PRP Records

Probable Primes Top 10000

(288515 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 ?
50012^354064+1870651106584Enzo Doria05/2016
500224568^21779+21779^24568106577Hans Havermann11/2020
50032^353992-57106563Lelio R Paula10/2011
50049*10^106559+59106560Robert Price01/2020
50057*10^106553+27106554Robert Price11/2020
500628847^4938+4938^28847106548Hans Havermann10/2020
5007NSW(139160)106535Robert Price12/2018
5008(7*10^106516+113)/3106517Robert Price02/2018
50092^353832-1853849106515Enzo Doria09/2015
5010(7^126037-1)/6106513Paul Bourdelais09/2008
50112^353794-18453106503Enzo Doria05/2013
5012(2^353761+2094)/2106493Stefano Morozzi09/2020
50132^353728+7695106483Lelio R Paula01/2017
501426476^10509+10509^26476106475Hans Havermann10/2020
50152^353672-303106466Yves Minet02/2012
50166^136811+101106460Lelio R Paula02/2017
50172^353641+1871981106457Enzo Doria05/2016
5018(8*10^106454-29)/3106455Robert Price07/2018
501927845^6654+6654^27845106454Hans Havermann11/2020
502010^106449-700001106449Robert Price08/2021
502125316^16017+16017^25316106444Hans Havermann11/2020
50222^353553+54615106431Lelio R Paula01/2017
50232^353544-18897106428Enzo Doria05/2013
502428894^4823+4823^28894106426Hans Havermann11/2020
502525696^13829+13829^25696106402Hans Havermann11/2020
50266^136729-133106396Lelio R Paula02/2017
50272^353418+1605106390Lelio R Paula01/2017
50282^353387+65106381Lelio R Paula10/2011
50292^353372+74311106376Enzo Doria04/2016
50302^353344-3693106368Yves Minet03/2017
5031(56*10^106351+619)/9106352Robert Price05/2021
50332^353277-20089106347Enzo Doria06/2013
50322^353275+72173106347Enzo Doria04/2016
50342^353268-17705106345Enzo Doria05/2013
50352^353267-19857106344Enzo Doria06/2013
5036(46*10^106343+143)/9106344Robert Price01/2019
5038(2^353189+3054)/2106321Stefano Morozzi09/2020
503735087^1072+1072^35087106321Hans Havermann10/2020
5039(2^353184+1290)/2106319Stefano Morozzi01/2021
504026985^8684+8684^26985106287Hans Havermann10/2020
5041(2^353051+606)/2106279Stefano Morozzi09/2020
5042222748^3+3^222748106278Anatoly F. Selevich12/2010
5043(9179*2^353019-1)/9106273Lelio R Paula05/2015
50442^353025+72257106272Enzo Doria04/2016
50472^352932-20345106244Enzo Doria06/2013
5045(2^353011-3)/745325861246794515484535106244Lelio R Paula12/2013
504625628^13983+13983^25628106244Hans Havermann10/2020
50482^352883-187106229Lelio R Paula10/2011
504920^81649-19^81649106228Jean-Louis Charton03/2011
5050(55*10^106222+377)/9106223Robert Price02/2019
50512^352814-131106208Lelio R Paula10/2011
50522^352752+73951106189Enzo Doria04/2016
50536^136434+5106167Lelio R Paula11/2014
505425296^15737+15737^25296106166Hans Havermann09/2020
50558*10^106157-13106158Robert Price08/2019
50567*5^151872-8106155Lelio R Paula11/2014
5057105^52520-2106153Lelio R Paula10/2017
50582^352601-1604809106144Enzo Doria05/2015
505912^98353-43106141Lelio R Paula02/2017
50602^352585-18901106139Enzo Doria05/2013
506126363^10614+10614^26363106135Hans Havermann09/2020
5062(2^352554-3)/193106128Lelio R Paula12/2013
50632^352540+15015106126Lelio R Paula01/2017
506425068^17119+17119^25068106125Hans Havermann09/2020
50652^352524-3149106121Yves Minet10/2014
5066(7*10^106119-67)/3106120Robert Price10/2021
50672^352486-1858781106109Enzo Doria04/2016
50682^352444+12705106097Lelio R Paula01/2017
506928561^5182+5182^28561106090Hans Havermann10/2020
5070(182*10^106083+43)/9106085Robert Price02/2020
5071(266*10^106066+1)/3106068Robert Price04/2020
50722^352228-18953106032Enzo Doria05/2013
5073(2^352223+1118)/2106030Stefano Morozzi09/2020
5074(2^352212+2250)/2106027Stefano Morozzi01/2021
5075(2^352136+2638)/2106004Stefano Morozzi09/2020
50762^352107+1872533105995Enzo Doria05/2016
5077(2^352096+2086)/2105992Stefano Morozzi09/2020
50782^352066-2591105983Yves Minet07/2014
50792^352030+715105972Lelio R Paula10/2011
50809*6^136176-5105967Lelio R Paula11/2014
508117099*2^351991+58329105965Paul Vanderveen12/2017
508228582^5097+5097^28582105963Hans Havermann09/2020
5083155^48377+2105962Lelio R Paula08/2013
5084(23*10^105944-119)/3105945Robert Price07/2021
50852^351865+1869707105922Enzo Doria05/2016
508624974^17427+17427^24974105921Hans Havermann09/2020
508725163^16194+16194^25163105920Hans Havermann09/2020
50882^351831+23105912Lelio R Paula10/2011
5089(2^351818+3798)/2105908Stefano Morozzi02/2021
50909*2^351784-5105899Lelio R Paula09/2014
5091(2^351776+2766)/2105895Stefano Morozzi01/2021
5092(85*10^105881+203)/9105882Robert Price09/2020
50932^351671-112387105864Enzo Doria06/2014
50942^351669-109501105863Enzo Doria04/2014
50952^351644+74731105856Enzo Doria04/2016
509613^95025-42105853Lelio R Paula12/2016
50972^351599+15015105842Lelio R Paula01/2017
509819^82763+90105834Lelio R Paula01/2017
5099(205*10^105831-1)/3105833Robert Price11/2021
510026050^11551+11551^26050105832Hans Havermann09/2020
5101(9179*2^351540-1)/221105826Lelio R Paula05/2015
510220^81329-51105812Lelio R Paula01/2017
5103(5*10^105811+211)/9105811Robert Price02/2018
51042^351483+28425105807Lelio R Paula01/2017
510525231^15610+15610^25231105804Hans Havermann09/2020
510615^89960+86105802Lelio R Paula02/2017
51072^351460-17289105801Enzo Doria05/2013
510819^82735+22105798Lelio R Paula01/2017
51092^351435-109077105793Enzo Doria04/2014
51102^351393+1089105780Lelio R Paula01/2017
51112^351364+72631105772Enzo Doria04/2016
5112(2^351333+3626)/2105762Stefano Morozzi09/2020
511326818^8783+8783^26818105761Hans Havermann09/2020
51162^351305+1872467105754Enzo Doria05/2016
51153^221649+16105754Lelio R Paula11/2016
511432511^1790+1790^32511105754Hans Havermann09/2020
51178*3^221637-5105749Lelio R Paula09/2014
51182^351279-2780449105746Enzo Doria03/2016
5119(2^351263+3198)/2105741Stefano Morozzi09/2020
512015^89903-26105735Lelio R Paula02/2017
51222^351213-73105726Lelio R Paula10/2011
5121(2^351214+1210)/2105726Stefano Morozzi09/2020
51232^351192-4589105720Yves Minet07/2011
512420^81250-33105709Lelio R Paula12/2016
5125(2^351133+3530)/2105702Stefano Morozzi09/2020
5126(2^351103+534)/2105693Stefano Morozzi09/2020
51272^351076-113159105685Enzo Doria07/2014
512893^53688-2105684Lelio R Paula09/2013
51292^351060-4559105680Yves Minet07/2011
5130((10^52836-1)*10000/9+5927)*10^52836+(10^52836-1)/9105676Hans Havermann08/2019
513111^101473-750105674Enzo Doria11/2012
51323*5^151181-8105672Lelio R Paula11/2014
513315^89831-34105650Lelio R Paula02/2017
513511^101448-360105648Enzo Doria08/2012
51343*7^125011+4105648Lelio R Paula11/2014
51362^350943-113269105645Enzo Doria07/2014
51372*10^105636-91105637Robert Price04/2020
513824231^22880+22880^24231105634Hans Havermann09/2020
513935296^983+983^35296105626Hans Havermann09/2020
51402^350868-19725105622Enzo Doria06/2013
51412^350858-59291105619Enzo Doria10/2015
51422^350851+135105617Lelio R Paula10/2011
51432^350841-741105614Lelio R Paula01/2017
51443*10^105582+77105583Robert Price09/2018
514524915^17284+17284^24915105581Hans Havermann09/2020
5146(5*10^105576-53)/3105577Robert Price09/2020
51478*10^105571+3105572Robert Price08/2015
51482^350674-78557105564Jorge Menendez03/2018
51492*5^151026-3105563Lelio R Paula11/2014
5150(2^350702+5)/34264674063105562Lelio R Paula12/2013
51516^135647-5^135647105554Jean-Louis Charton02/2009
51523^221211+236105545Lelio R Paula11/2016
5153(32*10^105530-77)/9105531Robert Price06/2018
515410^105515+33105516Lelio R Paula11/2016
515524644^19125+19125^24644105516Hans Havermann10/2020
515610^105515-41033105515Patrick De Geest12/2016
5157(29*2^350473-1)/267927105499Lelio R Paula03/2014
515817^85732-72105489Lelio R Paula01/2017
5159(2^350399+3618)/2105481Stefano Morozzi09/2020
5160(2^350379+1010)/2105475Stefano Morozzi09/2020
516125233^15118+15118^25233105462Hans Havermann09/2020
516226261^10366+10366^26261105454Hans Havermann09/2020
51632^350307-110329105453Enzo Doria05/2014
51642^350253-20365105437Enzo Doria06/2013
5165(3*29^72089-1075)/4105423Curtis Bright05/2015
5166(2^350187+2658)/2105417Stefano Morozzi09/2020
51672^350139-109009105403Enzo Doria04/2014
5168(2^350129+3026)/2105400Stefano Morozzi09/2020
5169(2^350097+2070)/2105390Stefano Morozzi09/2020
51703*5^150763+4105380Lelio R Paula11/2014
517112^97643+91105375Lelio R Paula02/2017
51726*5^150744-7105367Lelio R Paula11/2014
5173(2^350018+2074)/2105366Stefano Morozzi09/2020
51744*10^105364-39105365Robert Price09/2020
51762^349996-112169105360Enzo Doria06/2014
5175(2^349997+3702)/2105360Stefano Morozzi09/2020
5177(418*10^105343+23)/9105345Robert Price02/2020
517825490^13563+13563^25490105334Hans Havermann10/2020
517911^101142-1080105329Enzo Doria12/2012
5180(68*10^105320-41)/9105321Robert Price10/2013
518124800^17649+17649^24800105319Hans Havermann09/2020
51823^220712-9934105307Enzo Doria05/2014
51837*10^105296+9105297Robert Price09/2015
518489*10^105284-7105286Robert Price04/2020
51852^349739+1873373105282Enzo Doria06/2016
51867^124574+24105278Lelio R Paula11/2016
51872^349708-20957105273Enzo Doria06/2013
518834115^1218+1218^34115105267Hans Havermann09/2020
51892^349649-20469105255Enzo Doria06/2013
51902^349607-20109105243Enzo Doria06/2013
5191(85*10^105242+473)/9105243Robert Price01/2020
51922^349594-19085105239Enzo Doria05/2013
51932^349530+1874479105220Enzo Doria06/2016
5194(3^220528+8)/8081105215Lelio R Paula12/2013
5195(106*10^105199+17)/3105201Robert Price04/2021
5196(2^349452+3570)/2105196Stefano Morozzi09/2020
51973^220464-112852105189Enzo Doria07/2014
51982^349419-17349105186Enzo Doria05/2013
51992^349400-2579105180Yves Minet07/2014
52008*5^150471+3105176Lelio R Paula11/2014
5201(2^349359+2298)/2105168Stefano Morozzi02/2021
5202655^37342+37342^655105165Norbert Schneider08/2018
520313^94403+94105160Lelio R Paula12/2016
52042^349301-112309105151Enzo Doria06/2014
520530291^2960+2960^30291105149Hans Havermann09/2020
520627350^6981+6981^27350105132Hans Havermann09/2020
52089*2^349220+5105127Lelio R Paula09/2014
5207(2^349225+3122)/2105127Stefano Morozzi09/2020
52097*3^220317+8105119Lelio R Paula09/2014
52107^124386+88105119Lelio R Paula11/2016
5211(2^349197+570)/2105119Stefano Morozzi09/2020
52122^349171-19657105111Enzo Doria06/2013
5213(2^349115+590)/2105094Stefano Morozzi09/2020
5214(2^(6*58185+1)-5)/3105093Kevin Acres11/2013
5215(2^349111-5)/3105093Lelio R Paula12/2013
5216675^37142+37142^675105087Norbert Schneider08/2018
52172^348981-2797573105054Enzo Doria04/2016
52182^348869-6555105021Lelio R Paula01/2017
52195^150217+78104998Lelio R Paula11/2016
5220(88*10^104989-1)/3104991Robert Price04/2020
5221(28*10^104972+149)/3104973Robert Price12/2019
522224927^16262+16262^24927104972Hans Havermann10/2020
52232^348703-113005104971Enzo Doria06/2014
5224(191*10^104956-17)/3104958Robert Price11/2021
52262^348612-809104943Yves Minet05/2013
5225(73*10^104942-1)/9104943Robert Price01/2015
52272^348583-350407104934Enzo Doria06/2015
52282^348531-949104919Yves Minet05/2012
522920^80636-59104910Lelio R Paula12/2016
52308*10^104893-13104894Robert Price08/2019
52322^348437+35104890Lelio R Paula09/2011
523125208^14487+14487^25208104890Hans Havermann09/2020
52332^348348+135104864Lelio R Paula09/2011
5234(29*10^104858+349)/9104859Robert Price06/2021
52356*10^104852-31104853Robert Price07/2020
5237(2^348284+9)/25104843Lelio R Paula12/2013
523675^55914-74104843Norbert Schneider01/2015
52382^348268+255255104840Lelio R Paula01/2017
523935540^891+891^35540104839Hans Havermann09/2020
52405^149985-52104836Lelio R Paula11/2016
52412^348224-20249104826Enzo Doria06/2013
5242(2^348217+2522)/2104824Stefano Morozzi09/2020
52432^348212-20105104823Enzo Doria06/2013
524424647^17898+17898^24647104819Hans Havermann10/2020
524520^80562+19104814Lelio R Paula12/2016
52462*10^104811-87104812Robert Price04/2018
52472^348149-20053104804Enzo Doria06/2013
52482^348095-171104788Lelio R Paula09/2011
524925383^13412+13412^25383104769Hans Havermann09/2020
52502^348003-20377104760Enzo Doria06/2013


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Created by  Henri Lifchitz & Renaud Lifchitz : October, 26 2000, last modification: December, 01 2021 22:29 (Time in France)

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