PRP Records

Probable Primes Top 10000

(295148 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 ?
67512^350858-59291105619Enzo Doria10/2015
67522^350851+135105617Lelio R Paula10/2011
67532^350841-741105614Lelio R Paula01/2017
67543*10^105582+77105583Robert Price09/2018
675524915^17284+17284^24915105581Hans Havermann09/2020
6756(5*10^105576-53)/3105577Robert Price09/2020
67578*10^105571+3105572Robert Price08/2015
67582^350674-78557105564Jorge Menendez03/2018
67592*5^151026-3105563Lelio R Paula11/2014
6760(2^350702+5)/34264674063105562Lelio R Paula12/2013
67616^135647-5^135647105554Jean-Louis Charton02/2009
67623^221211+236105545Lelio R Paula11/2016
6763(32*10^105530-77)/9105531Robert Price06/2018
676410^105515+33105516Lelio R Paula11/2016
676524644^19125+19125^24644105516Hans Havermann10/2020
676610^105515-41033105515Patrick De Geest12/2016
6767(29*2^350473-1)/267927105499Lelio R Paula03/2014
67682^350455-430567105498Harrison Mesh06/2022
676917^85732-72105489Lelio R Paula01/2017
6770(2^350399+3618)/2105481Stefano Morozzi09/2020
6771(2^350379+1010)/2105475Stefano Morozzi09/2020
67722^350356+24241105468Enzo Doria10/2023
677325233^15118+15118^25233105462Hans Havermann09/2020
677426261^10366+10366^26261105454Hans Havermann09/2020
67752^350307-110329105453Enzo Doria05/2014
67762^350253-20365105437Enzo Doria06/2013
6777(3*29^72089-1075)/4105423Curtis Bright05/2015
6778(2^350187+2658)/2105417Stefano Morozzi09/2020
67794*10^105415-69105416Robert Price01/2022
6780(22*10^105407+179)/3105408Robert Price02/2022
67812^350139-109009105403Enzo Doria04/2014
6782(2^350129+3026)/2105400Stefano Morozzi09/2020
6783(2^350097+2070)/2105390Stefano Morozzi09/2020
67843*5^150763+4105380Lelio R Paula11/2014
678512^97643+91105375Lelio R Paula02/2017
67866*5^150744-7105367Lelio R Paula11/2014
6787(2^350018+2074)/2105366Stefano Morozzi09/2020
67884*10^105364-39105365Robert Price09/2020
67902^349996-112169105360Enzo Doria06/2014
6789(2^349997+3702)/2105360Stefano Morozzi09/2020
6791(418*10^105343+23)/9105345Robert Price02/2020
679225490^13563+13563^25490105334Hans Havermann10/2020
679311^101142-1080105329Enzo Doria12/2012
6794(68*10^105320-41)/9105321Robert Price10/2013
679524800^17649+17649^24800105319Hans Havermann09/2020
67963^220712-9934105307Enzo Doria05/2014
67977*10^105296+9105297Robert Price09/2015
679889*10^105284-7105286Robert Price04/2020
67992^349739+1873373105282Enzo Doria06/2016
68007^124574+24105278Lelio R Paula11/2016
68012^349708-20957105273Enzo Doria06/2013
680234115^1218+1218^34115105267Hans Havermann09/2020
68032^349649-20469105255Enzo Doria06/2013
68042^349607-20109105243Enzo Doria06/2013
6805(85*10^105242+473)/9105243Robert Price01/2020
68062^349594-19085105239Enzo Doria05/2013
68072^349530+1874479105220Enzo Doria06/2016
6808(3^220528+8)/8081105215Lelio R Paula12/2013
6809(106*10^105199+17)/3105201Robert Price04/2021
6810(2^349452+3570)/2105196Stefano Morozzi09/2020
68113^220464-112852105189Enzo Doria07/2014
68122^349419-17349105186Enzo Doria05/2013
68132^349400-2579105180Yves Minet07/2014
68148*5^150471+3105176Lelio R Paula11/2014
6815(2^349359+2298)/2105168Stefano Morozzi02/2021
6816655^37342+37342^655105165Norbert Schneider08/2018
681713^94403+94105160Lelio R Paula12/2016
68182^349301-112309105151Enzo Doria06/2014
681930291^2960+2960^30291105149Hans Havermann09/2020
682027350^6981+6981^27350105132Hans Havermann09/2020
68229*2^349220+5105127Lelio R Paula09/2014
6821(2^349225+3122)/2105127Stefano Morozzi09/2020
68237*3^220317+8105119Lelio R Paula09/2014
68247^124386+88105119Lelio R Paula11/2016
6825(2^349197+570)/2105119Stefano Morozzi09/2020
68262^349171-19657105111Enzo Doria06/2013
6827(2^349115+590)/2105094Stefano Morozzi09/2020
6828(2^(6*58185+1)-5)/3105093Kevin Acres11/2013
6829(2^349111-5)/3105093Lelio R Paula12/2013
6830675^37142+37142^675105087Norbert Schneider08/2018
68312^348981-2797573105054Enzo Doria04/2016
6832(445^39667+1)/446105050Jinyuan Wang05/2024
68332^348869-6555105021Lelio R Paula01/2017
68345^150217+78104998Lelio R Paula11/2016
6835(88*10^104989-1)/3104991Robert Price04/2020
6836(28*10^104972+149)/3104973Robert Price12/2019
683724927^16262+16262^24927104972Hans Havermann10/2020
68382^348703-113005104971Enzo Doria06/2014
6839(191*10^104956-17)/3104958Robert Price11/2021
68412^348612-809104943Yves Minet05/2013
6840(73*10^104942-1)/9104943Robert Price01/2015
68422^348583-350407104934Enzo Doria06/2015
68432^348531-949104919Yves Minet05/2012
684420^80636-59104910Lelio R Paula12/2016
68458*10^104893-13104894Robert Price08/2019
68472^348437+35104890Lelio R Paula09/2011
684625208^14487+14487^25208104890Hans Havermann09/2020
68482^348348+135104864Lelio R Paula09/2011
6849(29*10^104858+349)/9104859Robert Price06/2021
68506*10^104852-31104853Robert Price07/2020
6852(2^348284+9)/25104843Lelio R Paula12/2013
685175^55914-74104843Norbert Schneider01/2015
68532^348268+255255104840Lelio R Paula01/2017
685435540^891+891^35540104839Hans Havermann09/2020
68555^149985-52104836Lelio R Paula11/2016
68562^348224-20249104826Enzo Doria06/2013
6857(2^348217+2522)/2104824Stefano Morozzi09/2020
68582^348212-20105104823Enzo Doria06/2013
685924647^17898+17898^24647104819Hans Havermann10/2020
686020^80562+19104814Lelio R Paula12/2016
68612*10^104811-87104812Robert Price04/2018
68622^348149-20053104804Enzo Doria06/2013
68632^348095-171104788Lelio R Paula09/2011
686425383^13412+13412^25383104769Hans Havermann09/2020
68652^348003-20377104760Enzo Doria06/2013
68662^347994-741104757Lelio R Paula12/2016
6867(2^347993+2234)/2104757Stefano Morozzi01/2021
6868(2^347990+790)/2104756Stefano Morozzi09/2020
686925137^14702+14702^25137104756Hans Havermann09/2020
6870(13*2^347972-1)/282309104746Lelio R Paula03/2014
687112883^25484-25484^12883104740Norbert Schneider08/2022
68722^347910-109937104732Enzo Doria04/2014
6873(88*10^104709-637)/9104710Robert Price11/2020
6874(13*10^104702+71)/3104703Robert Price06/2021
68755^149794+28104702Lelio R Paula11/2016
6876105^51800-2104698Lelio R Paula10/2017
6877(16^86939+3^86939)/19104684Robert Price06/2013
6878(15^89009-1)/14104682Paul Bourdelais03/2010
68792^347731-18609104678Enzo Doria05/2013
68804*6^134519+7104677Lelio R Paula11/2014
6881(34*10^104672-259)/9104673Robert Price12/2021
688225321^13588+13588^25321104656Hans Havermann09/2020
68832^347625+5367104646Riley Fisher04/2023
68842^347612-18545104642Enzo Doria05/2013
68876^134465+95104635Lelio R Paula11/2016
6886(2^347588+3718)/2104635Stefano Morozzi09/2020
6885(166*10^104633-7)/3104635Robert Price11/2020
68882^347517-17301104614Enzo Doria05/2013
6889(2^347493+3186)/2104606Stefano Morozzi09/2020
6890(2^347490+2574)/2104605Stefano Morozzi09/2020
68913^219222-310104596Lelio R Paula11/2016
689225993^10554+10554^25993104581Hans Havermann09/2020
6893(15*2^347399-1)/13104578Lelio R Paula03/2014
68942^347372-17853104570Enzo Doria05/2013
68952^347314+99104552Lelio R Paula09/2011
68962^347300-22233104548Enzo Doria06/2013
68972^347287-19845104544Enzo Doria06/2013
68982^347258-231191104536Harrison Mesh06/2022
6899(31*2^347254-1)/891104533Lelio R Paula03/2014
69005*F(250091)*(F(250091)-1)+1104532Serge Batalov04/2015
69017*2^347239-3104531Lelio R Paula09/2014
6902(3^219098-8)/514147439969104525Lelio R Paula12/2013
69035*3^219047+8104513Lelio R Paula09/2014
69042^347148-109073104502Enzo Doria04/2014
69052^347129-20145104497Enzo Doria06/2013
69064*10^104461-57104462Robert Price10/2018
6907(7*10^(2*52227+1)+9*10^52227-7)/9104455Robert Price10/2023
6908(2^346989+590)/2104454Stefano Morozzi09/2020
69092^346923-19585104435Enzo Doria05/2013
6910(11*2^346864-1)/175104416Lelio R Paula03/2014
69112^346854+346854^2+1104414Robert Price06/2014
69122^346834+11715104408Lelio R Paula04/2015
691324276^19961+19961^24276104392Hans Havermann09/2020
691479^55009+78104387Norbert Schneider02/2015
69153^218744+58104368Lelio R Paula11/2016
69169*10^104361+89104362Robert Price11/2019
691725048^14665+14665^25048104358Hans Havermann09/2020
69182^346649+65104352Lelio R Paula09/2011
6919(19*33^68718-600883)/32104350Eric Chen05/2023
69202^346638-17265104349Enzo Doria05/2013
6921(2^346606+2082)/2104339Stefano Morozzi09/2020
6922(2^346607+2070)/2104339Stefano Morozzi09/2020
6923(2^346582+3202)/2104332Stefano Morozzi09/2020
692426092^9967+9967^26092104331Hans Havermann09/2020
69255*10^104326+77104327Robert Price12/2018
6926(2^346564+2026)/2104326Stefano Morozzi09/2020
6927(8925^26569-1)/(8925^163-1)104320Ryan Propper11/2023
69302^346527-111817104316Enzo Doria05/2014
69296^134055+101104316Lelio R Paula11/2016
6928fibonacci(499147)-4104316Jon Grantham08/2023
693192105!4+8104312Robert Price09/2019
6932(7^123407-5^123407)/2104291Jon Grantham08/2023
69336^134013+163104283Lelio R Paula11/2016
693410^(2*52140+1)-10^52140-1104281Robert Price07/2023
6935(22*10^104272-61)/3104273Robert Price03/2022
6936(2^346318+862)/2104252Stefano Morozzi02/2021
693818^83049-89104250Lelio R Paula01/2017
6937(2^346311+606)/2104250Stefano Morozzi09/2020
6939(166*10^104230+11)/3104232Robert Price03/2021
69402^346213+484049104221Enzo Doria04/2017
694118^83021-91104214Lelio R Paula01/2017
694210^104212+128779104213Patrick De Geest05/2016
694310^104212+237447104213Patrick De Geest05/2016
694410^104212+242139104213Patrick De Geest05/2016
694510^104212+269199104213Patrick De Geest05/2016
694624254^19803+19803^24254104213Hans Havermann09/2020
6947(10^104212-71)/1104212Serge Batalov12/2014
694823678^23821-23821^23678104202Norbert Schneider01/2020
6949(13*31^69863+12407)/30104191Eric Chen04/2024
69502^346078+7695104180Lelio R Paula12/2016
69512^346055-19537104173Enzo Doria05/2013
6952(3*2^346057+1)/77104173Lelio R Paula12/2013
69532^346037-20125104168Enzo Doria06/2013
6954(34*10^104168-7)/9/13/551179104162Makoto Morimoto05/2016
69556^133854-17993104159Enzo Doria03/2013
69562^345990+1874239104154Enzo Doria06/2016
69572^345988-20373104153Enzo Doria06/2013
6958(2^345965+2214)/2104146Stefano Morozzi09/2020
6959(26*10^104132-503)/9104133Robert Price07/2018
69603*5^148968+8104125Lelio R Paula11/2014
6961(7*10^104113+53)/3104114Robert Price05/2018
6962p(21253)#/2+8104113Robert Price01/2017
696333582^1259+1259^33582104106Hans Havermann09/2020
696432958^1441+1441^32958104104Hans Havermann09/2020
696529127^3748+3748^29127104095Hans Havermann09/2020
6966322^41507+41507^322104094Norbert Schneider12/2014
69676^133768-17423104092Enzo Doria03/2013
69682^345786-19557104092Enzo Doria05/2013
6969171^46606-2104072Lelio R Paula10/2017
6970(29*10^104071+91)/3104072Robert Price04/2020
6971norm(Mod(x,x^3-x-1)^852167-1)104070Paul Vanderveen09/2022
69722^345704-149104068Lelio R Paula09/2011
697325821^10712+10712^25821104056Hans Havermann09/2020
6974(2^345662+2038)/2104055Stefano Morozzi09/2020
69756^133704-17273104042Enzo Doria02/2013
6976(3*2^345590-1)/23104033Lelio R Paula03/2014
6977(19*2^345590+1)/33859104030Lelio R Paula12/2013
69782^345547+11104021Lelio R Paula09/2011
6979(19*10^104014-49)/3104015Robert Price05/2019
6980(2^345519+1794)/2104012Stefano Morozzi01/2021
69812^345504+723104008Lelio R Paula09/2011
69822^345498-20037104006Enzo Doria06/2013
698418^82854-37104005Lelio R Paula01/2017
6983(2^345497+2070)/2104005Stefano Morozzi09/2020
69852^345486-109065104002Enzo Doria04/2014
69862^345487-1851507104002Enzo Doria08/2015
69872^345476+777103999Lelio R Paula09/2011
6988(2^345477+1554)/2103999Stefano Morozzi09/2020
69894*10^103981-83103982Robert Price10/2018
6990(2^345327+3206)/2103954Stefano Morozzi09/2020
6991(5*2^345321-1)/3103953Lelio R Paula03/2014
6992(2^345267-9)/539049127103927Lelio R Paula12/2013
6993(19*10^103907+77)/3103908Robert Price05/2019
6994(78557*2^345163+1)/78589103905Lelio R Paula07/2014
69952^345106-112181103888Enzo Doria06/2014
6996(2^345105+1326)/2103887Stefano Morozzi02/2021
69972^345079+99103880Lelio R Paula09/2011
6998(2^345034+1198)/2103866Stefano Morozzi09/2020
699911^99736-1500103865Enzo Doria12/2012
7000(569^37699-1)/568103863Serge Batalov06/2022


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Created by  Henri Lifchitz & Renaud Lifchitz : October, 26 2000, last modification: May, 20 2024 09:22 (Time in France)

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