PRP Records

Probable Primes Top 10000

(252932 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 ?
3251(19*10^104014-49)/3104015Robert Price05/2019
32522^345504+723104008Lelio R Paula09/2011
32532^345498-20037104006Enzo Doria06/2013
325418^82854-37104005Lelio R Paula01/2017
32552^345486-109065104002Enzo Doria04/2014
32562^345487-1851507104002Enzo Doria08/2015
32572^345476+777103999Lelio R Paula09/2011
32584*10^103981-83103982Robert Price10/2018
3259(5*2^345321-1)/3103953Lelio R Paula03/2014
3260(2^345267-9)/539049127103927Lelio R Paula12/2013
3261(19*10^103907+77)/3103908Robert Price05/2019
3262(78557*2^345163+1)/78589103905Lelio R Paula07/2014
32632^345106-112181103888Enzo Doria06/2014
32642^345079+99103880Lelio R Paula09/2011
326511^99736-1500103865Enzo Doria12/2012
32662^344842-20157103808Enzo Doria06/2013
3267(47*2^344822+1)/1071103801Lelio R Paula05/2015
32682^344802-20765103796Enzo Doria06/2013
32692^344794-3821103794Yves Minet05/2011
32702^344782-109103103790Enzo Doria04/2014
32713^217521-112292103784Enzo Doria06/2014
32722^344759-3505103783Lelio R Paula11/2016
32732^344735-147103776Lelio R Paula09/2011
3274L(496533)-p(496533)103770Robert Price02/2018
32752*10^103749-69103750Robert Price03/2018
3276(55459*2^344617+1)/3103745Lelio R Paula07/2014
32772^344607-108891103738Enzo Doria03/2014
32782^344541-19561103718Enzo Doria05/2013
3279(1017*2^344529-1)/569103714Lelio R Paula05/2015
3280(4*10^103703-1)/3103704Serge Batalov08/2009
32812^344444-455103688Yves Minet03/2012
3282(13*53^238539*617^9)/10^307661103673Hans Havermann06/2017
32832^344317-109933103650Enzo Doria04/2014
32842^344309-1852033103648Enzo Doria08/2015
32852^344213-21253103619Enzo Doria06/2013
32862^344196-465103614Lelio R Paula11/2016
32872^344187-20001103611Enzo Doria06/2013
3288(117191#+(355573#)/(117191#))/(200233679)103602Makoto Morimoto10/2017
328920^79621-19^79621103590Jean-Louis Charton03/2011
3290Phi(155391,10)/1243129103586Maksym Voznyy09/2015
32912^344085-20365103580Enzo Doria06/2013
32925^148169+54103566Lelio R Paula11/2016
32932^344017-108795103560Enzo Doria03/2014
32942^343971-5077103546Lelio R Paula09/2011
3295(7*10^103531+71)/3103532Robert Price05/2018
32962^343899+141103524Lelio R Paula08/2011
3297(2^343933+1)/(3*98294339989393)103520Gord Palameta08/2018
32986^133029-67103517Lelio R Paula11/2016
3299(17*2^343877+1)/13625103515Lelio R Paula12/2013
3300(136*10^103474-1)/9103476Serge Batalov12/2014
33015^148014-24103458Lelio R Paula11/2016
33022^343604+9931103436Yves Minet01/2011
33032^343601-21189103435Enzo Doria06/2013
33042^343508-115229103407Enzo Doria06/2015
3305(509203*2^343491-1)/16147103403Lelio R Paula05/2015
33063^216685-113056103386Enzo Doria07/2014
330744^62903-43^62903103379Jean-Louis Charton08/2012
330811^99262-20103371Lelio R Paula12/2016
3309(509203*2^343357-1)/5103366Lelio R Paula05/2015
33102^343356-2791889103361Enzo Doria03/2016
3311(25*10^103360-241)/9103361Robert Price05/2018
3312Phi(104989,10)/2939693103350Maksym Voznyy09/2015
33132^343182-171103309Lelio R Paula08/2011
3314(23619^23619+23620^23620)/7187103294David Broadhurst09/2009
33152^343079-1835611103278Enzo Doria05/2015
33162^343063-1147103273Yves Minet06/2013
33179*6^132689+7103254Lelio R Paula11/2014
33182^342979-18085103247Enzo Doria05/2013
3319(16*10^103244-31)/3103245Robert Price03/2019
33202^342966-16995103244Lelio R Paula11/2016
3321(16*10^103214-31)/3103215Robert Price03/2019
3322(37*10^103211+611)/9103212Robert Price11/2018
33235^147650+16103203Lelio R Paula11/2016
3324gcd(Phi(852060,10),(10^42603+1)^3*(10^42603+1-10^21302)+(10^85206+10^42603)*(10^21302+1)+10^127809)103201Serge Batalov04/2015
33252^342817+2707067103199Enzo Doria03/2016
332643^63177-42103198Theodore Burton02/2007
33272^342805-21025103195Enzo Doria06/2013
33282^342714+12285103168Lelio R Paula11/2016
332918^82178-4481103156Enzo Doria03/2013
33302^342665-17349103153Enzo Doria05/2013
33312^342612+175103137Lelio R Paula08/2011
33325*2^342585-3103130Lelio R Paula09/2014
3333(16*10^103127+77)/3103128Robert Price03/2019
33342^342503-19209103104Enzo Doria05/2013
33352^342476+51103096Lelio R Paula08/2011
33362^342460-18885103091Enzo Doria05/2013
33377^121968+82103075Lelio R Paula10/2016
33382^342392-108863103071Enzo Doria03/2014
33393^216014+28103065Lelio R Paula11/2016
33402^342353-108879103059Enzo Doria03/2014
334110^103055+276081103056Patrick De Geest12/2016
334210^103055-53103055Lelio R Paula11/2016
3343(58*10^103046+419)/9103047Robert Price05/2019
33447^121933+4103046Lelio R Paula11/2014
334519^80560-68103017Lelio R Paula10/2016
33462^342209+76607103016Enzo Doria05/2016
3348328^40945+40945^328103013Norbert Schneider12/2014
334712^95454-91103013Lelio R Paula10/2016
334925833^9716+9716^25833103009Hans Havermann01/2019
335065^56809-64^56809102990Robert Price08/2013
33515^147338-6102985Lelio R Paula11/2014
33522^342084-112739102978Enzo Doria06/2014
33539*6^132330+7102974Lelio R Paula11/2014
33542^342034-16737102963Enzo Doria05/2013
3355(9787*2^342011-1)/25102959Lelio R Paula05/2015
3356(3^215802-5)/124343756102956Lelio R Paula12/2013
33572^341991-17421102950Enzo Doria05/2013
33582^341969-112225102943Enzo Doria06/2014
3359(9787*2^341864-1)/3102915Lelio R Paula05/2015
33612^341859+1869413102910Enzo Doria05/2016
336010^102909+61102910Lelio R Paula11/2016
336210^102909-67049102909Patrick De Geest12/2016
336323814^20935+20935^23814102898Hans Havermann02/2019
336428345^4264+4264^28345102888Hans Havermann02/2019
336525665^10204+10204^25665102886Hans Havermann02/2019
336626288^8181+8181^26288102860Hans Havermann02/2019
33672^341659+1836773102850Enzo Doria03/2016
33682^341608-110639102835Enzo Doria05/2014
336910^102824+49102825Lelio R Paula11/2016
337010^102824-168011102824Patrick De Geest12/2016
337111^98708-8102794Lelio R Paula10/2016
33722^341466+4429102792Lelio R Paula09/2011
33732^341460-107102790Lelio R Paula08/2011
3374(2^341388+47)/21014943102761Lelio R Paula12/2013
33752^341355+21102759Lelio R Paula08/2011
33762^341246+40755102726Lelio R Paula11/2016
3377(2^341256-5)/991699102723Lelio R Paula12/2013
33787^121547+78102720Lelio R Paula10/2016
33792^341223-461197102719Enzo Doria06/2015
338027838^4893+4893^27838102711Hans Havermann03/2019
33822^341190-20577102709Enzo Doria06/2013
3381(27*2^341212+1)/84674449102709Lelio R Paula12/2013
33836^131976-65102698Lelio R Paula10/2016
33842^341134+2533102692Henri Lifchitz09/2005
338513^92184-54102688Lelio R Paula10/2016
33862^341116-20873102687Enzo Doria06/2013
33872^341094-19953102680Enzo Doria06/2013
338823761^20950+20950^23761102676Hans Havermann03/2019
33892^341053+129102668Lelio R Paula08/2011
3391(31*2^341006-1)/3102655Lelio R Paula03/2014
33907^121471+94102655Lelio R Paula10/2016
33932^341004-173102653Lelio R Paula08/2011
339220^78901+3102653Lelio R Paula10/2016
33945^146853-52102646Lelio R Paula10/2016
33952^340969-216931102642Enzo Doria05/2014
3396122^49196+121102641Norbert Schneider10/2018
33972^340952+1870021102637Enzo Doria05/2016
33985*2^340940-3102634Lelio R Paula08/2014
3399(6^131891+1)/7102631Paul Bourdelais01/2010
340025876^9239+9239^25876102615Hans Havermann02/2019
3401(4*10^102612+83)/3102613Robert Price02/2018
340275^54717+74102598Norbert Schneider01/2015
3403(17*10^102597+13)/3102598Robert Price01/2019
34042^340806-20393102593Enzo Doria06/2013
3405(2^340790+5)/138267102583Lelio R Paula12/2013
34066^131821+77102577Lelio R Paula10/2016
34072^340688-29102558Henri Lifchitz05/2005
34082^340685-109101102557Enzo Doria04/2014
340965^56567-64102552Norbert Schneider11/2014
341026230^8121+8121^26230102550Hans Havermann03/2019
34112^340547-108897102515Enzo Doria03/2014
341225592^10119+10119^25592102500Hans Havermann02/2019
34137^121268+82102484Lelio R Paula10/2016
3414(6883*2^340443-1)/162401102483Lelio R Paula05/2015
34152^340434-5955102481Lelio R Paula11/2016
3416(2^340381+47)/7102465Lelio R Paula12/2013
3417111^50095+110102461Norbert Schneider04/2017
34182^340291-20301102438Enzo Doria06/2013
341912^94915+89102431Lelio R Paula10/2016
342024466^15349+15349^24466102417Hans Havermann03/2019
34212^340208-20373102413Enzo Doria06/2013
34226^131598-17273102404Enzo Doria02/2013
34232^340115-21181102385Enzo Doria06/2013
3424(55459*2^340090+1)/1591102379Lelio R Paula07/2014
342589^52511-88^52511102365Robert Price06/2015
34263^214539-112756102362Enzo Doria07/2014
34272^340000-19877102351Enzo Doria06/2013
34282^339990-114845102348Enzo Doria05/2015
3429(3^214516-2)/51383102346Lelio R Paula12/2013
343020^78661-99102341Lelio R Paula09/2016
34312^339951-19585102336Enzo Doria05/2013
3432(13*2^339943+1)/45102333Lelio R Paula12/2013
34332^339889+29327102317Yves Minet06/2010
343426348^7641+7641^26348102314Hans Havermann03/2019
34352^339834-109493102301Enzo Doria04/2014
3436(16*10^102299-19)/3102300Robert Price02/2019
3437(11^98221-5^98221)/6102286Robert Price01/2013
34383^214365+1820102279Lelio R Paula10/2016
343931978^1579+1579^31978102278Hans Havermann03/2019
3440(11*2^339705-1)/183102261Lelio R Paula03/2014
34412^339694-16995102259Lelio R Paula09/2016
3442(56*10^102255+691)/9102256Robert Price05/2019
3443122^49008+121102249Norbert Schneider10/2018
34447^120985-38102245Lelio R Paula10/2016
344510^102244+122961102245Patrick De Geest12/2016
344610^102244-27102244Lelio R Paula09/2016
34477^120982-62102242Lelio R Paula10/2016
34484*6^131382-5102236Lelio R Paula11/2014
34492^339586-1091102226Yves Minet11/2012
345011^98161-3072000102225Enzo Doria12/2012
34519*7^120961-4102225Lelio R Paula11/2014
34525*3^214250+2102224Serge Batalov10/2010
345312^94713-59102213Lelio R Paula10/2016
345412^94705+89102204Lelio R Paula10/2016
34552^339407-177102172Lelio R Paula08/2011
34564*10^102163-57102164Robert Price10/2018
34572^339355+65102157Lelio R Paula07/2011
3458(2^339323+47)/880715102141Lelio R Paula12/2013
34602^339168+21102100Lelio R Paula07/2011
34592^339167-108807102100Enzo Doria03/2014
34612^339156+163102097Lelio R Paula08/2011
34622^339081-4543102074Yves Minet03/2019
346324327^15668+15668^24327102053Hans Havermann02/2019
346425080^11711+11711^25080102041Hans Havermann02/2019
3465(2^338982-7)/1754517102038Lelio R Paula12/2013
34662^338891-18885102017Enzo Doria05/2013
34672^338829-113239101998Enzo Doria07/2014
34682^338828-113297101998Enzo Doria07/2014
34692^338796+93101988Donovan Johnson06/2008
3470lucasU(1373,1,32502)-lucasU(1373,1,32501)101978Mike Oakes05/2009
347125295^10744+10744^25295101969Hans Havermann01/2019
347225712^9243+9243^25712101969Hans Havermann01/2019
3473(71^55079-1)/70101964Paul Bourdelais08/2017
34752^338682-19865101954Enzo Doria06/2013
3474(2^(112895*3+1)+243)/7101954Kevin Acres12/2013
347628594^3673+3673^28594101939Hans Havermann02/2019
34772^338568+37101920Lelio R Paula07/2011
34782^338559-1858777101917Enzo Doria04/2016
3479(9*2^338520+1)/365101904Lelio R Paula12/2013
348024502^14419+14419^24502101903Hans Havermann01/2019
34812^338497-17041101898Enzo Doria05/2013
34822^338475+54615101892Lelio R Paula10/2016
34832^338426-19797101877Enzo Doria06/2013
34842^338368-20369101859Enzo Doria06/2013
34852^338366+74179101859Enzo Doria04/2016
348627088^5755+5755^27088101853Hans Havermann01/2019
34872^338280-19745101833Enzo Doria06/2013
3488(3*2^338236-1)/347101818Lelio R Paula03/2014
34896^130841+103101815Lelio R Paula10/2016
34902^338122-20117101785Enzo Doria06/2013
3491(2^338139+5)/905333101785Lelio R Paula12/2013
349235^65917-7092101781Enzo Doria03/2013
34932^338010-19833101752Enzo Doria06/2013
34943^213215-76101730Lelio R Paula09/2016
349523907^17998+17998^23907101730Hans Havermann01/2019
34962^337930+63101728Lelio R Paula07/2011
34972^337920+1869661101725Enzo Doria05/2016
349824116^16509+16509^24116101715Hans Havermann01/2019
34992^337859-19645101706Enzo Doria05/2013
35002^337754+1869169101675Enzo Doria05/2016


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Created by  Henri Lifchitz & Renaud Lifchitz : October, 26 2000, last modification: June, 18 2019 07:14 (Time in France)

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