PRP Records

Probable Primes Top 10000

(290751 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 ?
5251436^40459+40459^436106791Norbert Schneider03/2019
5252(21^80761+1)/22106783Paul Bourdelais03/2010
5253(115*10^106772-7)/9106774Robert Price02/2020
52542^354640-354640+1106758Robert Price10/2014
5255(2^354603+2606)/2106746Stefano Morozzi09/2020
52562^354585+95106741Lelio R Paula10/2011
5257(206*10^106737+1)/9106739Robert Price04/2022
52582^354553+189106732Lelio R Paula10/2011
5259(2^354546+1338)/2106729Stefano Morozzi02/2021
52602^354514-109031106720Enzo Doria04/2014
52612^354509-109465106718Enzo Doria04/2014
5262(15*2^354478-1)/26983106706Lelio R Paula03/2014
5263Phi(217618,10)/899798636917106693Makoto Kamada06/2019
526415^90710+28106684Lelio R Paula04/2017
52657^126237+34106683Lelio R Paula03/2017
52662^354385-115315106681Enzo Doria06/2015
52672^354327-19305106664Enzo Doria06/2013
5268(35*10^106649+1)/9106650Serge Batalov11/2010
526910^106636+97106637Lelio R Paula02/2017
527010^106636-22923106636Patrick De Geest03/2017
52712^354220-57106631Lelio R Paula10/2011
5272(68*10^106628-329)/9106629Robert Price03/2021
5273(29*10^106620-77)/3106621Robert Price02/2020
5274(746*10^106618+1)/9106620Robert Price03/2020
52752*10^106613+29106614Robert Price02/2021
52762^354157-17041106612Enzo Doria05/2013
527712^98778+73106600Lelio R Paula02/2017
527833333^1576+1576^33333106585Hans Havermann11/2020
52792^354064+1870651106584Enzo Doria05/2016
528024568^21779+21779^24568106577Hans Havermann11/2020
52812^353992-57106563Lelio R Paula10/2011
52829*10^106559+59106560Robert Price01/2020
52837*10^106553+27106554Robert Price11/2020
528428847^4938+4938^28847106548Hans Havermann10/2020
5285NSW(139160)106535Robert Price12/2018
5286(7*10^106516+113)/3106517Robert Price02/2018
52872^353832-1853849106515Enzo Doria09/2015
5288(7^126037-1)/6106513Paul Bourdelais09/2008
52892^353794-18453106503Enzo Doria05/2013
5290(2^353761+2094)/2106493Stefano Morozzi09/2020
52912^353728+7695106483Lelio R Paula01/2017
529226476^10509+10509^26476106475Hans Havermann10/2020
52932^353672-303106466Yves Minet02/2012
52946^136811+101106460Lelio R Paula02/2017
52952^353641+1871981106457Enzo Doria05/2016
5296(8*10^106454-29)/3106455Robert Price07/2018
529727845^6654+6654^27845106454Hans Havermann11/2020
529810^106449-700001106449Robert Price08/2021
529925316^16017+16017^25316106444Hans Havermann11/2020
53002^353553+54615106431Lelio R Paula01/2017
53012^353544-18897106428Enzo Doria05/2013
530228894^4823+4823^28894106426Hans Havermann11/2020
5303(19*10^106422+29)/3106423Robert Price12/2021
5304(694*10^106418+53)/9106420Robert Price02/2022
530525696^13829+13829^25696106402Hans Havermann11/2020
53066^136729-133106396Lelio R Paula02/2017
53072^353418+1605106390Lelio R Paula01/2017
53082^353387+65106381Lelio R Paula10/2011
53092^353372+74311106376Enzo Doria04/2016
53102^353344-3693106368Yves Minet03/2017
5311(772*10^106365-7)/9106367Robert Price06/2022
5312(56*10^106351+619)/9106352Robert Price05/2021
53142^353277-20089106347Enzo Doria06/2013
53132^353275+72173106347Enzo Doria04/2016
53152^353268-17705106345Enzo Doria05/2013
53162^353267-19857106344Enzo Doria06/2013
5317(46*10^106343+143)/9106344Robert Price01/2019
5318(2^353189+3054)/2106321Stefano Morozzi09/2020
531935087^1072+1072^35087106321Hans Havermann10/2020
5320(2^353184+1290)/2106319Stefano Morozzi01/2021
532126985^8684+8684^26985106287Hans Havermann10/2020
5322(2^353051+606)/2106279Stefano Morozzi09/2020
5324222748^3+3^222748106278Anatoly F. Selevich12/2010
5323(46*10^106277+107)/9106278Robert Price06/2022
5325(9179*2^353019-1)/9106273Lelio R Paula05/2015
53262^353025+72257106272Enzo Doria04/2016
53292^352932-20345106244Enzo Doria06/2013
5327(2^353011-3)/745325861246794515484535106244Lelio R Paula12/2013
532825628^13983+13983^25628106244Hans Havermann10/2020
53302^352883-187106229Lelio R Paula10/2011
533120^81649-19^81649106228Jean-Louis Charton03/2011
5332(55*10^106222+377)/9106223Robert Price02/2019
53332^352814-131106208Lelio R Paula10/2011
53342^352752+73951106189Enzo Doria04/2016
53356^136434+5106167Lelio R Paula11/2014
533625296^15737+15737^25296106166Hans Havermann09/2020
53378*10^106157-13106158Robert Price08/2019
53387*5^151872-8106155Lelio R Paula11/2014
5339105^52520-2106153Lelio R Paula10/2017
5340(23*10^106152-29)/3106153Robert Price03/2022
53412^352601-1604809106144Enzo Doria05/2015
534212^98353-43106141Lelio R Paula02/2017
53432^352585-18901106139Enzo Doria05/2013
534426363^10614+10614^26363106135Hans Havermann09/2020
5345(2^352554-3)/193106128Lelio R Paula12/2013
53462^352540+15015106126Lelio R Paula01/2017
534725068^17119+17119^25068106125Hans Havermann09/2020
53482^352524-3149106121Yves Minet10/2014
5349(7*10^106119-67)/3106120Robert Price10/2021
53502^352486-1858781106109Enzo Doria04/2016
53512^352444+12705106097Lelio R Paula01/2017
535228561^5182+5182^28561106090Hans Havermann10/2020
5353(182*10^106083+43)/9106085Robert Price02/2020
5354(266*10^106066+1)/3106068Robert Price04/2020
53552^352228-18953106032Enzo Doria05/2013
5356(2^352223+1118)/2106030Stefano Morozzi09/2020
5357(2^352212+2250)/2106027Stefano Morozzi01/2021
5358(2^352136+2638)/2106004Stefano Morozzi09/2020
53592^352107+1872533105995Enzo Doria05/2016
5360(2^352096+2086)/2105992Stefano Morozzi09/2020
53612^352066-2591105983Yves Minet07/2014
53622^352030+715105972Lelio R Paula10/2011
53639*6^136176-5105967Lelio R Paula11/2014
536417099*2^351991+58329105965Paul Vanderveen12/2017
536528582^5097+5097^28582105963Hans Havermann09/2020
5366155^48377+2105962Lelio R Paula08/2013
5367(23*10^105944-119)/3105945Robert Price07/2021
53682^351865+1869707105922Enzo Doria05/2016
536924974^17427+17427^24974105921Hans Havermann09/2020
537025163^16194+16194^25163105920Hans Havermann09/2020
53712^351831+23105912Lelio R Paula10/2011
5372(2^351818+3798)/2105908Stefano Morozzi02/2021
53739*2^351784-5105899Lelio R Paula09/2014
5374(2^351776+2766)/2105895Stefano Morozzi01/2021
5375(85*10^105881+203)/9105882Robert Price09/2020
53762^351671-112387105864Enzo Doria06/2014
53772^351669-109501105863Enzo Doria04/2014
53782^351644+74731105856Enzo Doria04/2016
537913^95025-42105853Lelio R Paula12/2016
53802^351599+15015105842Lelio R Paula01/2017
538119^82763+90105834Lelio R Paula01/2017
5382(205*10^105831-1)/3105833Robert Price11/2021
538326050^11551+11551^26050105832Hans Havermann09/2020
5384(9179*2^351540-1)/221105826Lelio R Paula05/2015
538520^81329-51105812Lelio R Paula01/2017
5386(5*10^105811+211)/9105811Robert Price02/2018
53872^351483+28425105807Lelio R Paula01/2017
538825231^15610+15610^25231105804Hans Havermann09/2020
538915^89960+86105802Lelio R Paula02/2017
53902^351460-17289105801Enzo Doria05/2013
539119^82735+22105798Lelio R Paula01/2017
53922^351435-109077105793Enzo Doria04/2014
53932^351393+1089105780Lelio R Paula01/2017
53942^351364+72631105772Enzo Doria04/2016
5395(2^351333+3626)/2105762Stefano Morozzi09/2020
539626818^8783+8783^26818105761Hans Havermann09/2020
53992^351305+1872467105754Enzo Doria05/2016
53983^221649+16105754Lelio R Paula11/2016
539732511^1790+1790^32511105754Hans Havermann09/2020
54008*3^221637-5105749Lelio R Paula09/2014
54012^351279-2780449105746Enzo Doria03/2016
5402(2^351263+3198)/2105741Stefano Morozzi09/2020
540315^89903-26105735Lelio R Paula02/2017
54052^351213-73105726Lelio R Paula10/2011
5404(2^351214+1210)/2105726Stefano Morozzi09/2020
54062^351192-4589105720Yves Minet07/2011
540720^81250-33105709Lelio R Paula12/2016
5408(2^351133+3530)/2105702Stefano Morozzi09/2020
5409(2^351103+534)/2105693Stefano Morozzi09/2020
54102^351076-113159105685Enzo Doria07/2014
541193^53688-2105684Lelio R Paula09/2013
54122^351060-4559105680Yves Minet07/2011
5413((10^52836-1)*10000/9+5927)*10^52836+(10^52836-1)/9105676Hans Havermann08/2019
541411^101473-750105674Enzo Doria11/2012
54153*5^151181-8105672Lelio R Paula11/2014
541615^89831-34105650Lelio R Paula02/2017
541811^101448-360105648Enzo Doria08/2012
54173*7^125011+4105648Lelio R Paula11/2014
54192^350943-113269105645Enzo Doria07/2014
54202*10^105636-91105637Robert Price04/2020
542124231^22880+22880^24231105634Hans Havermann09/2020
542235296^983+983^35296105626Hans Havermann09/2020
54232^350868-19725105622Enzo Doria06/2013
54242^350858-59291105619Enzo Doria10/2015
54252^350851+135105617Lelio R Paula10/2011
54262^350841-741105614Lelio R Paula01/2017
54273*10^105582+77105583Robert Price09/2018
542824915^17284+17284^24915105581Hans Havermann09/2020
5429(5*10^105576-53)/3105577Robert Price09/2020
54308*10^105571+3105572Robert Price08/2015
54312^350674-78557105564Jorge Menendez03/2018
54322*5^151026-3105563Lelio R Paula11/2014
5433(2^350702+5)/34264674063105562Lelio R Paula12/2013
54346^135647-5^135647105554Jean-Louis Charton02/2009
54353^221211+236105545Lelio R Paula11/2016
5436(32*10^105530-77)/9105531Robert Price06/2018
543710^105515+33105516Lelio R Paula11/2016
543824644^19125+19125^24644105516Hans Havermann10/2020
543910^105515-41033105515Patrick De Geest12/2016
5440(29*2^350473-1)/267927105499Lelio R Paula03/2014
54412^350455-430567105498Harrison Mesh06/2022
544217^85732-72105489Lelio R Paula01/2017
5443(2^350399+3618)/2105481Stefano Morozzi09/2020
5444(2^350379+1010)/2105475Stefano Morozzi09/2020
544525233^15118+15118^25233105462Hans Havermann09/2020
544626261^10366+10366^26261105454Hans Havermann09/2020
54472^350307-110329105453Enzo Doria05/2014
54482^350253-20365105437Enzo Doria06/2013
5449(3*29^72089-1075)/4105423Curtis Bright05/2015
5450(2^350187+2658)/2105417Stefano Morozzi09/2020
54514*10^105415-69105416Robert Price01/2022
5452(22*10^105407+179)/3105408Robert Price02/2022
54532^350139-109009105403Enzo Doria04/2014
5454(2^350129+3026)/2105400Stefano Morozzi09/2020
5455(2^350097+2070)/2105390Stefano Morozzi09/2020
54563*5^150763+4105380Lelio R Paula11/2014
545712^97643+91105375Lelio R Paula02/2017
54586*5^150744-7105367Lelio R Paula11/2014
5459(2^350018+2074)/2105366Stefano Morozzi09/2020
54604*10^105364-39105365Robert Price09/2020
54622^349996-112169105360Enzo Doria06/2014
5461(2^349997+3702)/2105360Stefano Morozzi09/2020
5463(418*10^105343+23)/9105345Robert Price02/2020
546425490^13563+13563^25490105334Hans Havermann10/2020
546511^101142-1080105329Enzo Doria12/2012
5466(68*10^105320-41)/9105321Robert Price10/2013
546724800^17649+17649^24800105319Hans Havermann09/2020
54683^220712-9934105307Enzo Doria05/2014
54697*10^105296+9105297Robert Price09/2015
547089*10^105284-7105286Robert Price04/2020
54712^349739+1873373105282Enzo Doria06/2016
54727^124574+24105278Lelio R Paula11/2016
54732^349708-20957105273Enzo Doria06/2013
547434115^1218+1218^34115105267Hans Havermann09/2020
54752^349649-20469105255Enzo Doria06/2013
54762^349607-20109105243Enzo Doria06/2013
5477(85*10^105242+473)/9105243Robert Price01/2020
54782^349594-19085105239Enzo Doria05/2013
54792^349530+1874479105220Enzo Doria06/2016
5480(3^220528+8)/8081105215Lelio R Paula12/2013
5481(106*10^105199+17)/3105201Robert Price04/2021
5482(2^349452+3570)/2105196Stefano Morozzi09/2020
54833^220464-112852105189Enzo Doria07/2014
54842^349419-17349105186Enzo Doria05/2013
54852^349400-2579105180Yves Minet07/2014
54868*5^150471+3105176Lelio R Paula11/2014
5487(2^349359+2298)/2105168Stefano Morozzi02/2021
5488655^37342+37342^655105165Norbert Schneider08/2018
548913^94403+94105160Lelio R Paula12/2016
54902^349301-112309105151Enzo Doria06/2014
549130291^2960+2960^30291105149Hans Havermann09/2020
549227350^6981+6981^27350105132Hans Havermann09/2020
54949*2^349220+5105127Lelio R Paula09/2014
5493(2^349225+3122)/2105127Stefano Morozzi09/2020
54957*3^220317+8105119Lelio R Paula09/2014
54967^124386+88105119Lelio R Paula11/2016
5497(2^349197+570)/2105119Stefano Morozzi09/2020
54982^349171-19657105111Enzo Doria06/2013
5499(2^349115+590)/2105094Stefano Morozzi09/2020
5500(2^(6*58185+1)-5)/3105093Kevin Acres11/2013


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Created by  Henri Lifchitz & Renaud Lifchitz : October, 26 2000, last modification: June, 23 2022 21:24 (Time in France)

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