PRP Records

Probable Primes Top 10000

(294687 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) !!!


Submit your PRPs


See the Top discoverers
See the Latest PRPs
Search by form



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 ?
65012^353268-17705106345Enzo Doria05/2013
65022^353267-19857106344Enzo Doria06/2013
6503(46*10^106343+143)/9106344Robert Price01/2019
6504(2^353189+3054)/2106321Stefano Morozzi09/2020
650535087^1072+1072^35087106321Hans Havermann10/2020
6506(2^353184+1290)/2106319Stefano Morozzi01/2021
650726985^8684+8684^26985106287Hans Havermann10/2020
6508(2^353051+606)/2106279Stefano Morozzi09/2020
6510222748^3+3^222748106278Anatoly F. Selevich12/2010
6509(46*10^106277+107)/9106278Robert Price06/2022
6511(9179*2^353019-1)/9106273Lelio R Paula05/2015
65122^353025+72257106272Enzo Doria04/2016
65152^352932-20345106244Enzo Doria06/2013
6513(2^353011-3)/745325861246794515484535106244Lelio R Paula12/2013
651425628^13983+13983^25628106244Hans Havermann10/2020
65162^352883-187106229Lelio R Paula10/2011
651720^81649-19^81649106228Jean-Louis Charton03/2011
6518(55*10^106222+377)/9106223Robert Price02/2019
65192^352814-131106208Lelio R Paula10/2011
65202^352752+73951106189Enzo Doria04/2016
652111876*25^75945+357106171Eric Chen10/2023
65226^136434+5106167Lelio R Paula11/2014
652325296^15737+15737^25296106166Hans Havermann09/2020
65248*10^106157-13106158Robert Price08/2019
65257*5^151872-8106155Lelio R Paula11/2014
6526105^52520-2106153Lelio R Paula10/2017
6527(23*10^106152-29)/3106153Robert Price03/2022
65282^352601-1604809106144Enzo Doria05/2015
652912^98353-43106141Lelio R Paula02/2017
65302^352585-18901106139Enzo Doria05/2013
653126363^10614+10614^26363106135Hans Havermann09/2020
6532(2^352554-3)/193106128Lelio R Paula12/2013
65332^352540+15015106126Lelio R Paula01/2017
653425068^17119+17119^25068106125Hans Havermann09/2020
65352^352524-3149106121Yves Minet10/2014
6536(7*10^106119-67)/3106120Robert Price10/2021
65372^352486-1858781106109Enzo Doria04/2016
65382^352444+12705106097Lelio R Paula01/2017
653928561^5182+5182^28561106090Hans Havermann10/2020
6540(182*10^106083+43)/9106085Robert Price02/2020
6541(266*10^106066+1)/3106068Robert Price04/2020
6542(7*10^106066-187)/9106066Tyler Busby01/2023
65432^352228-18953106032Enzo Doria05/2013
6544(2^352223+1118)/2106030Stefano Morozzi09/2020
6545(2^352212+2250)/2106027Stefano Morozzi01/2021
6546(2^352136+2638)/2106004Stefano Morozzi09/2020
65472^352107+1872533105995Enzo Doria05/2016
6548(2^352096+2086)/2105992Stefano Morozzi09/2020
65492^352066-2591105983Yves Minet07/2014
65502^352030+715105972Lelio R Paula10/2011
65519*6^136176-5105967Lelio R Paula11/2014
655217099*2^351991+58329105965Paul Vanderveen12/2017
655328582^5097+5097^28582105963Hans Havermann09/2020
6554155^48377+2105962Lelio R Paula08/2013
6555(23*10^105944-119)/3105945Robert Price07/2021
65562^351865+1869707105922Enzo Doria05/2016
655724974^17427+17427^24974105921Hans Havermann09/2020
655825163^16194+16194^25163105920Hans Havermann09/2020
65592^351831+23105912Lelio R Paula10/2011
6560(2^351818+3798)/2105908Stefano Morozzi02/2021
65619*2^351784-5105899Lelio R Paula09/2014
6562(2^351776+2766)/2105895Stefano Morozzi01/2021
6563(85*10^105881+203)/9105882Robert Price09/2020
65642^351671-112387105864Enzo Doria06/2014
65652^351669-109501105863Enzo Doria04/2014
65662^351644+74731105856Enzo Doria04/2016
656713^95025-42105853Lelio R Paula12/2016
65682^351599+15015105842Lelio R Paula01/2017
656919^82763+90105834Lelio R Paula01/2017
6570(205*10^105831-1)/3105833Robert Price11/2021
657126050^11551+11551^26050105832Hans Havermann09/2020
6572(9179*2^351540-1)/221105826Lelio R Paula05/2015
657320^81329-51105812Lelio R Paula01/2017
6574(5*10^105811+211)/9105811Robert Price02/2018
65752^351483+28425105807Lelio R Paula01/2017
657625231^15610+15610^25231105804Hans Havermann09/2020
657715^89960+86105802Lelio R Paula02/2017
65782^351460-17289105801Enzo Doria05/2013
657919^82735+22105798Lelio R Paula01/2017
65802^351435-109077105793Enzo Doria04/2014
65812^351393+1089105780Lelio R Paula01/2017
65822^351364+72631105772Enzo Doria04/2016
6583(2^351333+3626)/2105762Stefano Morozzi09/2020
658426818^8783+8783^26818105761Hans Havermann09/2020
65872^351305+1872467105754Enzo Doria05/2016
65863^221649+16105754Lelio R Paula11/2016
658532511^1790+1790^32511105754Hans Havermann09/2020
65888*3^221637-5105749Lelio R Paula09/2014
65892^351279-2780449105746Enzo Doria03/2016
6590(2^351263+3198)/2105741Stefano Morozzi09/2020
659115^89903-26105735Lelio R Paula02/2017
65932^351213-73105726Lelio R Paula10/2011
6592(2^351214+1210)/2105726Stefano Morozzi09/2020
65942^351192-4589105720Yves Minet07/2011
659520^81250-33105709Lelio R Paula12/2016
6596(2^351133+3530)/2105702Stefano Morozzi09/2020
6597(2^351103+534)/2105693Stefano Morozzi09/2020
65982^351076-113159105685Enzo Doria07/2014
659993^53688-2105684Lelio R Paula09/2013
66002^351060-4559105680Yves Minet07/2011
6601((10^52836-1)*10000/9+5927)*10^52836+(10^52836-1)/9105676Hans Havermann08/2019
660211^101473-750105674Enzo Doria11/2012
66033*5^151181-8105672Lelio R Paula11/2014
660415^89831-34105650Lelio R Paula02/2017
660611^101448-360105648Enzo Doria08/2012
66053*7^125011+4105648Lelio R Paula11/2014
66072^350943-113269105645Enzo Doria07/2014
66082*10^105636-91105637Robert Price04/2020
660924231^22880+22880^24231105634Hans Havermann09/2020
661035296^983+983^35296105626Hans Havermann09/2020
66112^350868-19725105622Enzo Doria06/2013
66122^350858-59291105619Enzo Doria10/2015
66132^350851+135105617Lelio R Paula10/2011
66142^350841-741105614Lelio R Paula01/2017
66153*10^105582+77105583Robert Price09/2018
661624915^17284+17284^24915105581Hans Havermann09/2020
6617(5*10^105576-53)/3105577Robert Price09/2020
66188*10^105571+3105572Robert Price08/2015
66192^350674-78557105564Jorge Menendez03/2018
66202*5^151026-3105563Lelio R Paula11/2014
6621(2^350702+5)/34264674063105562Lelio R Paula12/2013
66226^135647-5^135647105554Jean-Louis Charton02/2009
66233^221211+236105545Lelio R Paula11/2016
6624(32*10^105530-77)/9105531Robert Price06/2018
662510^105515+33105516Lelio R Paula11/2016
662624644^19125+19125^24644105516Hans Havermann10/2020
662710^105515-41033105515Patrick De Geest12/2016
6628(29*2^350473-1)/267927105499Lelio R Paula03/2014
66292^350455-430567105498Harrison Mesh06/2022
663017^85732-72105489Lelio R Paula01/2017
6631(2^350399+3618)/2105481Stefano Morozzi09/2020
6632(2^350379+1010)/2105475Stefano Morozzi09/2020
66332^350356+24241105468Enzo Doria10/2023
663425233^15118+15118^25233105462Hans Havermann09/2020
663526261^10366+10366^26261105454Hans Havermann09/2020
66362^350307-110329105453Enzo Doria05/2014
66372^350253-20365105437Enzo Doria06/2013
6638(3*29^72089-1075)/4105423Curtis Bright05/2015
6639(2^350187+2658)/2105417Stefano Morozzi09/2020
66404*10^105415-69105416Robert Price01/2022
6641(22*10^105407+179)/3105408Robert Price02/2022
66422^350139-109009105403Enzo Doria04/2014
6643(2^350129+3026)/2105400Stefano Morozzi09/2020
6644(2^350097+2070)/2105390Stefano Morozzi09/2020
66453*5^150763+4105380Lelio R Paula11/2014
664612^97643+91105375Lelio R Paula02/2017
66476*5^150744-7105367Lelio R Paula11/2014
6648(2^350018+2074)/2105366Stefano Morozzi09/2020
66494*10^105364-39105365Robert Price09/2020
66512^349996-112169105360Enzo Doria06/2014
6650(2^349997+3702)/2105360Stefano Morozzi09/2020
6652(418*10^105343+23)/9105345Robert Price02/2020
665325490^13563+13563^25490105334Hans Havermann10/2020
665411^101142-1080105329Enzo Doria12/2012
6655(68*10^105320-41)/9105321Robert Price10/2013
665624800^17649+17649^24800105319Hans Havermann09/2020
66573^220712-9934105307Enzo Doria05/2014
66587*10^105296+9105297Robert Price09/2015
665989*10^105284-7105286Robert Price04/2020
66602^349739+1873373105282Enzo Doria06/2016
66617^124574+24105278Lelio R Paula11/2016
66622^349708-20957105273Enzo Doria06/2013
666334115^1218+1218^34115105267Hans Havermann09/2020
66642^349649-20469105255Enzo Doria06/2013
66652^349607-20109105243Enzo Doria06/2013
6666(85*10^105242+473)/9105243Robert Price01/2020
66672^349594-19085105239Enzo Doria05/2013
66682^349530+1874479105220Enzo Doria06/2016
6669(3^220528+8)/8081105215Lelio R Paula12/2013
6670(106*10^105199+17)/3105201Robert Price04/2021
6671(2^349452+3570)/2105196Stefano Morozzi09/2020
66723^220464-112852105189Enzo Doria07/2014
66732^349419-17349105186Enzo Doria05/2013
66742^349400-2579105180Yves Minet07/2014
66758*5^150471+3105176Lelio R Paula11/2014
6676(2^349359+2298)/2105168Stefano Morozzi02/2021
6677655^37342+37342^655105165Norbert Schneider08/2018
667813^94403+94105160Lelio R Paula12/2016
66792^349301-112309105151Enzo Doria06/2014
668030291^2960+2960^30291105149Hans Havermann09/2020
668127350^6981+6981^27350105132Hans Havermann09/2020
66839*2^349220+5105127Lelio R Paula09/2014
6682(2^349225+3122)/2105127Stefano Morozzi09/2020
66847*3^220317+8105119Lelio R Paula09/2014
66857^124386+88105119Lelio R Paula11/2016
6686(2^349197+570)/2105119Stefano Morozzi09/2020
66872^349171-19657105111Enzo Doria06/2013
6688(2^349115+590)/2105094Stefano Morozzi09/2020
6689(2^(6*58185+1)-5)/3105093Kevin Acres11/2013
6690(2^349111-5)/3105093Lelio R Paula12/2013
6691675^37142+37142^675105087Norbert Schneider08/2018
66922^348981-2797573105054Enzo Doria04/2016
66932^348869-6555105021Lelio R Paula01/2017
66945^150217+78104998Lelio R Paula11/2016
6695(88*10^104989-1)/3104991Robert Price04/2020
6696(28*10^104972+149)/3104973Robert Price12/2019
669724927^16262+16262^24927104972Hans Havermann10/2020
66982^348703-113005104971Enzo Doria06/2014
6699(191*10^104956-17)/3104958Robert Price11/2021
67012^348612-809104943Yves Minet05/2013
6700(73*10^104942-1)/9104943Robert Price01/2015
67022^348583-350407104934Enzo Doria06/2015
67032^348531-949104919Yves Minet05/2012
670420^80636-59104910Lelio R Paula12/2016
67058*10^104893-13104894Robert Price08/2019
67072^348437+35104890Lelio R Paula09/2011
670625208^14487+14487^25208104890Hans Havermann09/2020
67082^348348+135104864Lelio R Paula09/2011
6709(29*10^104858+349)/9104859Robert Price06/2021
67106*10^104852-31104853Robert Price07/2020
6712(2^348284+9)/25104843Lelio R Paula12/2013
671175^55914-74104843Norbert Schneider01/2015
67132^348268+255255104840Lelio R Paula01/2017
671435540^891+891^35540104839Hans Havermann09/2020
67155^149985-52104836Lelio R Paula11/2016
67162^348224-20249104826Enzo Doria06/2013
6717(2^348217+2522)/2104824Stefano Morozzi09/2020
67182^348212-20105104823Enzo Doria06/2013
671924647^17898+17898^24647104819Hans Havermann10/2020
672020^80562+19104814Lelio R Paula12/2016
67212*10^104811-87104812Robert Price04/2018
67222^348149-20053104804Enzo Doria06/2013
67232^348095-171104788Lelio R Paula09/2011
672425383^13412+13412^25383104769Hans Havermann09/2020
67252^348003-20377104760Enzo Doria06/2013
67262^347994-741104757Lelio R Paula12/2016
6727(2^347993+2234)/2104757Stefano Morozzi01/2021
6728(2^347990+790)/2104756Stefano Morozzi09/2020
672925137^14702+14702^25137104756Hans Havermann09/2020
6730(13*2^347972-1)/282309104746Lelio R Paula03/2014
673112883^25484-25484^12883104740Norbert Schneider08/2022
67322^347910-109937104732Enzo Doria04/2014
6733(88*10^104709-637)/9104710Robert Price11/2020
6734(13*10^104702+71)/3104703Robert Price06/2021
67355^149794+28104702Lelio R Paula11/2016
6736105^51800-2104698Lelio R Paula10/2017
6737(16^86939+3^86939)/19104684Robert Price06/2013
6738(15^89009-1)/14104682Paul Bourdelais03/2010
67392^347731-18609104678Enzo Doria05/2013
67404*6^134519+7104677Lelio R Paula11/2014
6741(34*10^104672-259)/9104673Robert Price12/2021
674225321^13588+13588^25321104656Hans Havermann09/2020
67432^347625+5367104646Riley Fisher04/2023
67442^347612-18545104642Enzo Doria05/2013
67476^134465+95104635Lelio R Paula11/2016
6745(2^347588+3718)/2104635Stefano Morozzi09/2020
6746(166*10^104633-7)/3104635Robert Price11/2020
67482^347517-17301104614Enzo Doria05/2013
6749(2^347493+3186)/2104606Stefano Morozzi09/2020
6750(2^347490+2574)/2104605Stefano Morozzi09/2020


Find by discoverer :


Created by  Henri Lifchitz & Renaud Lifchitz : October, 26 2000, last modification: March, 27 2024 11:51 (Time in France)

Go back
Valid XHTML 1.0!    Valid CSS!