PRP Records

Probable Primes Top 10000

(280932 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 ?
47512^346527-111817104316Enzo Doria05/2014
475292105!4+8104312Robert Price09/2019
47536^134013+163104283Lelio R Paula11/2016
4754(2^346318+862)/2104252Stefano Morozzi02/2021
475518^83049-89104250Lelio R Paula01/2017
4756(2^346311+606)/2104250Stefano Morozzi09/2020
4757(166*10^104230+11)/3104232Robert Price03/2021
47582^346213+484049104221Enzo Doria04/2017
475918^83021-91104214Lelio R Paula01/2017
476110^104212+128779104213Patrick De Geest05/2016
476210^104212+237447104213Patrick De Geest05/2016
476310^104212+242139104213Patrick De Geest05/2016
476410^104212+269199104213Patrick De Geest05/2016
476024254^19803+19803^24254104213Hans Havermann09/2020
4765(10^104212-71)/1104212Serge Batalov12/2014
476623678^23821-23821^23678104202Norbert Schneider01/2020
47672^346078+7695104180Lelio R Paula12/2016
47682^346055-19537104173Enzo Doria05/2013
4769(3*2^346057+1)/77104173Lelio R Paula12/2013
47702^346037-20125104168Enzo Doria06/2013
4771(34*10^104168-7)/9/13/551179104162Makoto Morimoto05/2016
47726^133854-17993104159Enzo Doria03/2013
47732^345990+1874239104154Enzo Doria06/2016
47742^345988-20373104153Enzo Doria06/2013
4775(2^345965+2214)/2104146Stefano Morozzi09/2020
4776(26*10^104132-503)/9104133Robert Price07/2018
47773*5^148968+8104125Lelio R Paula11/2014
4778(7*10^104113+53)/3104114Robert Price05/2018
4779p(21253)#/2+8104113Robert Price01/2017
478033582^1259+1259^33582104106Hans Havermann09/2020
478132958^1441+1441^32958104104Hans Havermann09/2020
478229127^3748+3748^29127104095Hans Havermann09/2020
4783322^41507+41507^322104094Norbert Schneider12/2014
47846^133768-17423104092Enzo Doria03/2013
47852^345786-19557104092Enzo Doria05/2013
4787171^46606-2104072Lelio R Paula10/2017
4786(29*10^104071+91)/3104072Robert Price04/2020
47882^345704-149104068Lelio R Paula09/2011
478925821^10712+10712^25821104056Hans Havermann09/2020
4790(2^345662+2038)/2104055Stefano Morozzi09/2020
47916^133704-17273104042Enzo Doria02/2013
4792(3*2^345590-1)/23104033Lelio R Paula03/2014
4793(19*2^345590+1)/33859104030Lelio R Paula12/2013
47942^345547+11104021Lelio R Paula09/2011
4795(19*10^104014-49)/3104015Robert Price05/2019
4796(2^345519+1794)/2104012Stefano Morozzi01/2021
47972^345504+723104008Lelio R Paula09/2011
47982^345498-20037104006Enzo Doria06/2013
480018^82854-37104005Lelio R Paula01/2017
4799(2^345497+2070)/2104005Stefano Morozzi09/2020
48012^345486-109065104002Enzo Doria04/2014
48022^345487-1851507104002Enzo Doria08/2015
48042^345476+777103999Lelio R Paula09/2011
4803(2^345477+1554)/2103999Stefano Morozzi09/2020
48054*10^103981-83103982Robert Price10/2018
4806(2^345327+3206)/2103954Stefano Morozzi09/2020
4807(5*2^345321-1)/3103953Lelio R Paula03/2014
4808(2^345267-9)/539049127103927Lelio R Paula12/2013
4809(19*10^103907+77)/3103908Robert Price05/2019
4810(78557*2^345163+1)/78589103905Lelio R Paula07/2014
48112^345106-112181103888Enzo Doria06/2014
4812(2^345105+1326)/2103887Stefano Morozzi02/2021
48132^345079+99103880Lelio R Paula09/2011
4814(2^345034+1198)/2103866Stefano Morozzi09/2020
481511^99736-1500103865Enzo Doria12/2012
4816(2^345010+2082)/2103859Stefano Morozzi09/2020
481723263^23784-23784^23263103857Norbert Schneider01/2020
481823927^21814+21814^23927103813Hans Havermann09/2020
48192^344842-20157103808Enzo Doria06/2013
4820(47*2^344822+1)/1071103801Lelio R Paula05/2015
48212^344802-20765103796Enzo Doria06/2013
48222^344794-3821103794Yves Minet05/2011
48232^344782-109103103790Enzo Doria04/2014
48243^217521-112292103784Enzo Doria06/2014
48252^344759-3505103783Lelio R Paula11/2016
48262^344735-147103776Lelio R Paula09/2011
4827L(496533)-p(496533)103770Robert Price02/2018
48282*10^103749-69103750Robert Price03/2018
4829(55459*2^344617+1)/3103745Lelio R Paula07/2014
48302^344607-108891103738Enzo Doria03/2014
4831(2^344608+3798)/2103738Stefano Morozzi02/2021
4832(148*10^103718-1)/3103720Robert Price03/2020
48332^344541-19561103718Enzo Doria05/2013
4834(1017*2^344529-1)/569103714Lelio R Paula05/2015
4835(2^344503+1758)/2103706Stefano Morozzi09/2020
4836(4*10^103703-1)/3103704Serge Batalov08/2009
48372^344444-455103688Yves Minet03/2012
4838(13*53^238539*617^9)/10^307661103673Hans Havermann06/2017
4839(2^344367+2738)/2103665Stefano Morozzi01/2021
48412^344317-109933103650Enzo Doria04/2014
484026055^9508+9508^26055103650Hans Havermann09/2020
48422^344309-1852033103648Enzo Doria08/2015
484325729^10672+10672^25729103643Hans Havermann09/2020
4844(2^344289+1166)/2103642Stefano Morozzi09/2020
48453*10^103637+61103638Robert Price09/2020
4846(2^344246+1614)/2103629Stefano Morozzi09/2020
48472^344213-21253103619Enzo Doria06/2013
48482^344196-465103614Lelio R Paula11/2016
48492^344187-20001103611Enzo Doria06/2013
4850(117191#+(355573#)/(117191#))/(200233679)103602Makoto Morimoto10/2017
485120^79621-19^79621103590Jean-Louis Charton03/2011
4852Phi(155391,10)/1243129103586Maksym Voznyy09/2015
48532^344085-20365103580Enzo Doria06/2013
48545^148169+54103566Lelio R Paula11/2016
48552^344017-108795103560Enzo Doria03/2014
4856(2^343974+2670)/2103547Stefano Morozzi09/2020
48572^343971-5077103546Lelio R Paula09/2011
4858(7*10^103531+71)/3103532Robert Price05/2018
48592^343899+141103524Lelio R Paula08/2011
4860(2^343933+1)/(3*98294339989393)103520Gord Palameta08/2018
48616^133029-67103517Lelio R Paula11/2016
4862(17*2^343877+1)/13625103515Lelio R Paula12/2013
486366*10^103507+7103509Robert Price07/2020
486426297^8614+8614^26297103485Hans Havermann09/2020
4865(2^343764+2658)/2103483Stefano Morozzi09/2020
486626499^8036+8036^26499103480Hans Havermann09/2020
4867(136*10^103474-1)/9103476Serge Batalov12/2014
48685^148014-24103458Lelio R Paula11/2016
486928316^4503+4503^28316103453Hans Havermann09/2020
4870(22*10^103450+53)/3103451Robert Price07/2019
48712^343604+9931103436Yves Minet01/2011
48722^343601-21189103435Enzo Doria06/2013
48732^343508-115229103407Enzo Doria06/2015
4874(509203*2^343491-1)/16147103403Lelio R Paula05/2015
48753^216685-113056103386Enzo Doria07/2014
487624829^14580+14580^24829103382Hans Havermann08/2020
487791355!4+1024103381Robert Price09/2019
487844^62903-43^62903103379Jean-Louis Charton08/2012
487911^99262-20103371Lelio R Paula12/2016
4880(509203*2^343357-1)/5103366Lelio R Paula05/2015
4881(2^343363+3570)/2103363Stefano Morozzi09/2020
48832^343356-2791889103361Enzo Doria03/2016
4882(25*10^103360-241)/9103361Robert Price05/2018
4884Phi(104989,10)/2939693103350Maksym Voznyy09/2015
488524826^14511+14511^24826103319Hans Havermann09/2020
48862^343182-171103309Lelio R Paula08/2011
4887(23619^23619+23620^23620)/7187103294David Broadhurst09/2009
48882^343079-1835611103278Enzo Doria05/2015
48892^343063-1147103273Yves Minet06/2013
489024741^14930+14930^24741103271Hans Havermann09/2020
4891(16*10^103255-73)/3103256Robert Price07/2020
48929*6^132689+7103254Lelio R Paula11/2014
48932^342979-18085103247Enzo Doria05/2013
4894(16*10^103244-31)/3103245Robert Price03/2019
48952^342966-16995103244Lelio R Paula11/2016
489623797^21774+21774^23797103230Hans Havermann09/2020
489725388^11637+11637^25388103224Hans Havermann09/2020
4898(2^342876+2086)/2103216Stefano Morozzi09/2020
4899(16*10^103214-31)/3103215Robert Price03/2019
4901(37*10^103211+611)/9103212Robert Price11/2018
4900(238*10^103210-1)/3103212Robert Price04/2020
49025^147650+16103203Lelio R Paula11/2016
4903gcd(Phi(852060,10),(10^42603+1)^3*(10^42603+1-10^21302)+(10^85206+10^42603)*(10^21302+1)+10^127809)103201Serge Batalov04/2015
49042^342817+2707067103199Enzo Doria03/2016
490543^63177-42103198Theodore Burton02/2007
49062^342805-21025103195Enzo Doria06/2013
490724129^18890+18890^24129103182Hans Havermann09/2020
49082^342714+12285103168Lelio R Paula11/2016
490918^82178-4481103156Enzo Doria03/2013
49102^342665-17349103153Enzo Doria05/2013
491130408^2467+2467^30408103150Hans Havermann09/2020
4912(2^342615+3090)/2103138Stefano Morozzi09/2020
49132^342612+175103137Lelio R Paula08/2011
49145*2^342585-3103130Lelio R Paula09/2014
4915(16*10^103127+77)/3103128Robert Price03/2019
4916(2^342527+3774)/2103111Stefano Morozzi02/2021
49172^342503-19209103104Enzo Doria05/2013
4918(2^342484+2586)/2103098Stefano Morozzi09/2020
49192^342476+51103096Lelio R Paula08/2011
49202^342460-18885103091Enzo Doria05/2013
4921(2^342442+862)/2103086Stefano Morozzi02/2021
4922(194*10^103074-17)/3103076Robert Price09/2020
49237^121968+82103075Lelio R Paula10/2016
49242^342392-108863103071Enzo Doria03/2014
4925(2^342389+806)/2103070Stefano Morozzi01/2021
49263^216014+28103065Lelio R Paula11/2016
49272^342353-108879103059Enzo Doria03/2014
492810^103055+276081103056Patrick De Geest12/2016
492910^103055-53103055Lelio R Paula11/2016
4930(58*10^103046+419)/9103047Robert Price05/2019
49317^121933+4103046Lelio R Paula11/2014
4932(2^342235+3618)/2103023Stefano Morozzi09/2020
493319^80560-68103017Lelio R Paula10/2016
49342^342209+76607103016Enzo Doria05/2016
4936328^40945+40945^328103013Norbert Schneider12/2014
493512^95454-91103013Lelio R Paula10/2016
493725833^9716+9716^25833103009Hans Havermann01/2019
493865^56809-64^56809102990Robert Price08/2013
49395^147338-6102985Lelio R Paula11/2014
49402^342084-112739102978Enzo Doria06/2014
49419*6^132330+7102974Lelio R Paula11/2014
49422^342034-16737102963Enzo Doria05/2013
4943(9787*2^342011-1)/25102959Lelio R Paula05/2015
4944(3^215802-5)/124343756102956Lelio R Paula12/2013
49452^341991-17421102950Enzo Doria05/2013
49462^341969-112225102943Enzo Doria06/2014
4947(9787*2^341864-1)/3102915Lelio R Paula05/2015
49482^341859+1869413102910Enzo Doria05/2016
494910^102909+61102910Lelio R Paula11/2016
495010^102909-67049102909Patrick De Geest12/2016
495123814^20935+20935^23814102898Hans Havermann02/2019
495228345^4264+4264^28345102888Hans Havermann02/2019
495325665^10204+10204^25665102886Hans Havermann02/2019
495426288^8181+8181^26288102860Hans Havermann02/2019
49552^341659+1836773102850Enzo Doria03/2016
49562^341608-110639102835Enzo Doria05/2014
495710^102824+49102825Lelio R Paula11/2016
495810^102824-168011102824Patrick De Geest12/2016
495911^98708-8102794Lelio R Paula10/2016
49602^341466+4429102792Lelio R Paula09/2011
49612^341460-107102790Lelio R Paula08/2011
4962(2^341388+47)/21014943102761Lelio R Paula12/2013
49632^341355+21102759Lelio R Paula08/2011
49642^341246+40755102726Lelio R Paula11/2016
4965(2^341256-5)/991699102723Lelio R Paula12/2013
49667^121547+78102720Lelio R Paula10/2016
49672^341223-461197102719Enzo Doria06/2015
496827838^4893+4893^27838102711Hans Havermann03/2019
49702^341190-20577102709Enzo Doria06/2013
4969(27*2^341212+1)/84674449102709Lelio R Paula12/2013
49716^131976-65102698Lelio R Paula10/2016
49722^341134+2533102692Henri Lifchitz09/2005
497313^92184-54102688Lelio R Paula10/2016
49742^341116-20873102687Enzo Doria06/2013
49752^341094-19953102680Enzo Doria06/2013
497623761^20950+20950^23761102676Hans Havermann03/2019
49772^341053+129102668Lelio R Paula08/2011
4979(31*2^341006-1)/3102655Lelio R Paula03/2014
49787^121471+94102655Lelio R Paula10/2016
49812^341004-173102653Lelio R Paula08/2011
498020^78901+3102653Lelio R Paula10/2016
4982(2^341001+1674)/2102652Stefano Morozzi09/2020
49835^146853-52102646Lelio R Paula10/2016
49842^340969-216931102642Enzo Doria05/2014
4985122^49196+121102641Norbert Schneider10/2018
49862^340952+1870021102637Enzo Doria05/2016
49875*2^340940-3102634Lelio R Paula08/2014
4988(6^131891+1)/7102631Paul Bourdelais01/2010
498925876^9239+9239^25876102615Hans Havermann02/2019
4990(4*10^102612+83)/3102613Robert Price02/2018
499175^54717+74102598Norbert Schneider01/2015
4992(17*10^102597+13)/3102598Robert Price01/2019
49932^340806-20393102593Enzo Doria06/2013
4994(2^340790+5)/138267102583Lelio R Paula12/2013
49956^131821+77102577Lelio R Paula10/2016
4996(203*10^102561-11)/3102563Robert Price12/2020
49972^340688-29102558Henri Lifchitz05/2005
49982^340685-109101102557Enzo Doria04/2014
499965^56567-64102552Norbert Schneider11/2014
500026230^8121+8121^26230102550Hans Havermann03/2019


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Created by  Henri Lifchitz & Renaud Lifchitz : October, 26 2000, last modification: April, 13 2021 12:02 (Time in France)

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