PRP Records

Probable Primes Top 10000

(277054 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 ?
40012^354385-115315106681Enzo Doria06/2015
40022^354327-19305106664Enzo Doria06/2013
4003(35*10^106649+1)/9106650Serge Batalov11/2010
400410^106636+97106637Lelio R Paula02/2017
400510^106636-22923106636Patrick De Geest03/2017
40062^354220-57106631Lelio R Paula10/2011
4007(29*10^106620-77)/3106621Robert Price02/2020
4008(746*10^106618+1)/9106620Robert Price03/2020
40092^354157-17041106612Enzo Doria05/2013
401012^98778+73106600Lelio R Paula02/2017
401133333^1576+1576^33333106585Hans Havermann11/2020
40122^354064+1870651106584Enzo Doria05/2016
401324568^21779+21779^24568106577Hans Havermann11/2020
40142^353992-57106563Lelio R Paula10/2011
40159*10^106559+59106560Robert Price01/2020
40167*10^106553+27106554Robert Price11/2020
401728847^4938+4938^28847106548Hans Havermann10/2020
4018NSW(139160)106535Robert Price12/2018
4019(7*10^106516+113)/3106517Robert Price02/2018
40202^353832-1853849106515Enzo Doria09/2015
4021(7^126037-1)/6106513Paul Bourdelais09/2008
40222^353794-18453106503Enzo Doria05/2013
4023(2^353761+2094)/2106493Stefano Morozzi09/2020
40242^353728+7695106483Lelio R Paula01/2017
402526476^10509+10509^26476106475Hans Havermann10/2020
40262^353672-303106466Yves Minet02/2012
40276^136811+101106460Lelio R Paula02/2017
40282^353641+1871981106457Enzo Doria05/2016
4029(8*10^106454-29)/3106455Robert Price07/2018
403027845^6654+6654^27845106454Hans Havermann11/2020
403125316^16017+16017^25316106444Hans Havermann11/2020
40322^353553+54615106431Lelio R Paula01/2017
40332^353544-18897106428Enzo Doria05/2013
403428894^4823+4823^28894106426Hans Havermann11/2020
403525696^13829+13829^25696106402Hans Havermann11/2020
40366^136729-133106396Lelio R Paula02/2017
40372^353418+1605106390Lelio R Paula01/2017
40382^353387+65106381Lelio R Paula10/2011
40392^353372+74311106376Enzo Doria04/2016
40402^353344-3693106368Yves Minet03/2017
40422^353277-20089106347Enzo Doria06/2013
40412^353275+72173106347Enzo Doria04/2016
40432^353268-17705106345Enzo Doria05/2013
40442^353267-19857106344Enzo Doria06/2013
4045(46*10^106343+143)/9106344Robert Price01/2019
4047(2^353189+3054)/2106321Stefano Morozzi09/2020
404635087^1072+1072^35087106321Hans Havermann10/2020
4048(2^353184+1290)/2106319Stefano Morozzi01/2021
404926985^8684+8684^26985106287Hans Havermann10/2020
4050(2^353051+606)/2106279Stefano Morozzi09/2020
4051222748^3+3^222748106278Anatoly F. Selevich12/2010
4052(9179*2^353019-1)/9106273Lelio R Paula05/2015
40532^353025+72257106272Enzo Doria04/2016
40562^352932-20345106244Enzo Doria06/2013
4055(2^353011-3)/745325861246794515484535106244Lelio R Paula12/2013
405425628^13983+13983^25628106244Hans Havermann10/2020
40572^352883-187106229Lelio R Paula10/2011
405820^81649-19^81649106228Jean-Louis Charton03/2011
4059(55*10^106222+377)/9106223Robert Price02/2019
40602^352814-131106208Lelio R Paula10/2011
40612^352752+73951106189Enzo Doria04/2016
40626^136434+5106167Lelio R Paula11/2014
406325296^15737+15737^25296106166Hans Havermann09/2020
40648*10^106157-13106158Robert Price08/2019
40657*5^151872-8106155Lelio R Paula11/2014
4066105^52520-2106153Lelio R Paula10/2017
40672^352601-1604809106144Enzo Doria05/2015
406812^98353-43106141Lelio R Paula02/2017
40692^352585-18901106139Enzo Doria05/2013
407026363^10614+10614^26363106135Hans Havermann09/2020
4071(2^352554-3)/193106128Lelio R Paula12/2013
40722^352540+15015106126Lelio R Paula01/2017
407325068^17119+17119^25068106125Hans Havermann09/2020
40742^352524-3149106121Yves Minet10/2014
40752^352486-1858781106109Enzo Doria04/2016
40762^352444+12705106097Lelio R Paula01/2017
407728561^5182+5182^28561106090Hans Havermann10/2020
4078(182*10^106083+43)/9106085Robert Price02/2020
4079(266*10^106066+1)/3106068Robert Price04/2020
40802^352228-18953106032Enzo Doria05/2013
4081(2^352223+1118)/2106030Stefano Morozzi09/2020
4082(2^352212+2250)/2106027Stefano Morozzi01/2021
4083(2^352136+2638)/2106004Stefano Morozzi09/2020
40842^352107+1872533105995Enzo Doria05/2016
4085(2^352096+2086)/2105992Stefano Morozzi09/2020
40862^352066-2591105983Yves Minet07/2014
40872^352030+715105972Lelio R Paula10/2011
40889*6^136176-5105967Lelio R Paula11/2014
408917099*2^351991+58329105965Paul Vanderveen12/2017
409028582^5097+5097^28582105963Hans Havermann09/2020
4091155^48377+2105962Lelio R Paula08/2013
40922^351865+1869707105922Enzo Doria05/2016
409324974^17427+17427^24974105921Hans Havermann09/2020
409425163^16194+16194^25163105920Hans Havermann09/2020
40952^351831+23105912Lelio R Paula10/2011
40969*2^351784-5105899Lelio R Paula09/2014
4097(2^351776+2766)/2105895Stefano Morozzi01/2021
4098(85*10^105881+203)/9105882Robert Price09/2020
40992^351671-112387105864Enzo Doria06/2014
41002^351669-109501105863Enzo Doria04/2014
41012^351644+74731105856Enzo Doria04/2016
410213^95025-42105853Lelio R Paula12/2016
41032^351599+15015105842Lelio R Paula01/2017
410419^82763+90105834Lelio R Paula01/2017
410526050^11551+11551^26050105832Hans Havermann09/2020
4106(9179*2^351540-1)/221105826Lelio R Paula05/2015
410720^81329-51105812Lelio R Paula01/2017
4108(5*10^105811+211)/9105811Robert Price02/2018
41092^351483+28425105807Lelio R Paula01/2017
411025231^15610+15610^25231105804Hans Havermann09/2020
411115^89960+86105802Lelio R Paula02/2017
41122^351460-17289105801Enzo Doria05/2013
411319^82735+22105798Lelio R Paula01/2017
41142^351435-109077105793Enzo Doria04/2014
41152^351393+1089105780Lelio R Paula01/2017
41162^351364+72631105772Enzo Doria04/2016
4117(2^351333+3626)/2105762Stefano Morozzi09/2020
411826818^8783+8783^26818105761Hans Havermann09/2020
41212^351305+1872467105754Enzo Doria05/2016
41203^221649+16105754Lelio R Paula11/2016
411932511^1790+1790^32511105754Hans Havermann09/2020
41228*3^221637-5105749Lelio R Paula09/2014
41232^351279-2780449105746Enzo Doria03/2016
4124(2^351263+3198)/2105741Stefano Morozzi09/2020
412515^89903-26105735Lelio R Paula02/2017
41272^351213-73105726Lelio R Paula10/2011
4126(2^351214+1210)/2105726Stefano Morozzi09/2020
41282^351192-4589105720Yves Minet07/2011
412920^81250-33105709Lelio R Paula12/2016
4130(2^351133+3530)/2105702Stefano Morozzi09/2020
4131(2^351103+534)/2105693Stefano Morozzi09/2020
41322^351076-113159105685Enzo Doria07/2014
413393^53688-2105684Lelio R Paula09/2013
41342^351060-4559105680Yves Minet07/2011
4135((10^52836-1)*10000/9+5927)*10^52836+(10^52836-1)/9105676Hans Havermann08/2019
413611^101473-750105674Enzo Doria11/2012
41373*5^151181-8105672Lelio R Paula11/2014
413815^89831-34105650Lelio R Paula02/2017
414011^101448-360105648Enzo Doria08/2012
41393*7^125011+4105648Lelio R Paula11/2014
41412^350943-113269105645Enzo Doria07/2014
41422*10^105636-91105637Robert Price04/2020
414324231^22880+22880^24231105634Hans Havermann09/2020
414435296^983+983^35296105626Hans Havermann09/2020
41452^350868-19725105622Enzo Doria06/2013
41462^350858-59291105619Enzo Doria10/2015
41472^350851+135105617Lelio R Paula10/2011
41482^350841-741105614Lelio R Paula01/2017
41493*10^105582+77105583Robert Price09/2018
415024915^17284+17284^24915105581Hans Havermann09/2020
4151(5*10^105576-53)/3105577Robert Price09/2020
41528*10^105571+3105572Robert Price08/2015
41532^350674-78557105564Jorge Menendez03/2018
41542*5^151026-3105563Lelio R Paula11/2014
4155(2^350702+5)/34264674063105562Lelio R Paula12/2013
41566^135647-5^135647105554Jean-Louis Charton02/2009
41573^221211+236105545Lelio R Paula11/2016
4158(32*10^105530-77)/9105531Robert Price06/2018
415910^105515+33105516Lelio R Paula11/2016
416024644^19125+19125^24644105516Hans Havermann10/2020
416110^105515-41033105515Patrick De Geest12/2016
4162(29*2^350473-1)/267927105499Lelio R Paula03/2014
416317^85732-72105489Lelio R Paula01/2017
4164(2^350399+3618)/2105481Stefano Morozzi09/2020
4165(2^350379+1010)/2105475Stefano Morozzi09/2020
416625233^15118+15118^25233105462Hans Havermann09/2020
416726261^10366+10366^26261105454Hans Havermann09/2020
41682^350307-110329105453Enzo Doria05/2014
41692^350253-20365105437Enzo Doria06/2013
4170(3*29^72089-1075)/4105423Curtis Bright05/2015
4171(2^350187+2658)/2105417Stefano Morozzi09/2020
41722^350139-109009105403Enzo Doria04/2014
4173(2^350129+3026)/2105400Stefano Morozzi09/2020
4174(2^350097+2070)/2105390Stefano Morozzi09/2020
41753*5^150763+4105380Lelio R Paula11/2014
417612^97643+91105375Lelio R Paula02/2017
41776*5^150744-7105367Lelio R Paula11/2014
4178(2^350018+2074)/2105366Stefano Morozzi09/2020
41794*10^105364-39105365Robert Price09/2020
41812^349996-112169105360Enzo Doria06/2014
4180(2^349997+3702)/2105360Stefano Morozzi09/2020
4182(418*10^105343+23)/9105345Robert Price02/2020
418325490^13563+13563^25490105334Hans Havermann10/2020
418411^101142-1080105329Enzo Doria12/2012
4185(68*10^105320-41)/9105321Robert Price10/2013
418624800^17649+17649^24800105319Hans Havermann09/2020
41873^220712-9934105307Enzo Doria05/2014
41887*10^105296+9105297Robert Price09/2015
418989*10^105284-7105286Robert Price04/2020
41902^349739+1873373105282Enzo Doria06/2016
41917^124574+24105278Lelio R Paula11/2016
41922^349708-20957105273Enzo Doria06/2013
419334115^1218+1218^34115105267Hans Havermann09/2020
41942^349649-20469105255Enzo Doria06/2013
41952^349607-20109105243Enzo Doria06/2013
4196(85*10^105242+473)/9105243Robert Price01/2020
41972^349594-19085105239Enzo Doria05/2013
41982^349530+1874479105220Enzo Doria06/2016
4199(3^220528+8)/8081105215Lelio R Paula12/2013
4200(2^349452+3570)/2105196Stefano Morozzi09/2020
42013^220464-112852105189Enzo Doria07/2014
42022^349419-17349105186Enzo Doria05/2013
42032^349400-2579105180Yves Minet07/2014
42048*5^150471+3105176Lelio R Paula11/2014
4205655^37342+37342^655105165Norbert Schneider08/2018
420613^94403+94105160Lelio R Paula12/2016
42072^349301-112309105151Enzo Doria06/2014
420830291^2960+2960^30291105149Hans Havermann09/2020
420927350^6981+6981^27350105132Hans Havermann09/2020
42119*2^349220+5105127Lelio R Paula09/2014
4210(2^349225+3122)/2105127Stefano Morozzi09/2020
42127*3^220317+8105119Lelio R Paula09/2014
42147^124386+88105119Lelio R Paula11/2016
4213(2^349197+570)/2105119Stefano Morozzi09/2020
42152^349171-19657105111Enzo Doria06/2013
4216(2^349115+590)/2105094Stefano Morozzi09/2020
4217(2^(6*58185+1)-5)/3105093Kevin Acres11/2013
4218(2^349111-5)/3105093Lelio R Paula12/2013
4219675^37142+37142^675105087Norbert Schneider08/2018
42202^348981-2797573105054Enzo Doria04/2016
42212^348869-6555105021Lelio R Paula01/2017
42225^150217+78104998Lelio R Paula11/2016
4223(88*10^104989-1)/3104991Robert Price04/2020
4224(28*10^104972+149)/3104973Robert Price12/2019
422524927^16262+16262^24927104972Hans Havermann10/2020
42262^348703-113005104971Enzo Doria06/2014
42282^348612-809104943Yves Minet05/2013
4227(73*10^104942-1)/9104943Robert Price01/2015
42292^348583-350407104934Enzo Doria06/2015
42302^348531-949104919Yves Minet05/2012
423120^80636-59104910Lelio R Paula12/2016
42328*10^104893-13104894Robert Price08/2019
42342^348437+35104890Lelio R Paula09/2011
423325208^14487+14487^25208104890Hans Havermann09/2020
42352^348348+135104864Lelio R Paula09/2011
42366*10^104852-31104853Robert Price07/2020
4238(2^348284+9)/25104843Lelio R Paula12/2013
423775^55914-74104843Norbert Schneider01/2015
42392^348268+255255104840Lelio R Paula01/2017
424035540^891+891^35540104839Hans Havermann09/2020
42415^149985-52104836Lelio R Paula11/2016
42422^348224-20249104826Enzo Doria06/2013
4243(2^348217+2522)/2104824Stefano Morozzi09/2020
42442^348212-20105104823Enzo Doria06/2013
424524647^17898+17898^24647104819Hans Havermann10/2020
424620^80562+19104814Lelio R Paula12/2016
42472*10^104811-87104812Robert Price04/2018
42482^348149-20053104804Enzo Doria06/2013
42492^348095-171104788Lelio R Paula09/2011
425025383^13412+13412^25383104769Hans Havermann09/2020


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Created by  Henri Lifchitz & Renaud Lifchitz : October, 26 2000, last modification: January, 25 2021 11:23 (Time in France)

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