PRP Records

Probable Primes Top 10000

(291910 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 ?
5751655^37342+37342^655105165Norbert Schneider08/2018
575213^94403+94105160Lelio R Paula12/2016
57532^349301-112309105151Enzo Doria06/2014
575430291^2960+2960^30291105149Hans Havermann09/2020
575527350^6981+6981^27350105132Hans Havermann09/2020
57579*2^349220+5105127Lelio R Paula09/2014
5756(2^349225+3122)/2105127Stefano Morozzi09/2020
57587*3^220317+8105119Lelio R Paula09/2014
57597^124386+88105119Lelio R Paula11/2016
5760(2^349197+570)/2105119Stefano Morozzi09/2020
57612^349171-19657105111Enzo Doria06/2013
5762(2^349115+590)/2105094Stefano Morozzi09/2020
5763(2^(6*58185+1)-5)/3105093Kevin Acres11/2013
5764(2^349111-5)/3105093Lelio R Paula12/2013
5765675^37142+37142^675105087Norbert Schneider08/2018
57662^348981-2797573105054Enzo Doria04/2016
57672^348869-6555105021Lelio R Paula01/2017
57685^150217+78104998Lelio R Paula11/2016
5769(88*10^104989-1)/3104991Robert Price04/2020
5770(28*10^104972+149)/3104973Robert Price12/2019
577124927^16262+16262^24927104972Hans Havermann10/2020
57722^348703-113005104971Enzo Doria06/2014
5773(191*10^104956-17)/3104958Robert Price11/2021
57752^348612-809104943Yves Minet05/2013
5774(73*10^104942-1)/9104943Robert Price01/2015
57762^348583-350407104934Enzo Doria06/2015
57772^348531-949104919Yves Minet05/2012
577820^80636-59104910Lelio R Paula12/2016
57798*10^104893-13104894Robert Price08/2019
57812^348437+35104890Lelio R Paula09/2011
578025208^14487+14487^25208104890Hans Havermann09/2020
57822^348348+135104864Lelio R Paula09/2011
5783(29*10^104858+349)/9104859Robert Price06/2021
57846*10^104852-31104853Robert Price07/2020
5786(2^348284+9)/25104843Lelio R Paula12/2013
578575^55914-74104843Norbert Schneider01/2015
57872^348268+255255104840Lelio R Paula01/2017
578835540^891+891^35540104839Hans Havermann09/2020
57895^149985-52104836Lelio R Paula11/2016
57902^348224-20249104826Enzo Doria06/2013
5791(2^348217+2522)/2104824Stefano Morozzi09/2020
57922^348212-20105104823Enzo Doria06/2013
579324647^17898+17898^24647104819Hans Havermann10/2020
579420^80562+19104814Lelio R Paula12/2016
57952*10^104811-87104812Robert Price04/2018
57962^348149-20053104804Enzo Doria06/2013
57972^348095-171104788Lelio R Paula09/2011
579825383^13412+13412^25383104769Hans Havermann09/2020
57992^348003-20377104760Enzo Doria06/2013
58002^347994-741104757Lelio R Paula12/2016
5801(2^347993+2234)/2104757Stefano Morozzi01/2021
5802(2^347990+790)/2104756Stefano Morozzi09/2020
580325137^14702+14702^25137104756Hans Havermann09/2020
5804(13*2^347972-1)/282309104746Lelio R Paula03/2014
580512883^25484-25484^12883104740Norbert Schneider08/2022
58062^347910-109937104732Enzo Doria04/2014
5807(88*10^104709-637)/9104710Robert Price11/2020
5808(13*10^104702+71)/3104703Robert Price06/2021
58095^149794+28104702Lelio R Paula11/2016
5810105^51800-2104698Lelio R Paula10/2017
5811(16^86939+3^86939)/19104684Robert Price06/2013
5812(15^89009-1)/14104682Paul Bourdelais03/2010
58132^347731-18609104678Enzo Doria05/2013
58144*6^134519+7104677Lelio R Paula11/2014
5815(34*10^104672-259)/9104673Robert Price12/2021
581625321^13588+13588^25321104656Hans Havermann09/2020
58172^347612-18545104642Enzo Doria05/2013
58206^134465+95104635Lelio R Paula11/2016
5818(2^347588+3718)/2104635Stefano Morozzi09/2020
5819(166*10^104633-7)/3104635Robert Price11/2020
58212^347517-17301104614Enzo Doria05/2013
5822(2^347493+3186)/2104606Stefano Morozzi09/2020
5823(2^347490+2574)/2104605Stefano Morozzi09/2020
58243^219222-310104596Lelio R Paula11/2016
582525993^10554+10554^25993104581Hans Havermann09/2020
5826(15*2^347399-1)/13104578Lelio R Paula03/2014
58272^347372-17853104570Enzo Doria05/2013
58282^347314+99104552Lelio R Paula09/2011
58292^347300-22233104548Enzo Doria06/2013
58302^347287-19845104544Enzo Doria06/2013
58312^347258-231191104536Harrison Mesh06/2022
5832(31*2^347254-1)/891104533Lelio R Paula03/2014
58335*F(250091)*(F(250091)-1)+1104532Serge Batalov04/2015
58347*2^347239-3104531Lelio R Paula09/2014
5835(3^219098-8)/514147439969104525Lelio R Paula12/2013
58365*3^219047+8104513Lelio R Paula09/2014
58372^347148-109073104502Enzo Doria04/2014
58382^347129-20145104497Enzo Doria06/2013
58394*10^104461-57104462Robert Price10/2018
5840(2^346989+590)/2104454Stefano Morozzi09/2020
58412^346923-19585104435Enzo Doria05/2013
5842(11*2^346864-1)/175104416Lelio R Paula03/2014
58432^346854+346854^2+1104414Robert Price06/2014
58442^346834+11715104408Lelio R Paula04/2015
584524276^19961+19961^24276104392Hans Havermann09/2020
584679^55009+78104387Norbert Schneider02/2015
58473^218744+58104368Lelio R Paula11/2016
58489*10^104361+89104362Robert Price11/2019
584925048^14665+14665^25048104358Hans Havermann09/2020
58502^346649+65104352Lelio R Paula09/2011
58512^346638-17265104349Enzo Doria05/2013
5852(2^346606+2082)/2104339Stefano Morozzi09/2020
5853(2^346607+2070)/2104339Stefano Morozzi09/2020
5854(2^346582+3202)/2104332Stefano Morozzi09/2020
585526092^9967+9967^26092104331Hans Havermann09/2020
58565*10^104326+77104327Robert Price12/2018
5857(2^346564+2026)/2104326Stefano Morozzi09/2020
58592^346527-111817104316Enzo Doria05/2014
58586^134055+101104316Lelio R Paula11/2016
586092105!4+8104312Robert Price09/2019
58616^134013+163104283Lelio R Paula11/2016
5862(22*10^104272-61)/3104273Robert Price03/2022
5863(2^346318+862)/2104252Stefano Morozzi02/2021
586518^83049-89104250Lelio R Paula01/2017
5864(2^346311+606)/2104250Stefano Morozzi09/2020
5866(166*10^104230+11)/3104232Robert Price03/2021
58672^346213+484049104221Enzo Doria04/2017
586818^83021-91104214Lelio R Paula01/2017
586910^104212+128779104213Patrick De Geest05/2016
587010^104212+237447104213Patrick De Geest05/2016
587110^104212+242139104213Patrick De Geest05/2016
587210^104212+269199104213Patrick De Geest05/2016
587324254^19803+19803^24254104213Hans Havermann09/2020
5874(10^104212-71)/1104212Serge Batalov12/2014
587523678^23821-23821^23678104202Norbert Schneider01/2020
58762^346078+7695104180Lelio R Paula12/2016
58772^346055-19537104173Enzo Doria05/2013
5878(3*2^346057+1)/77104173Lelio R Paula12/2013
58792^346037-20125104168Enzo Doria06/2013
5880(34*10^104168-7)/9/13/551179104162Makoto Morimoto05/2016
58816^133854-17993104159Enzo Doria03/2013
58822^345990+1874239104154Enzo Doria06/2016
58832^345988-20373104153Enzo Doria06/2013
5884(2^345965+2214)/2104146Stefano Morozzi09/2020
5885(26*10^104132-503)/9104133Robert Price07/2018
58863*5^148968+8104125Lelio R Paula11/2014
5887(7*10^104113+53)/3104114Robert Price05/2018
5888p(21253)#/2+8104113Robert Price01/2017
588933582^1259+1259^33582104106Hans Havermann09/2020
589032958^1441+1441^32958104104Hans Havermann09/2020
589129127^3748+3748^29127104095Hans Havermann09/2020
5892322^41507+41507^322104094Norbert Schneider12/2014
58936^133768-17423104092Enzo Doria03/2013
58942^345786-19557104092Enzo Doria05/2013
5895171^46606-2104072Lelio R Paula10/2017
5896(29*10^104071+91)/3104072Robert Price04/2020
5897norm(Mod(x,x^3-x-1)^852167-1)104070Paul Vanderveen09/2022
58982^345704-149104068Lelio R Paula09/2011
589925821^10712+10712^25821104056Hans Havermann09/2020
5900(2^345662+2038)/2104055Stefano Morozzi09/2020
59016^133704-17273104042Enzo Doria02/2013
5902(3*2^345590-1)/23104033Lelio R Paula03/2014
5903(19*2^345590+1)/33859104030Lelio R Paula12/2013
59042^345547+11104021Lelio R Paula09/2011
5905(19*10^104014-49)/3104015Robert Price05/2019
5906(2^345519+1794)/2104012Stefano Morozzi01/2021
59072^345504+723104008Lelio R Paula09/2011
59082^345498-20037104006Enzo Doria06/2013
591018^82854-37104005Lelio R Paula01/2017
5909(2^345497+2070)/2104005Stefano Morozzi09/2020
59112^345486-109065104002Enzo Doria04/2014
59122^345487-1851507104002Enzo Doria08/2015
59132^345476+777103999Lelio R Paula09/2011
5914(2^345477+1554)/2103999Stefano Morozzi09/2020
59154*10^103981-83103982Robert Price10/2018
5916(2^345327+3206)/2103954Stefano Morozzi09/2020
5917(5*2^345321-1)/3103953Lelio R Paula03/2014
5918(2^345267-9)/539049127103927Lelio R Paula12/2013
5919(19*10^103907+77)/3103908Robert Price05/2019
5920(78557*2^345163+1)/78589103905Lelio R Paula07/2014
59212^345106-112181103888Enzo Doria06/2014
5922(2^345105+1326)/2103887Stefano Morozzi02/2021
59232^345079+99103880Lelio R Paula09/2011
5924(2^345034+1198)/2103866Stefano Morozzi09/2020
592511^99736-1500103865Enzo Doria12/2012
5926(569^37699-1)/568103863Serge Batalov06/2022
5927(2^345010+2082)/2103859Stefano Morozzi09/2020
592823263^23784-23784^23263103857Norbert Schneider01/2020
59293*10^103844+31103845Robert Price06/2021
593023927^21814+21814^23927103813Hans Havermann09/2020
59312^344842-20157103808Enzo Doria06/2013
5932(47*2^344822+1)/1071103801Lelio R Paula05/2015
59332^344802-20765103796Enzo Doria06/2013
59342^344794-3821103794Yves Minet05/2011
59352^344782-109103103790Enzo Doria04/2014
59363^217521-112292103784Enzo Doria06/2014
59372^344759-3505103783Lelio R Paula11/2016
59382^344735-147103776Lelio R Paula09/2011
5939L(496533)-p(496533)103770Robert Price02/2018
59402*10^103749-69103750Robert Price03/2018
5941(55459*2^344617+1)/3103745Lelio R Paula07/2014
59422^344607-108891103738Enzo Doria03/2014
5944(2^344608+3798)/2103738Stefano Morozzi02/2021
5943(1097^34123-1)/1096103738Serge Batalov06/2022
5945(148*10^103718-1)/3103720Robert Price03/2020
59462^344541-19561103718Enzo Doria05/2013
5947(1017*2^344529-1)/569103714Lelio R Paula05/2015
5948(8896^26263-1)/8895103714Serge Batalov06/2022
5949(2^344503+1758)/2103706Stefano Morozzi09/2020
5950(4*10^103703-1)/3103704Serge Batalov08/2009
59512^344444-455103688Yves Minet03/2012
5952(4*10^103678-43)/3103679Robert Price01/2022
5953(13*53^238539*617^9)/10^307661103673Hans Havermann06/2017
5954(2^344367+2738)/2103665Stefano Morozzi01/2021
59562^344317-109933103650Enzo Doria04/2014
595526055^9508+9508^26055103650Hans Havermann09/2020
59572^344309-1852033103648Enzo Doria08/2015
595825729^10672+10672^25729103643Hans Havermann09/2020
5959(2^344289+1166)/2103642Stefano Morozzi09/2020
59603*10^103637+61103638Robert Price09/2020
5961(2^344246+1614)/2103629Stefano Morozzi09/2020
59622^344213-21253103619Enzo Doria06/2013
59632^344196-465103614Lelio R Paula11/2016
59642^344187-20001103611Enzo Doria06/2013
5965(117191#+(355573#)/(117191#))/(200233679)103602Makoto Morimoto10/2017
5966(237^43627-1)/236103601Serge Batalov06/2022
596720^79621-19^79621103590Jean-Louis Charton03/2011
5968Phi(155391,10)/1243129103586Maksym Voznyy09/2015
59692^344085-20365103580Enzo Doria06/2013
59705^148169+54103566Lelio R Paula11/2016
59712^344017-108795103560Enzo Doria03/2014
5972(2^343974+2670)/2103547Stefano Morozzi09/2020
59732^343971-5077103546Lelio R Paula09/2011
5974(7*10^103531+71)/3103532Robert Price05/2018
59752^343899+141103524Lelio R Paula08/2011
5976(2^343933+1)/(3*98294339989393)103520Gord Palameta08/2018
59776^133029-67103517Lelio R Paula11/2016
5978(17*2^343877+1)/13625103515Lelio R Paula12/2013
597966*10^103507+7103509Robert Price07/2020
598026297^8614+8614^26297103485Hans Havermann09/2020
5981(2^343764+2658)/2103483Stefano Morozzi09/2020
598226499^8036+8036^26499103480Hans Havermann09/2020
5983(136*10^103474-1)/9103476Serge Batalov12/2014
59845^148014-24103458Lelio R Paula11/2016
598528316^4503+4503^28316103453Hans Havermann09/2020
5986(22*10^103450+53)/3103451Robert Price07/2019
59872^343604+9931103436Yves Minet01/2011
59882^343601-21189103435Enzo Doria06/2013
5989(10^103423+173)/3103423Robert Price05/2021
59902^343508-115229103407Enzo Doria06/2015
5991(8766^26227-1)/8765103404Serge Batalov06/2022
5992(509203*2^343491-1)/16147103403Lelio R Paula05/2015
59933^216685-113056103386Enzo Doria07/2014
599424829^14580+14580^24829103382Hans Havermann08/2020
599591355!4+1024103381Robert Price09/2019
599644^62903-43^62903103379Jean-Louis Charton08/2012
599711^99262-20103371Lelio R Paula12/2016
5998(509203*2^343357-1)/5103366Lelio R Paula05/2015
5999(2^343363+3570)/2103363Stefano Morozzi09/2020
60002^343356-2791889103361Enzo Doria03/2016


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Created by  Henri Lifchitz & Renaud Lifchitz : October, 26 2000, last modification: February, 02 2023 13:22 (Time in France)

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