PRP Records

Probable Primes Top 10000

(253466 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 ?
32512^348003-20377104760Enzo Doria06/2013
32522^347994-741104757Lelio R Paula12/2016
3253(13*2^347972-1)/282309104746Lelio R Paula03/2014
32542^347910-109937104732Enzo Doria04/2014
32555^149794+28104702Lelio R Paula11/2016
3256105^51800-2104698Lelio R Paula10/2017
3257(16^86939+3^86939)/19104684Robert Price06/2013
3258(15^89009-1)/14104682Paul Bourdelais03/2010
32592^347731-18609104678Enzo Doria05/2013
32604*6^134519+7104677Lelio R Paula11/2014
32612^347612-18545104642Enzo Doria05/2013
32626^134465+95104635Lelio R Paula11/2016
32632^347517-17301104614Enzo Doria05/2013
32643^219222-310104596Lelio R Paula11/2016
3265(15*2^347399-1)/13104578Lelio R Paula03/2014
32662^347372-17853104570Enzo Doria05/2013
32672^347314+99104552Lelio R Paula09/2011
32682^347300-22233104548Enzo Doria06/2013
32692^347287-19845104544Enzo Doria06/2013
3270(31*2^347254-1)/891104533Lelio R Paula03/2014
32715*F(250091)*(F(250091)-1)+1104532Serge Batalov04/2015
32727*2^347239-3104531Lelio R Paula09/2014
3273(3^219098-8)/514147439969104525Lelio R Paula12/2013
32745*3^219047+8104513Lelio R Paula09/2014
32752^347148-109073104502Enzo Doria04/2014
32762^347129-20145104497Enzo Doria06/2013
32774*10^104461-57104462Robert Price10/2018
32782^346923-19585104435Enzo Doria05/2013
3279(11*2^346864-1)/175104416Lelio R Paula03/2014
32802^346854+346854^2+1104414Robert Price06/2014
32812^346834+11715104408Lelio R Paula04/2015
328279^55009+78104387Norbert Schneider02/2015
32833^218744+58104368Lelio R Paula11/2016
32842^346649+65104352Lelio R Paula09/2011
32852^346638-17265104349Enzo Doria05/2013
32865*10^104326+77104327Robert Price12/2018
32882^346527-111817104316Enzo Doria05/2014
32876^134055+101104316Lelio R Paula11/2016
32896^134013+163104283Lelio R Paula11/2016
329018^83049-89104250Lelio R Paula01/2017
32912^346213+484049104221Enzo Doria04/2017
329218^83021-91104214Lelio R Paula01/2017
329310^104212+128779104213Patrick De Geest05/2016
329410^104212+237447104213Patrick De Geest05/2016
329510^104212+242139104213Patrick De Geest05/2016
329610^104212+269199104213Patrick De Geest05/2016
3297(10^104212-71)/1104212Serge Batalov12/2014
32982^346078+7695104180Lelio R Paula12/2016
32992^346055-19537104173Enzo Doria05/2013
3300(3*2^346057+1)/77104173Lelio R Paula12/2013
33012^346037-20125104168Enzo Doria06/2013
3302(34*10^104168-7)/9/13/551179104162Makoto Morimoto05/2016
33036^133854-17993104159Enzo Doria03/2013
33042^345990+1874239104154Enzo Doria06/2016
33052^345988-20373104153Enzo Doria06/2013
3306(26*10^104132-503)/9104133Robert Price07/2018
33073*5^148968+8104125Lelio R Paula11/2014
3308(7*10^104113+53)/3104114Robert Price05/2018
3309p(21253)#/2+8104113Robert Price01/2017
3310322^41507+41507^322104094Norbert Schneider12/2014
33116^133768-17423104092Enzo Doria03/2013
33122^345786-19557104092Enzo Doria05/2013
3313171^46606-2104072Lelio R Paula10/2017
33142^345704-149104068Lelio R Paula09/2011
33156^133704-17273104042Enzo Doria02/2013
3316(3*2^345590-1)/23104033Lelio R Paula03/2014
3317(19*2^345590+1)/33859104030Lelio R Paula12/2013
33182^345547+11104021Lelio R Paula09/2011
3319(19*10^104014-49)/3104015Robert Price05/2019
33202^345504+723104008Lelio R Paula09/2011
33212^345498-20037104006Enzo Doria06/2013
332218^82854-37104005Lelio R Paula01/2017
33232^345486-109065104002Enzo Doria04/2014
33242^345487-1851507104002Enzo Doria08/2015
33252^345476+777103999Lelio R Paula09/2011
33264*10^103981-83103982Robert Price10/2018
3327(5*2^345321-1)/3103953Lelio R Paula03/2014
3328(2^345267-9)/539049127103927Lelio R Paula12/2013
3329(19*10^103907+77)/3103908Robert Price05/2019
3330(78557*2^345163+1)/78589103905Lelio R Paula07/2014
33312^345106-112181103888Enzo Doria06/2014
33322^345079+99103880Lelio R Paula09/2011
333311^99736-1500103865Enzo Doria12/2012
33342^344842-20157103808Enzo Doria06/2013
3335(47*2^344822+1)/1071103801Lelio R Paula05/2015
33362^344802-20765103796Enzo Doria06/2013
33372^344794-3821103794Yves Minet05/2011
33382^344782-109103103790Enzo Doria04/2014
33393^217521-112292103784Enzo Doria06/2014
33402^344759-3505103783Lelio R Paula11/2016
33412^344735-147103776Lelio R Paula09/2011
3342L(496533)-p(496533)103770Robert Price02/2018
33432*10^103749-69103750Robert Price03/2018
3344(55459*2^344617+1)/3103745Lelio R Paula07/2014
33452^344607-108891103738Enzo Doria03/2014
33462^344541-19561103718Enzo Doria05/2013
3347(1017*2^344529-1)/569103714Lelio R Paula05/2015
3348(4*10^103703-1)/3103704Serge Batalov08/2009
33492^344444-455103688Yves Minet03/2012
3350(13*53^238539*617^9)/10^307661103673Hans Havermann06/2017
33512^344317-109933103650Enzo Doria04/2014
33522^344309-1852033103648Enzo Doria08/2015
33532^344213-21253103619Enzo Doria06/2013
33542^344196-465103614Lelio R Paula11/2016
33552^344187-20001103611Enzo Doria06/2013
3356(117191#+(355573#)/(117191#))/(200233679)103602Makoto Morimoto10/2017
335720^79621-19^79621103590Jean-Louis Charton03/2011
3358Phi(155391,10)/1243129103586Maksym Voznyy09/2015
33592^344085-20365103580Enzo Doria06/2013
33605^148169+54103566Lelio R Paula11/2016
33612^344017-108795103560Enzo Doria03/2014
33622^343971-5077103546Lelio R Paula09/2011
3363(7*10^103531+71)/3103532Robert Price05/2018
33642^343899+141103524Lelio R Paula08/2011
3365(2^343933+1)/(3*98294339989393)103520Gord Palameta08/2018
33666^133029-67103517Lelio R Paula11/2016
3367(17*2^343877+1)/13625103515Lelio R Paula12/2013
3368(136*10^103474-1)/9103476Serge Batalov12/2014
33695^148014-24103458Lelio R Paula11/2016
3370(22*10^103450+53)/3103451Robert Price07/2019
33712^343604+9931103436Yves Minet01/2011
33722^343601-21189103435Enzo Doria06/2013
33732^343508-115229103407Enzo Doria06/2015
3374(509203*2^343491-1)/16147103403Lelio R Paula05/2015
33753^216685-113056103386Enzo Doria07/2014
337644^62903-43^62903103379Jean-Louis Charton08/2012
337711^99262-20103371Lelio R Paula12/2016
3378(509203*2^343357-1)/5103366Lelio R Paula05/2015
33792^343356-2791889103361Enzo Doria03/2016
3380(25*10^103360-241)/9103361Robert Price05/2018
3381Phi(104989,10)/2939693103350Maksym Voznyy09/2015
33822^343182-171103309Lelio R Paula08/2011
3383(23619^23619+23620^23620)/7187103294David Broadhurst09/2009
33842^343079-1835611103278Enzo Doria05/2015
33852^343063-1147103273Yves Minet06/2013
33869*6^132689+7103254Lelio R Paula11/2014
33872^342979-18085103247Enzo Doria05/2013
3388(16*10^103244-31)/3103245Robert Price03/2019
33892^342966-16995103244Lelio R Paula11/2016
3390(16*10^103214-31)/3103215Robert Price03/2019
3391(37*10^103211+611)/9103212Robert Price11/2018
33925^147650+16103203Lelio R Paula11/2016
3393gcd(Phi(852060,10),(10^42603+1)^3*(10^42603+1-10^21302)+(10^85206+10^42603)*(10^21302+1)+10^127809)103201Serge Batalov04/2015
33942^342817+2707067103199Enzo Doria03/2016
339543^63177-42103198Theodore Burton02/2007
33962^342805-21025103195Enzo Doria06/2013
33972^342714+12285103168Lelio R Paula11/2016
339818^82178-4481103156Enzo Doria03/2013
33992^342665-17349103153Enzo Doria05/2013
34002^342612+175103137Lelio R Paula08/2011
34015*2^342585-3103130Lelio R Paula09/2014
3402(16*10^103127+77)/3103128Robert Price03/2019
34032^342503-19209103104Enzo Doria05/2013
34042^342476+51103096Lelio R Paula08/2011
34052^342460-18885103091Enzo Doria05/2013
34067^121968+82103075Lelio R Paula10/2016
34072^342392-108863103071Enzo Doria03/2014
34083^216014+28103065Lelio R Paula11/2016
34092^342353-108879103059Enzo Doria03/2014
341010^103055+276081103056Patrick De Geest12/2016
341110^103055-53103055Lelio R Paula11/2016
3412(58*10^103046+419)/9103047Robert Price05/2019
34137^121933+4103046Lelio R Paula11/2014
341419^80560-68103017Lelio R Paula10/2016
34152^342209+76607103016Enzo Doria05/2016
3417328^40945+40945^328103013Norbert Schneider12/2014
341612^95454-91103013Lelio R Paula10/2016
341825833^9716+9716^25833103009Hans Havermann01/2019
341965^56809-64^56809102990Robert Price08/2013
34205^147338-6102985Lelio R Paula11/2014
34212^342084-112739102978Enzo Doria06/2014
34229*6^132330+7102974Lelio R Paula11/2014
34232^342034-16737102963Enzo Doria05/2013
3424(9787*2^342011-1)/25102959Lelio R Paula05/2015
3425(3^215802-5)/124343756102956Lelio R Paula12/2013
34262^341991-17421102950Enzo Doria05/2013
34272^341969-112225102943Enzo Doria06/2014
3428(9787*2^341864-1)/3102915Lelio R Paula05/2015
34292^341859+1869413102910Enzo Doria05/2016
343010^102909+61102910Lelio R Paula11/2016
343110^102909-67049102909Patrick De Geest12/2016
343223814^20935+20935^23814102898Hans Havermann02/2019
343328345^4264+4264^28345102888Hans Havermann02/2019
343425665^10204+10204^25665102886Hans Havermann02/2019
343526288^8181+8181^26288102860Hans Havermann02/2019
34362^341659+1836773102850Enzo Doria03/2016
34372^341608-110639102835Enzo Doria05/2014
343810^102824+49102825Lelio R Paula11/2016
343910^102824-168011102824Patrick De Geest12/2016
344011^98708-8102794Lelio R Paula10/2016
34412^341466+4429102792Lelio R Paula09/2011
34422^341460-107102790Lelio R Paula08/2011
3443(2^341388+47)/21014943102761Lelio R Paula12/2013
34442^341355+21102759Lelio R Paula08/2011
34452^341246+40755102726Lelio R Paula11/2016
3446(2^341256-5)/991699102723Lelio R Paula12/2013
34477^121547+78102720Lelio R Paula10/2016
34482^341223-461197102719Enzo Doria06/2015
344927838^4893+4893^27838102711Hans Havermann03/2019
34512^341190-20577102709Enzo Doria06/2013
3450(27*2^341212+1)/84674449102709Lelio R Paula12/2013
34526^131976-65102698Lelio R Paula10/2016
34532^341134+2533102692Henri Lifchitz09/2005
345413^92184-54102688Lelio R Paula10/2016
34552^341116-20873102687Enzo Doria06/2013
34562^341094-19953102680Enzo Doria06/2013
345723761^20950+20950^23761102676Hans Havermann03/2019
34582^341053+129102668Lelio R Paula08/2011
3459(31*2^341006-1)/3102655Lelio R Paula03/2014
34607^121471+94102655Lelio R Paula10/2016
34622^341004-173102653Lelio R Paula08/2011
346120^78901+3102653Lelio R Paula10/2016
34635^146853-52102646Lelio R Paula10/2016
34642^340969-216931102642Enzo Doria05/2014
3465122^49196+121102641Norbert Schneider10/2018
34662^340952+1870021102637Enzo Doria05/2016
34675*2^340940-3102634Lelio R Paula08/2014
3468(6^131891+1)/7102631Paul Bourdelais01/2010
346925876^9239+9239^25876102615Hans Havermann02/2019
3470(4*10^102612+83)/3102613Robert Price02/2018
347275^54717+74102598Norbert Schneider01/2015
3471(17*10^102597+13)/3102598Robert Price01/2019
34732^340806-20393102593Enzo Doria06/2013
3474(2^340790+5)/138267102583Lelio R Paula12/2013
34756^131821+77102577Lelio R Paula10/2016
34762^340688-29102558Henri Lifchitz05/2005
34772^340685-109101102557Enzo Doria04/2014
347865^56567-64102552Norbert Schneider11/2014
347926230^8121+8121^26230102550Hans Havermann03/2019
34802^340547-108897102515Enzo Doria03/2014
348125592^10119+10119^25592102500Hans Havermann02/2019
34827^121268+82102484Lelio R Paula10/2016
3483(6883*2^340443-1)/162401102483Lelio R Paula05/2015
34842^340434-5955102481Lelio R Paula11/2016
3485(2^340381+47)/7102465Lelio R Paula12/2013
3486111^50095+110102461Norbert Schneider04/2017
34872^340291-20301102438Enzo Doria06/2013
348812^94915+89102431Lelio R Paula10/2016
348924466^15349+15349^24466102417Hans Havermann03/2019
34902^340208-20373102413Enzo Doria06/2013
34916^131598-17273102404Enzo Doria02/2013
34922^340115-21181102385Enzo Doria06/2013
3493(55459*2^340090+1)/1591102379Lelio R Paula07/2014
349489^52511-88^52511102365Robert Price06/2015
34953^214539-112756102362Enzo Doria07/2014
34962^340000-19877102351Enzo Doria06/2013
34972^339990-114845102348Enzo Doria05/2015
3498(3^214516-2)/51383102346Lelio R Paula12/2013
349920^78661-99102341Lelio R Paula09/2016
35002^339951-19585102336Enzo Doria05/2013


Find by discoverer :


Created by  Henri Lifchitz & Renaud Lifchitz : October, 26 2000, last modification: August, 20 2019 14:10 (Time in France)

Go back
Valid XHTML 1.0!    Valid CSS!