PRP Records

Probable Primes Top 10000

(295149 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 ?
4751(167*10^126637-17)/3126639Robert Price03/2020
47524*10^126625+87126626Robert Price08/2018
4753(31*2^420556+1)/7126601Lelio R Paula05/2014
47547*10^126600-99126601Robert Price06/2019
47552^420424-59189126561Enzo Doria10/2015
475628717^25534+25534^28717126560Hans Havermann03/2021
4757(86*10^126542+103)/9126543Robert Price12/2021
4758(19*10^126517-7)/3126518Robert Price12/2023
475928922^23655+23655^28922126503Hans Havermann03/2021
47602^420126+71893126471Enzo Doria04/2016
476125982^28643-28643^25982126450Frank Doornink03/2024
4762(43*10^126441+47)/9126442Robert Price12/2018
47638*10^126408+71126409Robert Price05/2022
47642^419866+1877059126393Enzo Doria07/2016
476529315^20484+20484^29315126390Hans Havermann03/2021
476629433^19676+19676^29433126384Hans Havermann03/2021
4767F(604711)126377Henri Lifchitz02/2005
47682^419757+72707126360Enzo Doria04/2016
47692^419720-21569126349Enzo Doria07/2013
47702^419637+29126324Henri Lifchitz02/2006
477131004^11865+11865^31004126319Hans Havermann03/2021
47722^419612+1876741126316Enzo Doria07/2016
47732^419520+2793271126289Enzo Doria03/2016
4774(2^419447-5)/369126264Lelio R Paula05/2014
47752^419328-1859939126231Enzo Doria03/2016
47762^419282-1851507126217Enzo Doria08/2015
4777(133*10^126212+17)/3126214Robert Price11/2021
47782^419251+1866143126208Enzo Doria03/2016
477911^121185+2126202Robert Price05/2014
478028203^28352+28352^28203126175Norbert Schneider01/2021
4781(23*2^419036-1)/1393126141Lelio R Paula05/2014
47822^418851+23126087Robert Price09/2015
4783(2^418849-9)/2681126083Lelio R Paula05/2014
47842^418829+167126081Lelio R Paula01/2012
478531037^11530+11530^31037126067Hans Havermann03/2021
47864*10^126064-69126065Robert Price01/2022
4787(31*2^418782-1)/75891126063Lelio R Paula05/2014
4788(19*2^418754-1)/15126058Lelio R Paula05/2014
4789(35*10^126048-323)/9126049Robert Price10/2021
479033016^6551+6551^33016126000Hans Havermann03/2021
47912^418548-111546435125996Paul Bourdelais10/2021
479225134^28625-28625^25134125958Frank Doornink12/2023
479334736^4227+4227^34736125954Hans Havermann03/2021
479426197^28502-28502^26197125930Frank Doornink03/2024
47952^418319-109501125927Enzo Doria04/2014
47962^418316-112373125926Enzo Doria06/2014
479740398^1309+1309^40398125919Hans Havermann03/2021
4798(8*10^125894-29)/3125895Robert Price07/2018
4799(26*10^125886-413)/9125887Robert Price05/2018
480010^(2*62938+1)-7*10^62938-1125877Robert Price07/2023
480155*10^125847+9125849Robert Price03/2022
48024*10^125832+57125833Robert Price05/2022
48032^417968+1869811125821Enzo Doria06/2016
48042^417902+63125802Lelio R Paula09/2015
4805(10^125792-91)/9125792Serge Batalov12/2014
480630438^13573+13573^30438125791Hans Havermann03/2021
480732867^6714+6714^32867125782Hans Havermann03/2021
480831155^10892+10892^31155125777Hans Havermann03/2021
4809(35*10^125754-593)/9125755Robert Price07/2018
481030455^13464+13464^30455125754Hans Havermann03/2021
4811(32*10^125751-77)/9125752Robert Price06/2018
48122^417704+77011125742Enzo Doria05/2016
481329755^16816+16816^29755125737Hans Havermann03/2021
4814(22*10^125734+203)/9125735Robert Price10/2021
481529918^15915+15915^29918125710Hans Havermann03/2021
4816(10^125706+149)/3125706Serge Batalov12/2014
481728531^25368+25368^28531125659Hans Havermann03/2021
48182^417419-115309125656Enzo Doria07/2015
4819(46*10^125642+593)/9125643Robert Price04/2022
48202^417315+213953125625Enzo Doria10/2023
48212^417300+77281125620Enzo Doria05/2016
482230638^12537+12537^30638125561Hans Havermann03/2021
48232^417095-1657125559Yves Minet07/2014
482430162^14525+14525^30162125538Hans Havermann03/2021
4825(56*10^125535+583)/9125536Robert Price08/2021
4826(23*10^125517-179)/3125518Robert Price06/2022
48279*10^125516+29125517Robert Price03/2022
4828(88*10^125492-637)/9125493Robert Price11/2020
482928958^21525+21525^28958125474Hans Havermann02/2021
48322^416773-25125462Lelio R Paula09/2015
4830(10^125482+7)/162685667/1639829194459125462Alfred Reich07/2021
483126078^28409-28409^26078125462Frank Doornink03/2024
483333889^5032+5032^33889125449Hans Havermann03/2021
4834(289511#+292834)/(2^3*146417)125444Makoto Morimoto10/2017
4835(2861^36481+1)/(2861^191+1)125438Martin Hopf12/2023
4836(11*2^416691+1)/43125436Lelio R Paula05/2014
4837(289511#+1896)/(2*3^3*79*780193*9911849)125434Makoto Morimoto06/2019
48382^416641-2*416641+1125422Robert Price05/2018
483933392^5697+5697^33392125409Hans Havermann03/2021
4840(21*2^416566-1)/17125399Lelio R Paula05/2014
48412^416530+1870429125389Enzo Doria05/2016
4842(56*10^125385+691)/9125386Robert Price05/2019
484327953^28198+28198^27953125381Norbert Schneider01/2021
484431074^10837+10837^31074125381Hans Havermann03/2021
484533745^5194+5194^33745125380Hans Havermann03/2021
48462^416490+1875109125376Enzo Doria09/2016
484728360^26331+26331^28360125365Hans Havermann03/2021
48482^416416-114929125354Enzo Doria05/2015
484925805^28412-28412^25805125346Frank Doornink03/2024
4850(77*10^125330-293)/9125331Robert Price09/2019
4851(172*10^125292-1)/9125294Serge Batalov12/2014
48522^416134+1865899125269Enzo Doria03/2016
4853153^57337-152125264Norbert Schneider12/2018
4854(599*10^125224+13)/9125226Robert Price02/2022
4855(9*2^415992+1)/13560845125220Lelio R Paula05/2014
485630054^14657+14657^30054125207Hans Havermann03/2021
4857(23^91943-1)/22125201Robert Price01/2012
48582^415884-933075125194Paul Bourdelais06/2021
485943125^27010-106125185Enzo Doria08/2012
4860(38*10^125166+349)/9125167Robert Price10/2018
486110^125166-5001125166Robert Price12/2021
48622^415765-112603125158Enzo Doria06/2014
48638*10^125088-13125089Robert Price08/2019
4864(25*10^125076-13)/3125077Robert Price09/2019
4865(11*10^125054+73)/3125055Robert Price08/2021
4866(29*10^125021-113)/3125022Robert Price10/2019
48672^415290-113591125015Enzo Doria08/2014
48682^415276-460919125011Enzo Doria06/2015
48692^415259+77243125006Enzo Doria05/2016
4870(67*10^124990+77)/9124991Robert Price10/2021
48712^415144-3683124971Yves Minet10/2011
48722^415092+111546435124956Paul Bourdelais10/2021
487331936^8173+8173^31936124946Hans Havermann03/2021
487427458^28145-28145^27458124927Frank Doornink03/2024
48755^178715-4124917Tyler NeSmith07/2021
487629767^15700+15700^29767124900Hans Havermann03/2021
48772^414874+79124890Lelio R Paula01/2015
487825292^28361-28361^25292124874Frank Doornink01/2024
4879(2^414765+7)/1389124854Lelio R Paula05/2014
48802^414618+79459124813Enzo Doria06/2016
4881(61*10^124809-1)/3124811Robert Price01/2020
4882(29*10^124765-71)/3124766Robert Price07/2021
48832^414432-1846709124757Enzo Doria07/2015
48842*10^124751-51124752Robert Price04/2018
4885(56*10^124735+367)/9124736Robert Price06/2019
488627362^28111-28111^27362124733Frank Doornink03/2024
4887(13*2^414274-1)/153124708Lelio R Paula05/2014
4888(23*10^124690+37)/3124691Robert Price02/2022
488956*10^124656-3124658Robert Price03/2020
4890(7*10^124648+197)/3124649Robert Price07/2018
48922^414032-5124637Henri Lifchitz07/2006
48912^414032+1872331124637Enzo Doria05/2016
489337373^2158+2158^37373124604Hans Havermann03/2021
489429811^15112+15112^29811124590Hans Havermann03/2021
48952^413781-2023124561Riley Fisher09/2023
489614120^30009-30009^14120124533Norbert Schneider02/2015
489729757^15296+15296^29757124521Hans Havermann03/2021
489835056^3561+3561^35056124504Hans Havermann03/2021
489940588^1167+1167^40588124487Hans Havermann02/2021
4900(85*10^124485-49)/9124486Robert Price12/2020
490164^68909-63^68909124463Robert Price07/2013
490235016^3581+3581^35016124448Hans Havermann03/2021
49032^413387+76253124442Enzo Doria04/2016
490428749^21298+21298^28749124436Hans Havermann03/2021
49052^413352+524287124432Paul Underwood09/2018
4906287117#+391613124424Nicolas PALAU01/2017
4907(4*10^124420+83)/3124421Robert Price02/2018
490834578^3965+3965^34578124421Hans Havermann03/2021
4909(68*10^124392-329)/9124393Robert Price03/2021
4910(27*2^413207-1)/108335124385Lelio R Paula05/2014
491110^124383+58407124384Patrick De Geest08/2021
491310^124383-8000001124383Robert Price04/2021
491210^124383-5801124383Patrick De Geest08/2021
491426091^28154-28154^26091124342Frank Doornink03/2024
4915(41*10^124335-383)/9124336Robert Price11/2018
4916(304*10^124329-43)/9124331Robert Price02/2020
491734716^3811+3811^34716124320Hans Havermann03/2021
491826892^28063-28063^26892124309Frank Doornink03/2024
49192^412868-120599124286Paul Bourdelais02/2012
492010^124248+899089124249Patrick De Geest05/2021
492210^124248-1000001124248Robert Price08/2020
492110^124248-501903124248Patrick De Geest05/2021
492345^75145-2124231Lelio R Paula08/2015
492429901^14272+14272^29901124224Hans Havermann03/2021
49252^412645-112213124219Enzo Doria06/2014
492629837^14500+14500^29837124163Hans Havermann03/2021
492728074^26455+26455^28074124158Hans Havermann03/2021
49282^412285+213317124111Enzo Doria09/2023
49292^412248+74611124100Enzo Doria04/2016
4930(22*10^124096-13)/9124097Robert Price06/2018
4931(455*10^124093+31)/9124095Robert Price06/2021
49322^412192-3329124083Yves Minet12/2014
4933(25*2^412191-1)/23124082Lelio R Paula05/2014
4935(25*10^124076-67)/3124077Robert Price06/2019
493428132^25735+25735^28132124077Hans Havermann03/2021
4936F(593689)124074Henri Lifchitz01/2005
4937(11*2^412161+1)/19124073Lelio R Paula05/2014
493826372^28057-28057^26372124045Frank Doornink03/2024
493927528^27937-27937^27528124034Frank Doornink03/2024
494035364^3215+3215^35364124028Hans Havermann03/2021
4942(266*10^124022-11)/3124024Robert Price04/2020
494129987^13674+13674^29987124024Hans Havermann03/2021
49432^411932-111546435124004Paul Bourdelais10/2021
49442^411884-113279123990Enzo Doria07/2014
4945(2^411832+1)/257123972Lelio R Paula05/2014
4946(2^411833+2)/514123972Stefano Morozzi03/2020
4947(26*10^123970-89)/9123971Robert Price06/2018
49482^411790-1853531123962Enzo Doria08/2015
4949(5^177337+1)/6123953Paul Bourdelais11/2008
4950(101*10^123950+7)/9123952Robert Price02/2022
49512^411711-113257123938Enzo Doria07/2014
4952(23*2^411675-1)/3123928Lelio R Paula05/2014
495336289^2598+2598^36289123914Hans Havermann03/2021
4954(11*10^123899-179)/3123900Robert Price09/2018
495532276^6879+6879^32276123860Hans Havermann02/2021
49562^411325-351103123822Enzo Doria06/2015
4957(646*10^123817+11)/9123819Robert Price10/2021
495830738^10643+10643^30738123784Hans Havermann03/2021
495931074^9607+9607^31074123755Hans Havermann03/2021
49602^411052+1872481123739Enzo Doria05/2016
496134365^3986+3986^34365123733Hans Havermann03/2021
49622^410997+39123723Lelio R Paula05/2014
4963(649^43987-1)/648123700Michael Stocker05/2020
4964(148*10^123688-1)/3123690Robert Price03/2020
496536825^2284+2284^36825123684Hans Havermann03/2021
496629582^15171+15171^29582123683Hans Havermann03/2021
496710^123671+3593037123672Paul Bourdelais10/2021
49688*10^123657+87123658Robert Price10/2019
496930505^11302+11302^30505123642Hans Havermann03/2021
497029956^13401+13401^29956123633Hans Havermann03/2021
4971155^56438+154123618Norbert Schneider01/2019
49722^410596-39123602Lelio R Paula05/2014
4973(41*10^123600-221)/9123601Robert Price10/2021
497428995^18302+18302^28995123592Hans Havermann03/2021
497528302^23269+23269^28302123589Hans Havermann03/2021
49762^410540-115079123585Enzo Doria06/2015
4977(7*10^123563+107)/3123564Robert Price02/2018
49789*10^123549+89123550Robert Price11/2019
4979(197*10^123545+7)/3123547Robert Price12/2020
4980(3*2^410392-1)/9229123537Lelio R Paula05/2014
49812^410342+212449123526Enzo Doria08/2023
4982(29*10^123510+277)/9123511Robert Price11/2021
498328118^24687+24687^28118123508Hans Havermann03/2021
498439994^1225+1225^39994123507Hans Havermann03/2021
49852^410206-113081123485Enzo Doria07/2014
4986(25*2^410192+1)/10397123478Lelio R Paula04/2014
498728974^18215+18215^28974123442Hans Havermann03/2021
498828901^18618+18618^28901123406Hans Havermann03/2021
49892^409909-189123395Enzo Doria05/2014
49902^409896-109043123391Enzo Doria04/2014
49912^409890+75409123390Enzo Doria04/2016
499281254^33+33^81254123386Hans Havermann03/2021
499333463^4854+4854^33463123348Hans Havermann03/2021
499434061^4182+4182^34061123348Hans Havermann03/2021
4995133^58076-2123345Lelio R Paula10/2017
4996F(590041)123311Henri Lifchitz01/2005
4997(82*10^123299+377)/9123300Robert Price03/2022
49982^409566-113501123292Enzo Doria08/2014
49992^409533+77747123282Enzo Doria05/2016
50002^409436-112799123253Enzo Doria06/2014


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Created by  Henri Lifchitz & Renaud Lifchitz : October, 26 2000, last modification: May, 22 2024 21:19 (Time in France)

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