PRP Records

Probable Primes Top 10000

(247113 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 ?
30012^348212-20105104823Enzo Doria06/2013
300220^80562+19104814Lelio R Paula12/2016
30032*10^104811-87104812Robert Price04/2018
30042^348149-20053104804Enzo Doria06/2013
30052^348095-171104788Lelio R Paula09/2011
30062^348003-20377104760Enzo Doria06/2013
30072^347994-741104757Lelio R Paula12/2016
3008(13*2^347972-1)/282309104746Lelio R Paula03/2014
30092^347910-109937104732Enzo Doria04/2014
30105^149794+28104702Lelio R Paula11/2016
3011105^51800-2104698Lelio R Paula10/2017
3012(16^86939+3^86939)/19104684Robert Price06/2013
3013(15^89009-1)/14104682Paul Bourdelais03/2010
30142^347731-18609104678Enzo Doria05/2013
30154*6^134519+7104677Lelio R Paula11/2014
30162^347612-18545104642Enzo Doria05/2013
30176^134465+95104635Lelio R Paula11/2016
30182^347517-17301104614Enzo Doria05/2013
30193^219222-310104596Lelio R Paula11/2016
3020(15*2^347399-1)/13104578Lelio R Paula03/2014
30212^347372-17853104570Enzo Doria05/2013
30222^347314+99104552Lelio R Paula09/2011
30232^347300-22233104548Enzo Doria06/2013
30242^347287-19845104544Enzo Doria06/2013
3025(31*2^347254-1)/891104533Lelio R Paula03/2014
30265*F(250091)*(F(250091)-1)+1104532Serge Batalov04/2015
30277*2^347239-3104531Lelio R Paula09/2014
3028(3^219098-8)/514147439969104525Lelio R Paula12/2013
30295*3^219047+8104513Lelio R Paula09/2014
30302^347148-109073104502Enzo Doria04/2014
30312^347129-20145104497Enzo Doria06/2013
30324*10^104461-57104462Robert Price10/2018
30332^346923-19585104435Enzo Doria05/2013
3034(11*2^346864-1)/175104416Lelio R Paula03/2014
30352^346854+346854^2+1104414Robert Price06/2014
30362^346834+11715104408Lelio R Paula04/2015
303779^55009+78104387Norbert Schneider02/2015
30383^218744+58104368Lelio R Paula11/2016
30392^346649+65104352Lelio R Paula09/2011
30402^346638-17265104349Enzo Doria05/2013
30422^346527-111817104316Enzo Doria05/2014
30416^134055+101104316Lelio R Paula11/2016
30436^134013+163104283Lelio R Paula11/2016
304418^83049-89104250Lelio R Paula01/2017
30452^346213+484049104221Enzo Doria04/2017
304618^83021-91104214Lelio R Paula01/2017
304710^104212+128779104213Patrick De Geest05/2016
304810^104212+237447104213Patrick De Geest05/2016
304910^104212+242139104213Patrick De Geest05/2016
305010^104212+269199104213Patrick De Geest05/2016
3051(10^104212-71)/1104212Serge Batalov12/2014
30522^346078+7695104180Lelio R Paula12/2016
30542^346055-19537104173Enzo Doria05/2013
3053(3*2^346057+1)/77104173Lelio R Paula12/2013
30552^346037-20125104168Enzo Doria06/2013
3056(34*10^104168-7)/9/13/551179104162Makoto Morimoto05/2016
30576^133854-17993104159Enzo Doria03/2013
30582^345990+1874239104154Enzo Doria06/2016
30592^345988-20373104153Enzo Doria06/2013
3060(26*10^104132-503)/9104133Robert Price07/2018
30613*5^148968+8104125Lelio R Paula11/2014
3062(7*10^104113+53)/3104114Robert Price05/2018
3063p(21253)#/2+8104113Robert Price01/2017
3064322^41507+41507^322104094Norbert Schneider12/2014
30656^133768-17423104092Enzo Doria03/2013
30662^345786-19557104092Enzo Doria05/2013
3067171^46606-2104072Lelio R Paula10/2017
30682^345704-149104068Lelio R Paula09/2011
30696^133704-17273104042Enzo Doria02/2013
3070(3*2^345590-1)/23104033Lelio R Paula03/2014
3071(19*2^345590+1)/33859104030Lelio R Paula12/2013
30722^345547+11104021Lelio R Paula09/2011
30732^345504+723104008Lelio R Paula09/2011
30742^345498-20037104006Enzo Doria06/2013
307518^82854-37104005Lelio R Paula01/2017
30762^345486-109065104002Enzo Doria04/2014
30772^345487-1851507104002Enzo Doria08/2015
30782^345476+777103999Lelio R Paula09/2011
30794*10^103981-83103982Robert Price10/2018
3080(5*2^345321-1)/3103953Lelio R Paula03/2014
3081(2^345267-9)/539049127103927Lelio R Paula12/2013
3082(78557*2^345163+1)/78589103905Lelio R Paula07/2014
30832^345106-112181103888Enzo Doria06/2014
30842^345079+99103880Lelio R Paula09/2011
308511^99736-1500103865Enzo Doria12/2012
30862^344842-20157103808Enzo Doria06/2013
3087(47*2^344822+1)/1071103801Lelio R Paula05/2015
30882^344802-20765103796Enzo Doria06/2013
30892^344794-3821103794Yves Minet05/2011
30902^344782-109103103790Enzo Doria04/2014
30913^217521-112292103784Enzo Doria06/2014
30922^344759-3505103783Lelio R Paula11/2016
30932^344735-147103776Lelio R Paula09/2011
3094L(496533)-p(496533)103770Robert Price02/2018
30952*10^103749-69103750Robert Price03/2018
3096(55459*2^344617+1)/3103745Lelio R Paula07/2014
30972^344607-108891103738Enzo Doria03/2014
30982^344541-19561103718Enzo Doria05/2013
3099(1017*2^344529-1)/569103714Lelio R Paula05/2015
3100(4*10^103703-1)/3103704Serge Batalov08/2009
31012^344444-455103688Yves Minet03/2012
3102(13*53^238539*617^9)/10^307661103673Hans Havermann06/2017
31032^344317-109933103650Enzo Doria04/2014
31042^344309-1852033103648Enzo Doria08/2015
31052^344213-21253103619Enzo Doria06/2013
31062^344196-465103614Lelio R Paula11/2016
31072^344187-20001103611Enzo Doria06/2013
3108(117191#+(355573#)/(117191#))/(200233679)103602Makoto Morimoto10/2017
310920^79621-19^79621103590Jean-Louis Charton03/2011
3110Phi(155391,10)/1243129103586Maksym Voznyy09/2015
31112^344085-20365103580Enzo Doria06/2013
31125^148169+54103566Lelio R Paula11/2016
31132^344017-108795103560Enzo Doria03/2014
31142^343971-5077103546Lelio R Paula09/2011
3115(7*10^103531+71)/3103532Robert Price05/2018
31162^343899+141103524Lelio R Paula08/2011
3117(2^343933+1)/(3*98294339989393)103520Gord Palameta08/2018
31186^133029-67103517Lelio R Paula11/2016
3119(17*2^343877+1)/13625103515Lelio R Paula12/2013
3120(136*10^103474-1)/9103476Serge Batalov12/2014
31215^148014-24103458Lelio R Paula11/2016
31222^343604+9931103436Yves Minet01/2011
31232^343601-21189103435Enzo Doria06/2013
31242^343508-115229103407Enzo Doria06/2015
3125(509203*2^343491-1)/16147103403Lelio R Paula05/2015
31263^216685-113056103386Enzo Doria07/2014
312744^62903-43^62903103379Jean-Louis Charton08/2012
312811^99262-20103371Lelio R Paula12/2016
3129(509203*2^343357-1)/5103366Lelio R Paula05/2015
31312^343356-2791889103361Enzo Doria03/2016
3130(25*10^103360-241)/9103361Robert Price05/2018
3132Phi(104989,10)/2939693103350Maksym Voznyy09/2015
31332^343182-171103309Lelio R Paula08/2011
3134(23619^23619+23620^23620)/7187103294David Broadhurst09/2009
31352^343079-1835611103278Enzo Doria05/2015
31362^343063-1147103273Yves Minet06/2013
31379*6^132689+7103254Lelio R Paula11/2014
31382^342979-18085103247Enzo Doria05/2013
31392^342966-16995103244Lelio R Paula11/2016
3140(37*10^103211+611)/9103212Robert Price11/2018
31415^147650+16103203Lelio R Paula11/2016
3142gcd(Phi(852060,10),(10^42603+1)^3*(10^42603+1-10^21302)+(10^85206+10^42603)*(10^21302+1)+10^127809)103201Serge Batalov04/2015
31432^342817+2707067103199Enzo Doria03/2016
314443^63177-42103198Theodore Burton02/2007
31452^342805-21025103195Enzo Doria06/2013
31462^342714+12285103168Lelio R Paula11/2016
314718^82178-4481103156Enzo Doria03/2013
31482^342665-17349103153Enzo Doria05/2013
31492^342612+175103137Lelio R Paula08/2011
31505*2^342585-3103130Lelio R Paula09/2014
31512^342503-19209103104Enzo Doria05/2013
31522^342476+51103096Lelio R Paula08/2011
31532^342460-18885103091Enzo Doria05/2013
31547^121968+82103075Lelio R Paula10/2016
31552^342392-108863103071Enzo Doria03/2014
31563^216014+28103065Lelio R Paula11/2016
31572^342353-108879103059Enzo Doria03/2014
315810^103055+276081103056Patrick De Geest12/2016
315910^103055-53103055Lelio R Paula11/2016
31607^121933+4103046Lelio R Paula11/2014
316119^80560-68103017Lelio R Paula10/2016
31622^342209+76607103016Enzo Doria05/2016
3164328^40945+40945^328103013Norbert Schneider12/2014
316312^95454-91103013Lelio R Paula10/2016
316565^56809-64^56809102990Robert Price08/2013
31665^147338-6102985Lelio R Paula11/2014
31672^342084-112739102978Enzo Doria06/2014
31689*6^132330+7102974Lelio R Paula11/2014
31692^342034-16737102963Enzo Doria05/2013
3170(9787*2^342011-1)/25102959Lelio R Paula05/2015
3171(3^215802-5)/124343756102956Lelio R Paula12/2013
31722^341991-17421102950Enzo Doria05/2013
31732^341969-112225102943Enzo Doria06/2014
3174(9787*2^341864-1)/3102915Lelio R Paula05/2015
31752^341859+1869413102910Enzo Doria05/2016
317610^102909+61102910Lelio R Paula11/2016
317710^102909-67049102909Patrick De Geest12/2016
31782^341659+1836773102850Enzo Doria03/2016
31792^341608-110639102835Enzo Doria05/2014
318010^102824+49102825Lelio R Paula11/2016
318110^102824-168011102824Patrick De Geest12/2016
318211^98708-8102794Lelio R Paula10/2016
31832^341466+4429102792Lelio R Paula09/2011
31842^341460-107102790Lelio R Paula08/2011
3185(2^341388+47)/21014943102761Lelio R Paula12/2013
31862^341355+21102759Lelio R Paula08/2011
31872^341246+40755102726Lelio R Paula11/2016
3188(2^341256-5)/991699102723Lelio R Paula12/2013
31897^121547+78102720Lelio R Paula10/2016
31902^341223-461197102719Enzo Doria06/2015
31922^341190-20577102709Enzo Doria06/2013
3191(27*2^341212+1)/84674449102709Lelio R Paula12/2013
31936^131976-65102698Lelio R Paula10/2016
31942^341134+2533102692Henri Lifchitz09/2005
319513^92184-54102688Lelio R Paula10/2016
31962^341116-20873102687Enzo Doria06/2013
31972^341094-19953102680Enzo Doria06/2013
31982^341053+129102668Lelio R Paula08/2011
3199(31*2^341006-1)/3102655Lelio R Paula03/2014
32007^121471+94102655Lelio R Paula10/2016
32022^341004-173102653Lelio R Paula08/2011
320120^78901+3102653Lelio R Paula10/2016
32035^146853-52102646Lelio R Paula10/2016
32042^340969-216931102642Enzo Doria05/2014
3205122^49196+121102641Norbert Schneider10/2018
32062^340952+1870021102637Enzo Doria05/2016
32075*2^340940-3102634Lelio R Paula08/2014
3208(6^131891+1)/7102631Paul Bourdelais01/2010
3209(4*10^102612+83)/3102613Robert Price02/2018
321075^54717+74102598Norbert Schneider01/2015
32112^340806-20393102593Enzo Doria06/2013
3212(2^340790+5)/138267102583Lelio R Paula12/2013
32136^131821+77102577Lelio R Paula10/2016
32142^340688-29102558Henri Lifchitz05/2005
32152^340685-109101102557Enzo Doria04/2014
321665^56567-64102552Norbert Schneider11/2014
32172^340547-108897102515Enzo Doria03/2014
32187^121268+82102484Lelio R Paula10/2016
3219(6883*2^340443-1)/162401102483Lelio R Paula05/2015
32202^340434-5955102481Lelio R Paula11/2016
3221(2^340381+47)/7102465Lelio R Paula12/2013
3222111^50095+110102461Norbert Schneider04/2017
32232^340291-20301102438Enzo Doria06/2013
322412^94915+89102431Lelio R Paula10/2016
32252^340208-20373102413Enzo Doria06/2013
32266^131598-17273102404Enzo Doria02/2013
32272^340115-21181102385Enzo Doria06/2013
3228(55459*2^340090+1)/1591102379Lelio R Paula07/2014
322989^52511-88^52511102365Robert Price06/2015
32303^214539-112756102362Enzo Doria07/2014
32312^340000-19877102351Enzo Doria06/2013
32322^339990-114845102348Enzo Doria05/2015
3233(3^214516-2)/51383102346Lelio R Paula12/2013
323420^78661-99102341Lelio R Paula09/2016
32352^339951-19585102336Enzo Doria05/2013
3236(13*2^339943+1)/45102333Lelio R Paula12/2013
32372^339889+29327102317Yves Minet06/2010
32382^339834-109493102301Enzo Doria04/2014
3239(11^98221-5^98221)/6102286Robert Price01/2013
32403^214365+1820102279Lelio R Paula10/2016
3241(11*2^339705-1)/183102261Lelio R Paula03/2014
32422^339694-16995102259Lelio R Paula09/2016
3243122^49008+121102249Norbert Schneider10/2018
32457^120985-38102245Lelio R Paula10/2016
324410^102244+122961102245Patrick De Geest12/2016
324610^102244-27102244Lelio R Paula09/2016
32477^120982-62102242Lelio R Paula10/2016
32484*6^131382-5102236Lelio R Paula11/2014
32492^339586-1091102226Yves Minet11/2012
325011^98161-3072000102225Enzo Doria12/2012


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Created by  Henri Lifchitz & Renaud Lifchitz : October, 26 2000, last modification: December, 11 2018 05:54 (Time in France)

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