PRP Records

Probable Primes Top 10000

(300940 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 ?
700118^85619-95107476Lelio R Paula04/2017
7002(2^357013+2526)/2107472Stefano Morozzi09/2020
70033^225248-130107471Lelio R Paula03/2017
7004(5*2^356961+1)/143107455Lelio R Paula03/2014
700527029^9448+9448^27029107450Hans Havermann11/2020
70062^356935-18085107449Enzo Doria05/2013
700755396^87+87^55396107442Hans Havermann10/2020
7008(14*10^107439-137)/3107440Robert Price04/2021
7009164^48505-48505^164107432Norman Luhn09/2024
701010^107409+37107410Lelio R Paula02/2017
701110^107409-329633107409Patrick De Geest03/2017
7012(2^356799+3134)/2107407Stefano Morozzi09/2020
70132^356787-109027107404Enzo Doria04/2014
7014(2^356767+78557)/5107397Lelio R Paula12/2013
70153*10^107389+77107390Robert Price09/2018
7016(11*10^107385+61)/9107386Tyler Busby01/2023
70175^153622-42107378Lelio R Paula02/2017
70182^356699-97305107378Lelio R Paula03/2017
701913129^26072-26072^13129107371Norbert Schneider09/2022
70202^356654+85107364Lelio R Paula11/2011
70212^356641-19921107360Enzo Doria06/2013
70225*10^107355+11107356Robert Price08/2019
70232^356623-465107355Lelio R Paula03/2017
702419^83945-92107345Lelio R Paula02/2017
702525491^16246+16246^25491107337Hans Havermann11/2020
702610^107334+28149107335Patrick De Geest03/2017
702710^107334-83107334Lelio R Paula02/2017
70282^356518+885107323Lelio R Paula03/2017
7029(59*10^107322+391)/9107323Robert Price03/2021
7030(3*2^356506-1)/467107317Lelio R Paula03/2014
7031(2^356468+1162)/2107308Stefano Morozzi09/2020
70322^356442-114713107300Enzo Doria04/2015
70332^356425+72257107295Enzo Doria04/2016
70342^356351-112237107273Enzo Doria06/2014
7036(6^137845-11)/5107264Paul Bourdelais11/2011
70352^356322+74539107264Enzo Doria04/2016
70372^356274+1874479107250Enzo Doria06/2016
703824606^22819+22819^24606107241Hans Havermann10/2020
7039(2^356243+3686)/2107240Stefano Morozzi09/2020
704020^82422-93107234Lelio R Paula02/2017
70412^356157-20365107214Enzo Doria06/2013
70428*10^107209+99107210Robert Price03/2021
70432^356129-18949107206Enzo Doria05/2013
70442^356100-109587107197Enzo Doria04/2014
70452*10^107173-37107174Robert Price11/2021
7046(2^355978+3262)/2107160Stefano Morozzi02/2021
7047(31*2^355970+1)/5107159Lelio R Paula03/2014
70482^355968-64875107158Lelio R Paula01/2017
70492^355952+1870321107153Enzo Doria05/2016
705027069^9088+9088^27069107152Hans Havermann11/2020
70512^355915-117107142Lelio R Paula11/2011
7052(16*10^107140+77)/3107141Robert Price03/2019
705324628^22369+22369^24628107124Hans Havermann11/2020
7054(19*2^355838-1)/15107119Lelio R Paula03/2014
70553^224495-8107112Lelio R Paula12/2013
70563*10^107096+23107097Robert Price03/2022
705725077^18632+18632^25077107086Hans Havermann10/2020
70587^126691-44107067Lelio R Paula03/2017
70594^177830-8243107065Mike Oakes02/2011
7060(509*10^107057+13)/9107059Robert Price05/2022
70612^355604+214051107048Enzo Doria10/2023
7062(2^355562+1702)/2107035Stefano Morozzi09/2020
706310^107028+3593037107029Paul Bourdelais10/2021
706410^107028-43301107028Alfred Reich08/2024
70652^355524-21237107024Enzo Doria06/2013
7067(10223*2^355515+1)/4855107022Lelio R Paula07/2014
706624843^20320+20320^24843107022Hans Havermann10/2020
70682^355494-19901107015Enzo Doria06/2013
70692^355454-869688105107003Lelio R Paula01/2017
70704*10^106997+13106998Robert Price02/2021
7071(8*10^106985-629)/9106985Robert Price01/2022
70722^355366+54615106976Lelio R Paula01/2017
7073(31*2^355346-1)/1563106969Lelio R Paula03/2014
70742^355275-19861106949Enzo Doria06/2013
707527503^7738+7738^27503106949Hans Havermann11/2020
7076(85*10^106943+77)/9106944Robert Price07/2022
7077(9179*2^355234-1)/1915106937Lelio R Paula05/2015
70784*10^106914-93106915Robert Price07/2020
70794*10^106892-3106893Robert Price10/2015
7080(66^58741+1)/67106881Paul Bourdelais08/2017
70812^355001+335931106866Enzo Doria08/2024
70822^354946-3106850M. Frind & P. Underwood08/2002
7083(2^354945+3134)/2106849Stefano Morozzi09/2020
7084(46^64384+1)/(46^128+1)106843Martin Hopf12/2023
70852^354873-18693106828Enzo Doria05/2013
7086(2^354831+3186)/2106815Stefano Morozzi09/2020
70882^354828+4257106814Lelio R Paula01/2017
708725216^17217+17217^25216106814Hans Havermann10/2020
7089(2^354799+1218)/2106805Stefano Morozzi09/2020
7090436^40459+40459^436106791Norbert Schneider03/2019
7091(21^80761+1)/22106783Paul Bourdelais03/2010
7092(115*10^106772-7)/9106774Robert Price02/2020
70932^354640-354640+1106758Robert Price10/2014
7094(2^354603+2606)/2106746Stefano Morozzi09/2020
70952^354585+95106741Lelio R Paula10/2011
7096(206*10^106737+1)/9106739Robert Price04/2022
70972^354553+189106732Lelio R Paula10/2011
7099(2^354546+1338)/2106729Stefano Morozzi02/2021
7098(8*10^106729-71)/9106729Serge Batalov11/2022
71002^354514-109031106720Enzo Doria04/2014
71012^354509-109465106718Enzo Doria04/2014
7102fibonacci(510628)+2106715Jon Grantham08/2023
7103(15*2^354478-1)/26983106706Lelio R Paula03/2014
7104Phi(217618,10)/899798636917106693Makoto Kamada06/2019
710515^90710+28106684Lelio R Paula04/2017
71067^126237+34106683Lelio R Paula03/2017
71072^354385-115315106681Enzo Doria06/2015
71082^354327-19305106664Enzo Doria06/2013
7109(35*10^106649+1)/9106650Serge Batalov11/2010
711010^106636+97106637Lelio R Paula02/2017
711110^106636-22923106636Patrick De Geest03/2017
71122^354220-57106631Lelio R Paula10/2011
7113(68*10^106628-329)/9106629Robert Price03/2021
7114(29*10^106620-77)/3106621Robert Price02/2020
7115(746*10^106618+1)/9106620Robert Price03/2020
71162*10^106613+29106614Robert Price02/2021
71172^354157-17041106612Enzo Doria05/2013
711812^98778+73106600Lelio R Paula02/2017
711933333^1576+1576^33333106585Hans Havermann11/2020
71202^354064+1870651106584Enzo Doria05/2016
712124568^21779+21779^24568106577Hans Havermann11/2020
71222^353992-57106563Lelio R Paula10/2011
71239*10^106559+59106560Robert Price01/2020
71247*10^106553+27106554Robert Price11/2020
712528847^4938+4938^28847106548Hans Havermann10/2020
7126NSW(139160)106535Robert Price12/2018
7127f(278321)106535Robert Price07/2023
7128(7*10^106516+113)/3106517Robert Price02/2018
71292^353832-1853849106515Enzo Doria09/2015
7130(7^126037-1)/6106513Paul Bourdelais09/2008
71312^353794-18453106503Enzo Doria05/2013
7132(2^353761+2094)/2106493Stefano Morozzi09/2020
71332^353728+7695106483Lelio R Paula01/2017
713426476^10509+10509^26476106475Hans Havermann10/2020
71352^353672-303106466Yves Minet02/2012
71366^136811+101106460Lelio R Paula02/2017
71372^353641+1871981106457Enzo Doria05/2016
7138(8*10^106454-29)/3106455Robert Price07/2018
713927845^6654+6654^27845106454Hans Havermann11/2020
714010^106449-700001106449Robert Price08/2021
714125316^16017+16017^25316106444Hans Havermann11/2020
71422^353553+54615106431Lelio R Paula01/2017
71432^353544-18897106428Enzo Doria05/2013
714428894^4823+4823^28894106426Hans Havermann11/2020
7145(19*10^106422+29)/3106423Robert Price12/2021
7146(694*10^106418+53)/9106420Robert Price02/2022
71476*10^106412-13106413Robert Price07/2022
714825696^13829+13829^25696106402Hans Havermann11/2020
71496^136729-133106396Lelio R Paula02/2017
71502^353418+1605106390Lelio R Paula01/2017
71512^353387+65106381Lelio R Paula10/2011
71522^353372+74311106376Enzo Doria04/2016
71532^353344-3693106368Yves Minet03/2017
7154(772*10^106365-7)/9106367Robert Price06/2022
7155(56*10^106351+619)/9106352Robert Price05/2021
71562^353277-20089106347Enzo Doria06/2013
71572^353275+72173106347Enzo Doria04/2016
71582^353268-17705106345Enzo Doria05/2013
71592^353267-19857106344Enzo Doria06/2013
7160(46*10^106343+143)/9106344Robert Price01/2019
7161(2^353189+3054)/2106321Stefano Morozzi09/2020
716235087^1072+1072^35087106321Hans Havermann10/2020
7163(2^353184+1290)/2106319Stefano Morozzi01/2021
7164F(508799)/24738824977/1990778864897106310Serge Batalov07/2024
716526985^8684+8684^26985106287Hans Havermann10/2020
7166(2^353051+606)/2106279Stefano Morozzi09/2020
7168222748^3+3^222748106278Anatoly F. Selevich12/2010
7167(46*10^106277+107)/9106278Robert Price06/2022
7169(9179*2^353019-1)/9106273Lelio R Paula05/2015
71702^353025+72257106272Enzo Doria04/2016
71732^352932-20345106244Enzo Doria06/2013
7171(2^353011-3)/745325861246794515484535106244Lelio R Paula12/2013
717225628^13983+13983^25628106244Hans Havermann10/2020
71742^352883-187106229Lelio R Paula10/2011
717520^81649-19^81649106228Jean-Louis Charton03/2011
7176(55*10^106222+377)/9106223Robert Price02/2019
71772^352814-131106208Lelio R Paula10/2011
71782^352752+73951106189Enzo Doria04/2016
717911876*25^75945+357106171Eric Chen10/2023
71806^136434+5106167Lelio R Paula11/2014
718125296^15737+15737^25296106166Hans Havermann09/2020
71828*10^106157-13106158Robert Price08/2019
71832^352641+225677106156Enzo Doria08/2024
71847*5^151872-8106155Lelio R Paula11/2014
7185105^52520-2106153Lelio R Paula10/2017
7186(23*10^106152-29)/3106153Robert Price03/2022
71872^352601-1604809106144Enzo Doria05/2015
718812^98353-43106141Lelio R Paula02/2017
71892^352585-18901106139Enzo Doria05/2013
719026363^10614+10614^26363106135Hans Havermann09/2020
7191(2^352554-3)/193106128Lelio R Paula12/2013
71922^352540+15015106126Lelio R Paula01/2017
719325068^17119+17119^25068106125Hans Havermann09/2020
71942^352524-3149106121Yves Minet10/2014
7195(7*10^106119-67)/3106120Robert Price10/2021
71962^352486-1858781106109Enzo Doria04/2016
71972^352444+12705106097Lelio R Paula01/2017
719828561^5182+5182^28561106090Hans Havermann10/2020
7199(182*10^106083+43)/9106085Robert Price02/2020
7200(266*10^106066+1)/3106068Robert Price04/2020
7201(7*10^106066-187)/9106066Tyler Busby01/2023
72022^352228-18953106032Enzo Doria05/2013
7203(2^352223+1118)/2106030Stefano Morozzi09/2020
7204(2^352212+2250)/2106027Stefano Morozzi01/2021
7205(2^352136+2638)/2106004Stefano Morozzi09/2020
72062^352107+1872533105995Enzo Doria05/2016
7207(2^352096+2086)/2105992Stefano Morozzi09/2020
72082^352066-2591105983Yves Minet07/2014
72092^352030+715105972Lelio R Paula10/2011
72109*6^136176-5105967Lelio R Paula11/2014
721117099*2^351991+58329105965Paul Vanderveen12/2017
7212122^50789-50789^122105965Norman Luhn09/2024
721328582^5097+5097^28582105963Hans Havermann09/2020
7214155^48377+2105962Lelio R Paula08/2013
7215(23*10^105944-119)/3105945Robert Price07/2021
72162^351865+1869707105922Enzo Doria05/2016
721724974^17427+17427^24974105921Hans Havermann09/2020
721825163^16194+16194^25163105920Hans Havermann09/2020
72192^351831+23105912Lelio R Paula10/2011
7220(2^351818+3798)/2105908Stefano Morozzi02/2021
72219*2^351784-5105899Lelio R Paula09/2014
7222(2^351776+2766)/2105895Stefano Morozzi01/2021
7223(85*10^105881+203)/9105882Robert Price09/2020
72242^351671-112387105864Enzo Doria06/2014
72252^351669-109501105863Enzo Doria04/2014
72262^351644+74731105856Enzo Doria04/2016
722713^95025-42105853Lelio R Paula12/2016
72282^351599+15015105842Lelio R Paula01/2017
722919^82763+90105834Lelio R Paula01/2017
7230(205*10^105831-1)/3105833Robert Price11/2021
723126050^11551+11551^26050105832Hans Havermann09/2020
7232(9179*2^351540-1)/221105826Lelio R Paula05/2015
723320^81329-51105812Lelio R Paula01/2017
7234(5*10^105811+211)/9105811Robert Price02/2018
72352^351483+28425105807Lelio R Paula01/2017
723625231^15610+15610^25231105804Hans Havermann09/2020
723715^89960+86105802Lelio R Paula02/2017
72382^351460-17289105801Enzo Doria05/2013
723919^82735+22105798Lelio R Paula01/2017
72402^351435-109077105793Enzo Doria04/2014
72412^351393+1089105780Lelio R Paula01/2017
72422^351364+72631105772Enzo Doria04/2016
7243(2^351333+3626)/2105762Stefano Morozzi09/2020
724426818^8783+8783^26818105761Hans Havermann09/2020
72472^351305+1872467105754Enzo Doria05/2016
72463^221649+16105754Lelio R Paula11/2016
724532511^1790+1790^32511105754Hans Havermann09/2020
72488*3^221637-5105749Lelio R Paula09/2014
72492^351279-2780449105746Enzo Doria03/2016
7250(2^351263+3198)/2105741Stefano Morozzi09/2020


Find by discoverer :


Created by  Henri Lifchitz & Renaud Lifchitz : October, 26 2000, last modification: February, 10 2025 11:16 (Time in France)

Go back
Valid XHTML 1.0!    Valid CSS!