PRP Records

Probable Primes Top 10000

(172742 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 (> 30000) Who ? When ?
2501(31*2^347254-1)/891104533Lelio R Paula03/2014
25025*F(250091)*(F(250091)-1)+1104532Serge Batalov04/2015
25037*2^347239-3104531Lelio R Paula09/2014
2504(3^219098-8)/514147439969104525Lelio R Paula12/2013
25055*3^219047+8104513Lelio R Paula09/2014
25062^347148-109073104502Enzo Doria04/2014
25072^347129-20145104497Enzo Doria06/2013
25082^346923-19585104435Enzo Doria05/2013
2509(11*2^346864-1)/175104416Lelio R Paula03/2014
25102^346854+346854^2+1104414Robert Price06/2014
25112^346834+11715104408Lelio R Paula04/2015
251279^55009+78104387Norbert Schneider02/2015
25133^218744+58104368Lelio R Paula11/2016
25142^346649+65104352Lelio R Paula09/2011
25152^346638-17265104349Enzo Doria05/2013
25172^346527-111817104316Enzo Doria05/2014
25166^134055+101104316Lelio R Paula11/2016
25186^134013+163104283Lelio R Paula11/2016
251918^83049-89104250Lelio R Paula01/2017
25202^346213+484049104221Enzo Doria04/2017
252118^83021-91104214Lelio R Paula01/2017
252210^104212+128779104213Patrick De Geest05/2016
252310^104212+237447104213Patrick De Geest05/2016
252410^104212+242139104213Patrick De Geest05/2016
252510^104212+269199104213Patrick De Geest05/2016
2526(10^104212-71)/1104212Serge Batalov12/2014
25272^346078+7695104180Lelio R Paula12/2016
25282^346055-19537104173Enzo Doria05/2013
2529(3*2^346057+1)/77104173Lelio R Paula12/2013
25302^346037-20125104168Enzo Doria06/2013
2531(34*10^104168-7)/9/13/551179104162Makoto Morimoto05/2016
25326^133854-17993104159Enzo Doria03/2013
25332^345990+1874239104154Enzo Doria06/2016
25342^345988-20373104153Enzo Doria06/2013
25353*5^148968+8104125Lelio R Paula11/2014
2536p(21253)#/2+8104113Robert Price01/2017
2537322^41507+41507^322104094Norbert Schneider12/2014
25386^133768-17423104092Enzo Doria03/2013
25392^345786-19557104092Enzo Doria05/2013
25402^345704-149104068Lelio R Paula09/2011
25416^133704-17273104042Enzo Doria02/2013
2542(3*2^345590-1)/23104033Lelio R Paula03/2014
2543(19*2^345590+1)/33859104030Lelio R Paula12/2013
25442^345547+11104021Lelio R Paula09/2011
25452^345504+723104008Lelio R Paula09/2011
25462^345498-20037104006Enzo Doria06/2013
254718^82854-37104005Lelio R Paula01/2017
25482^345486-109065104002Enzo Doria04/2014
25492^345487-1851507104002Enzo Doria08/2015
25502^345476+777103999Lelio R Paula09/2011
2551(5*2^345321-1)/3103953Lelio R Paula03/2014
2552(2^345267-9)/539049127103927Lelio R Paula12/2013
2553(78557*2^345163+1)/78589103905Lelio R Paula07/2014
25542^345106-112181103888Enzo Doria06/2014
25552^345079+99103880Lelio R Paula09/2011
255611^99736-1500103865Enzo Doria12/2012
25572^344842-20157103808Enzo Doria06/2013
2558(47*2^344822+1)/1071103801Lelio R Paula05/2015
25592^344802-20765103796Enzo Doria06/2013
25602^344794-3821103794Yves Minet05/2011
25612^344782-109103103790Enzo Doria04/2014
25623^217521-112292103784Enzo Doria06/2014
25632^344759-3505103783Lelio R Paula11/2016
25642^344735-147103776Lelio R Paula09/2011
2565(55459*2^344617+1)/3103745Lelio R Paula07/2014
25662^344607-108891103738Enzo Doria03/2014
25672^344541-19561103718Enzo Doria05/2013
2568(1017*2^344529-1)/569103714Lelio R Paula05/2015
2569(4*10^103703-1)/3103704Serge Batalov08/2009
25702^344444-455103688Yves Minet03/2012
25712^344317-109933103650Enzo Doria04/2014
25722^344309-1852033103648Enzo Doria08/2015
25732^344213-21253103619Enzo Doria06/2013
25742^344196-465103614Lelio R Paula11/2016
25752^344187-20001103611Enzo Doria06/2013
257620^79621-19^79621103590Jean-Louis Charton03/2011
2577Phi(155391,10)/1243129103586Maksym Voznyy09/2015
25782^344085-20365103580Enzo Doria06/2013
25795^148169+54103566Lelio R Paula11/2016
25802^344017-108795103560Enzo Doria03/2014
25812^343971-5077103546Lelio R Paula09/2011
25822^343899+141103524Lelio R Paula08/2011
25836^133029-67103517Lelio R Paula11/2016
2584(17*2^343877+1)/13625103515Lelio R Paula12/2013
2585(136*10^103474-1)/9103476Serge Batalov12/2014
25865^148014-24103458Lelio R Paula11/2016
25872^343604+9931103436Yves Minet01/2011
25882^343601-21189103435Enzo Doria06/2013
25892^343508-115229103407Enzo Doria06/2015
2590(509203*2^343491-1)/16147103403Lelio R Paula05/2015
25913^216685-113056103386Enzo Doria07/2014
259244^62903-43^62903103379Jean-Louis Charton08/2012
259311^99262-20103371Lelio R Paula12/2016
2594(509203*2^343357-1)/5103366Lelio R Paula05/2015
25952^343356-2791889103361Enzo Doria03/2016
2596Phi(104989,10)/2939693103350Maksym Voznyy09/2015
25972^343182-171103309Lelio R Paula08/2011
2598(23619^23619+23620^23620)/7187103294David Broadhurst09/2009
25992^343079-1835611103278Enzo Doria05/2015
26002^343063-1147103273Yves Minet06/2013
26019*6^132689+7103254Lelio R Paula11/2014
26022^342979-18085103247Enzo Doria05/2013
26032^342966-16995103244Lelio R Paula11/2016
26045^147650+16103203Lelio R Paula11/2016
2605gcd(Phi(852060,10),(10^42603+1)^3*(10^42603+1-10^21302)+(10^85206+10^42603)*(10^21302+1)+10^127809)103201Serge Batalov04/2015
26062^342817+2707067103199Enzo Doria03/2016
260743^63177-42103198Theodore Burton02/2007
26082^342805-21025103195Enzo Doria06/2013
26092^342714+12285103168Lelio R Paula11/2016
261018^82178-4481103156Enzo Doria03/2013
26112^342665-17349103153Enzo Doria05/2013
26122^342612+175103137Lelio R Paula08/2011
26135*2^342585-3103130Lelio R Paula09/2014
26142^342503-19209103104Enzo Doria05/2013
26152^342476+51103096Lelio R Paula08/2011
26162^342460-18885103091Enzo Doria05/2013
26177^121968+82103075Lelio R Paula10/2016
26182^342392-108863103071Enzo Doria03/2014
26193^216014+28103065Lelio R Paula11/2016
26202^342353-108879103059Enzo Doria03/2014
262110^103055+276081103056Patrick De Geest12/2016
262210^103055-53103055Lelio R Paula11/2016
26237^121933+4103046Lelio R Paula11/2014
262419^80560-68103017Lelio R Paula10/2016
26252^342209+76607103016Enzo Doria05/2016
2627328^40945+40945^328103013Norbert Schneider12/2014
262612^95454-91103013Lelio R Paula10/2016
262865^56809-64^56809102990Robert Price08/2013
26295^147338-6102985Lelio R Paula11/2014
26302^342084-112739102978Enzo Doria06/2014
26319*6^132330+7102974Lelio R Paula11/2014
26322^342034-16737102963Enzo Doria05/2013
2633(9787*2^342011-1)/25102959Lelio R Paula05/2015
2634(3^215802-5)/124343756102956Lelio R Paula12/2013
26352^341991-17421102950Enzo Doria05/2013
26362^341969-112225102943Enzo Doria06/2014
2637(9787*2^341864-1)/3102915Lelio R Paula05/2015
26392^341859+1869413102910Enzo Doria05/2016
263810^102909+61102910Lelio R Paula11/2016
264010^102909-67049102909Patrick De Geest12/2016
26412^341659+1836773102850Enzo Doria03/2016
26422^341608-110639102835Enzo Doria05/2014
264310^102824+49102825Lelio R Paula11/2016
264410^102824-168011102824Patrick De Geest12/2016
264511^98708-8102794Lelio R Paula10/2016
26462^341466+4429102792Lelio R Paula09/2011
26472^341460-107102790Lelio R Paula08/2011
2648(2^341388+47)/21014943102761Lelio R Paula12/2013
26492^341355+21102759Lelio R Paula08/2011
26502^341246+40755102726Lelio R Paula11/2016
2651(2^341256-5)/991699102723Lelio R Paula12/2013
26527^121547+78102720Lelio R Paula10/2016
26532^341223-461197102719Enzo Doria06/2015
26542^341190-20577102709Enzo Doria06/2013
2655(27*2^341212+1)/84674449102709Lelio R Paula12/2013
26566^131976-65102698Lelio R Paula10/2016
26572^341134+2533102692Henri Lifchitz09/2005
265813^92184-54102688Lelio R Paula10/2016
26592^341116-20873102687Enzo Doria06/2013
26602^341094-19953102680Enzo Doria06/2013
26612^341053+129102668Lelio R Paula08/2011
2662(31*2^341006-1)/3102655Lelio R Paula03/2014
26637^121471+94102655Lelio R Paula10/2016
26652^341004-173102653Lelio R Paula08/2011
266420^78901+3102653Lelio R Paula10/2016
26665^146853-52102646Lelio R Paula10/2016
26672^340969-216931102642Enzo Doria05/2014
26682^340952+1870021102637Enzo Doria05/2016
26695*2^340940-3102634Lelio R Paula08/2014
2670(6^131891+1)/7102631Paul Bourdelais01/2010
267175^54717+74102598Norbert Schneider01/2015
26722^340806-20393102593Enzo Doria06/2013
2673(2^340790+5)/138267102583Lelio R Paula12/2013
26746^131821+77102577Lelio R Paula10/2016
26752^340688-29102558Henri Lifchitz05/2005
26762^340685-109101102557Enzo Doria04/2014
267765^56567-64102552Norbert Schneider11/2014
26782^340547-108897102515Enzo Doria03/2014
26797^121268+82102484Lelio R Paula10/2016
2680(6883*2^340443-1)/162401102483Lelio R Paula05/2015
26812^340434-5955102481Lelio R Paula11/2016
2682(2^340381+47)/7102465Lelio R Paula12/2013
26832^340291-20301102438Enzo Doria06/2013
268412^94915+89102431Lelio R Paula10/2016
26852^340208-20373102413Enzo Doria06/2013
26866^131598-17273102404Enzo Doria02/2013
26872^340115-21181102385Enzo Doria06/2013
2688(55459*2^340090+1)/1591102379Lelio R Paula07/2014
268989^52511-88^52511102365Robert Price06/2015
26903^214539-112756102362Enzo Doria07/2014
26912^340000-19877102351Enzo Doria06/2013
26922^339990-114845102348Enzo Doria05/2015
2693(3^214516-2)/51383102346Lelio R Paula12/2013
269420^78661-99102341Lelio R Paula09/2016
26952^339951-19585102336Enzo Doria05/2013
2696(13*2^339943+1)/45102333Lelio R Paula12/2013
26972^339889+29327102317Yves Minet06/2010
26982^339834-109493102301Enzo Doria04/2014
2699(11^98221-5^98221)/6102286Robert Price01/2013
27003^214365+1820102279Lelio R Paula10/2016
2701(11*2^339705-1)/183102261Lelio R Paula03/2014
27022^339694-16995102259Lelio R Paula09/2016
27037^120985-38102245Lelio R Paula10/2016
270410^102244+122961102245Patrick De Geest12/2016
270510^102244-27102244Lelio R Paula09/2016
27067^120982-62102242Lelio R Paula10/2016
27074*6^131382-5102236Lelio R Paula11/2014
27082^339586-1091102226Yves Minet11/2012
270911^98161-3072000102225Enzo Doria12/2012
27109*7^120961-4102225Lelio R Paula11/2014
27115*3^214250+2102224Serge Batalov10/2010
271212^94713-59102213Lelio R Paula10/2016
271312^94705+89102204Lelio R Paula10/2016
27142^339407-177102172Lelio R Paula08/2011
27152^339355+65102157Lelio R Paula07/2011
2716(2^339323+47)/880715102141Lelio R Paula12/2013
27172^339168+21102100Lelio R Paula07/2011
27182^339167-108807102100Enzo Doria03/2014
27192^339156+163102097Lelio R Paula08/2011
2720(2^338982-7)/1754517102038Lelio R Paula12/2013
27212^338891-18885102017Enzo Doria05/2013
27222^338829-113239101998Enzo Doria07/2014
27232^338828-113297101998Enzo Doria07/2014
27242^338796+93101988Donovan Johnson06/2008
2725lucasU(1373,1,32502)-lucasU(1373,1,32501)101978Mike Oakes05/2009
27262^338682-19865101954Enzo Doria06/2013
2727(2^(112895*3+1)+243)/7101954Kevin Acres12/2013
27282^338568+37101920Lelio R Paula07/2011
27292^338559-1858777101917Enzo Doria04/2016
2730(9*2^338520+1)/365101904Lelio R Paula12/2013
27312^338497-17041101898Enzo Doria05/2013
27322^338475+54615101892Lelio R Paula10/2016
27332^338426-19797101877Enzo Doria06/2013
27342^338368-20369101859Enzo Doria06/2013
27352^338366+74179101859Enzo Doria04/2016
27362^338280-19745101833Enzo Doria06/2013
2737(3*2^338236-1)/347101818Lelio R Paula03/2014
27386^130841+103101815Lelio R Paula10/2016
27392^338122-20117101785Enzo Doria06/2013
2740(2^338139+5)/905333101785Lelio R Paula12/2013
274135^65917-7092101781Enzo Doria03/2013
27422^338010-19833101752Enzo Doria06/2013
27433^213215-76101730Lelio R Paula09/2016
27442^337930+63101728Lelio R Paula07/2011
27452^337920+1869661101725Enzo Doria05/2016
27462^337859-19645101706Enzo Doria05/2013
27472^337754+1869169101675Enzo Doria05/2016
2748(31*2^337677-1)/593101650Lelio R Paula03/2014
274911^97605-24101646Lelio R Paula10/2016
27508^112539-112539101633Robert Price01/2014


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Created by  Henri Lifchitz & Renaud Lifchitz : October, 26 2000, last modification: April, 21 2017 08:01 (Time in France)

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