702Stefano Morozzi09/2020
5716(2^351103+534)/2105693Stefano Morozzi09/2020
57172^351076-113159105685Enzo Doria07/2014
571893^53688-2105684Lelio R Paula09/2013
57192^351060-4559105680Yves Minet07/2011
5720((10^52836-1)*10000/9+5927)*10^52836+(10^52836-1)/9105676Hans Havermann08/2019
572111^101473-750105674Enzo Doria11/2012
57223*5^151181-8105672Lelio R Paula11/2014
572315^89831-34105650Lelio R Paula02/2017
572511^101448-360105648Enzo Doria08/2012
57243*7^125011+4105648Lelio R Paula11/2014
57262^350943-113269105645Enzo Doria07/2014
57272*10^105636-91105637Robert Price04/2020
572824231^22880+22880^24231105634Hans Havermann09/2020
572935296^983+983^35296105626Hans Havermann09/2020
57302^350868-19725105622Enzo Doria06/2013
57312^350858-59291105619Enzo Doria10/2015
57322^350851+135105617Lelio R Paula10/2011
57332^350841-741105614Lelio R Paula01/2017
57343*10^105582+77105583Robert Price09/2018
573524915^17284+17284^24915105581Hans Havermann09/2020
5736(5*10^105576-53)/3105577Robert Price09/2020
57378*10^105571+3105572Robert Price08/2015
57382^350674-78557105564Jorge Menendez03/2018
57392*5^151026-3105563Lelio R Paula11/2014
5740(2^350702+5)/34264674063105562Lelio R Paula12/2013
57416^135647-5^135647105554Jean-Louis Charton02/2009
57423^221211+236105545Lelio R Paula11/2016
5743(32*10^105530-77)/9105531Robert Price06/2018
574410^105515+33105516Lelio R Paula11/2016
574524644^19125+19125^24644105516Hans Havermann10/2020
574610^105515-41033105515Patrick De Geest12/2016
5747(29*2^350473-1)/267927105499Lelio R Paula03/2014
57482^350455-430567105498Harrison Mesh06/2022
574917^85732-72105489Lelio R Paula01/2017
5750(2^350399+3618)/2105481Stefano Morozzi09/2020


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Created by  Henri Lifchitz & Renaud Lifchitz : October, 26 2000, last modification: March, 20 2023 09:01 (Time in France)

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