PRP Records

Probable Primes Top 10000

(224660 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 ?
3001(10^104212-71)/1104212Serge Batalov12/2014
30022^346078+7695104180Lelio R Paula12/2016
30042^346055-19537104173Enzo Doria05/2013
3003(3*2^346057+1)/77104173Lelio R Paula12/2013
30052^346037-20125104168Enzo Doria06/2013
3006(34*10^104168-7)/9/13/551179104162Makoto Morimoto05/2016
30076^133854-17993104159Enzo Doria03/2013
30082^345990+1874239104154Enzo Doria06/2016
30092^345988-20373104153Enzo Doria06/2013
3010(26*10^104132-503)/9104133Robert Price07/2018
30113*5^148968+8104125Lelio R Paula11/2014
3012(7*10^104113+53)/3104114Robert Price05/2018
3013p(21253)#/2+8104113Robert Price01/2017
3014322^41507+41507^322104094Norbert Schneider12/2014
30156^133768-17423104092Enzo Doria03/2013
30162^345786-19557104092Enzo Doria05/2013
3017171^46606-2104072Lelio R Paula10/2017
30182^345704-149104068Lelio R Paula09/2011
30196^133704-17273104042Enzo Doria02/2013
3020(3*2^345590-1)/23104033Lelio R Paula03/2014
3021(19*2^345590+1)/33859104030Lelio R Paula12/2013
30222^345547+11104021Lelio R Paula09/2011
30232^345504+723104008Lelio R Paula09/2011
30242^345498-20037104006Enzo Doria06/2013
302518^82854-37104005Lelio R Paula01/2017
30262^345486-109065104002Enzo Doria04/2014
30272^345487-1851507104002Enzo Doria08/2015
30282^345476+777103999Lelio R Paula09/2011
30294*10^103981-83103982Robert Price10/2018
3030(5*2^345321-1)/3103953Lelio R Paula03/2014
3031(2^345267-9)/539049127103927Lelio R Paula12/2013
3032(78557*2^345163+1)/78589103905Lelio R Paula07/2014
30332^345106-112181103888Enzo Doria06/2014
30342^345079+99103880Lelio R Paula09/2011
303511^99736-1500103865Enzo Doria12/2012
30362^344842-20157103808Enzo Doria06/2013
3037(47*2^344822+1)/1071103801Lelio R Paula05/2015
30382^344802-20765103796Enzo Doria06/2013
30392^344794-3821103794Yves Minet05/2011
30402^344782-109103103790Enzo Doria04/2014
30413^217521-112292103784Enzo Doria06/2014
30422^344759-3505103783Lelio R Paula11/2016
30432^344735-147103776Lelio R Paula09/2011
3044L(496533)-p(496533)103770Robert Price02/2018
30452*10^103749-69103750Robert Price03/2018
3046(55459*2^344617+1)/3103745Lelio R Paula07/2014
30472^344607-108891103738Enzo Doria03/2014
30482^344541-19561103718Enzo Doria05/2013
3049(1017*2^344529-1)/569103714Lelio R Paula05/2015
3050(4*10^103703-1)/3103704Serge Batalov08/2009
30512^344444-455103688Yves Minet03/2012
3052(13*53^238539*617^9)/10^307661103673Hans Havermann06/2017
30532^344317-109933103650Enzo Doria04/2014
30542^344309-1852033103648Enzo Doria08/2015
30552^344213-21253103619Enzo Doria06/2013
30562^344196-465103614Lelio R Paula11/2016
30572^344187-20001103611Enzo Doria06/2013
3058(117191#+(355573#)/(117191#))/(200233679)103602Makoto Morimoto10/2017
305920^79621-19^79621103590Jean-Louis Charton03/2011
3060Phi(155391,10)/1243129103586Maksym Voznyy09/2015
30612^344085-20365103580Enzo Doria06/2013
30625^148169+54103566Lelio R Paula11/2016
30632^344017-108795103560Enzo Doria03/2014
30642^343971-5077103546Lelio R Paula09/2011
3065(7*10^103531+71)/3103532Robert Price05/2018
30662^343899+141103524Lelio R Paula08/2011
3067(2^343933+1)/(3*98294339989393)103520Gord Palameta08/2018
30686^133029-67103517Lelio R Paula11/2016
3069(17*2^343877+1)/13625103515Lelio R Paula12/2013
3070(136*10^103474-1)/9103476Serge Batalov12/2014
30715^148014-24103458Lelio R Paula11/2016
30722^343604+9931103436Yves Minet01/2011
30732^343601-21189103435Enzo Doria06/2013
30742^343508-115229103407Enzo Doria06/2015
3075(509203*2^343491-1)/16147103403Lelio R Paula05/2015
30763^216685-113056103386Enzo Doria07/2014
307744^62903-43^62903103379Jean-Louis Charton08/2012
307811^99262-20103371Lelio R Paula12/2016
3079(509203*2^343357-1)/5103366Lelio R Paula05/2015
30812^343356-2791889103361Enzo Doria03/2016
3080(25*10^103360-241)/9103361Robert Price05/2018
3082Phi(104989,10)/2939693103350Maksym Voznyy09/2015
30832^343182-171103309Lelio R Paula08/2011
3084(23619^23619+23620^23620)/7187103294David Broadhurst09/2009
30852^343079-1835611103278Enzo Doria05/2015
30862^343063-1147103273Yves Minet06/2013
30879*6^132689+7103254Lelio R Paula11/2014
30882^342979-18085103247Enzo Doria05/2013
30892^342966-16995103244Lelio R Paula11/2016
30905^147650+16103203Lelio R Paula11/2016
3091gcd(Phi(852060,10),(10^42603+1)^3*(10^42603+1-10^21302)+(10^85206+10^42603)*(10^21302+1)+10^127809)103201Serge Batalov04/2015
30922^342817+2707067103199Enzo Doria03/2016
309343^63177-42103198Theodore Burton02/2007
30942^342805-21025103195Enzo Doria06/2013
30952^342714+12285103168Lelio R Paula11/2016
309618^82178-4481103156Enzo Doria03/2013
30972^342665-17349103153Enzo Doria05/2013
30982^342612+175103137Lelio R Paula08/2011
30995*2^342585-3103130Lelio R Paula09/2014
31002^342503-19209103104Enzo Doria05/2013
31012^342476+51103096Lelio R Paula08/2011
31022^342460-18885103091Enzo Doria05/2013
31037^121968+82103075Lelio R Paula10/2016
31042^342392-108863103071Enzo Doria03/2014
31053^216014+28103065Lelio R Paula11/2016
31062^342353-108879103059Enzo Doria03/2014
310710^103055+276081103056Patrick De Geest12/2016
310810^103055-53103055Lelio R Paula11/2016
31097^121933+4103046Lelio R Paula11/2014
311019^80560-68103017Lelio R Paula10/2016
31112^342209+76607103016Enzo Doria05/2016
3113328^40945+40945^328103013Norbert Schneider12/2014
311212^95454-91103013Lelio R Paula10/2016
311465^56809-64^56809102990Robert Price08/2013
31155^147338-6102985Lelio R Paula11/2014
31162^342084-112739102978Enzo Doria06/2014
31179*6^132330+7102974Lelio R Paula11/2014
31182^342034-16737102963Enzo Doria05/2013
3119(9787*2^342011-1)/25102959Lelio R Paula05/2015
3120(3^215802-5)/124343756102956Lelio R Paula12/2013
31212^341991-17421102950Enzo Doria05/2013
31222^341969-112225102943Enzo Doria06/2014
3123(9787*2^341864-1)/3102915Lelio R Paula05/2015
31242^341859+1869413102910Enzo Doria05/2016
312510^102909+61102910Lelio R Paula11/2016
312610^102909-67049102909Patrick De Geest12/2016
31272^341659+1836773102850Enzo Doria03/2016
31282^341608-110639102835Enzo Doria05/2014
312910^102824+49102825Lelio R Paula11/2016
313010^102824-168011102824Patrick De Geest12/2016
313111^98708-8102794Lelio R Paula10/2016
31322^341466+4429102792Lelio R Paula09/2011
31332^341460-107102790Lelio R Paula08/2011
3134(2^341388+47)/21014943102761Lelio R Paula12/2013
31352^341355+21102759Lelio R Paula08/2011
31362^341246+40755102726Lelio R Paula11/2016
3137(2^341256-5)/991699102723Lelio R Paula12/2013
31387^121547+78102720Lelio R Paula10/2016
31392^341223-461197102719Enzo Doria06/2015
31412^341190-20577102709Enzo Doria06/2013
3140(27*2^341212+1)/84674449102709Lelio R Paula12/2013
31426^131976-65102698Lelio R Paula10/2016
31432^341134+2533102692Henri Lifchitz09/2005
314413^92184-54102688Lelio R Paula10/2016
31452^341116-20873102687Enzo Doria06/2013
31462^341094-19953102680Enzo Doria06/2013
31472^341053+129102668Lelio R Paula08/2011
3148(31*2^341006-1)/3102655Lelio R Paula03/2014
31497^121471+94102655Lelio R Paula10/2016
31512^341004-173102653Lelio R Paula08/2011
315020^78901+3102653Lelio R Paula10/2016
31525^146853-52102646Lelio R Paula10/2016
31532^340969-216931102642Enzo Doria05/2014
31542^340952+1870021102637Enzo Doria05/2016
31555*2^340940-3102634Lelio R Paula08/2014
3156(6^131891+1)/7102631Paul Bourdelais01/2010
3157(4*10^102612+83)/3102613Robert Price02/2018
315875^54717+74102598Norbert Schneider01/2015
31592^340806-20393102593Enzo Doria06/2013
3160(2^340790+5)/138267102583Lelio R Paula12/2013
31616^131821+77102577Lelio R Paula10/2016
31622^340688-29102558Henri Lifchitz05/2005
31632^340685-109101102557Enzo Doria04/2014
316465^56567-64102552Norbert Schneider11/2014
31652^340547-108897102515Enzo Doria03/2014
31667^121268+82102484Lelio R Paula10/2016
3167(6883*2^340443-1)/162401102483Lelio R Paula05/2015
31682^340434-5955102481Lelio R Paula11/2016
3169(2^340381+47)/7102465Lelio R Paula12/2013
3170111^50095+110102461Norbert Schneider04/2017
31712^340291-20301102438Enzo Doria06/2013
317212^94915+89102431Lelio R Paula10/2016
31732^340208-20373102413Enzo Doria06/2013
31746^131598-17273102404Enzo Doria02/2013
31752^340115-21181102385Enzo Doria06/2013
3176(55459*2^340090+1)/1591102379Lelio R Paula07/2014
317789^52511-88^52511102365Robert Price06/2015
31783^214539-112756102362Enzo Doria07/2014
31792^340000-19877102351Enzo Doria06/2013
31802^339990-114845102348Enzo Doria05/2015
3181(3^214516-2)/51383102346Lelio R Paula12/2013
318220^78661-99102341Lelio R Paula09/2016
31832^339951-19585102336Enzo Doria05/2013
3184(13*2^339943+1)/45102333Lelio R Paula12/2013
31852^339889+29327102317Yves Minet06/2010
31862^339834-109493102301Enzo Doria04/2014
3187(11^98221-5^98221)/6102286Robert Price01/2013
31883^214365+1820102279Lelio R Paula10/2016
3189(11*2^339705-1)/183102261Lelio R Paula03/2014
31902^339694-16995102259Lelio R Paula09/2016
31917^120985-38102245Lelio R Paula10/2016
319210^102244+122961102245Patrick De Geest12/2016
319310^102244-27102244Lelio R Paula09/2016
31947^120982-62102242Lelio R Paula10/2016
31954*6^131382-5102236Lelio R Paula11/2014
31962^339586-1091102226Yves Minet11/2012
319711^98161-3072000102225Enzo Doria12/2012
31989*7^120961-4102225Lelio R Paula11/2014
31995*3^214250+2102224Serge Batalov10/2010
320012^94713-59102213Lelio R Paula10/2016
320112^94705+89102204Lelio R Paula10/2016
32022^339407-177102172Lelio R Paula08/2011
32034*10^102163-57102164Robert Price10/2018
32042^339355+65102157Lelio R Paula07/2011
3205(2^339323+47)/880715102141Lelio R Paula12/2013
32062^339168+21102100Lelio R Paula07/2011
32072^339167-108807102100Enzo Doria03/2014
32082^339156+163102097Lelio R Paula08/2011
3209(2^338982-7)/1754517102038Lelio R Paula12/2013
32102^338891-18885102017Enzo Doria05/2013
32112^338829-113239101998Enzo Doria07/2014
32122^338828-113297101998Enzo Doria07/2014
32132^338796+93101988Donovan Johnson06/2008
3214lucasU(1373,1,32502)-lucasU(1373,1,32501)101978Mike Oakes05/2009
3215(71^55079-1)/70101964Paul Bourdelais08/2017
32162^338682-19865101954Enzo Doria06/2013
3217(2^(112895*3+1)+243)/7101954Kevin Acres12/2013
32182^338568+37101920Lelio R Paula07/2011
32192^338559-1858777101917Enzo Doria04/2016
3220(9*2^338520+1)/365101904Lelio R Paula12/2013
32212^338497-17041101898Enzo Doria05/2013
32222^338475+54615101892Lelio R Paula10/2016
32232^338426-19797101877Enzo Doria06/2013
32242^338368-20369101859Enzo Doria06/2013
32252^338366+74179101859Enzo Doria04/2016
32262^338280-19745101833Enzo Doria06/2013
3227(3*2^338236-1)/347101818Lelio R Paula03/2014
32286^130841+103101815Lelio R Paula10/2016
32292^338122-20117101785Enzo Doria06/2013
3230(2^338139+5)/905333101785Lelio R Paula12/2013
323135^65917-7092101781Enzo Doria03/2013
32322^338010-19833101752Enzo Doria06/2013
32333^213215-76101730Lelio R Paula09/2016
32342^337930+63101728Lelio R Paula07/2011
32352^337920+1869661101725Enzo Doria05/2016
32362^337859-19645101706Enzo Doria05/2013
32372^337754+1869169101675Enzo Doria05/2016
32383*10^101657-37101658Robert Price07/2018
3239(31*2^337677-1)/593101650Lelio R Paula03/2014
324011^97605-24101646Lelio R Paula10/2016
32418^112539-112539101633Robert Price01/2014
32422^337515-19869101603Enzo Doria06/2013
32432^337473+719101590Lelio R Paula08/2011
3244(2^337485-509203)/656647157101585Lelio R Paula12/2013
32452^337452-108815101584Enzo Doria03/2014
32462^337453+1185101584Lelio R Paula09/2016
32472^337410-113561101571Enzo Doria08/2014
32482^337387+855101564Lelio R Paula09/2016
32492^337367-17295101558Lelio R Paula09/2016
32502^337342-109035101551Enzo Doria04/2014


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Created by  Henri Lifchitz & Renaud Lifchitz : October, 26 2000, last modification: October, 15 2018 21:33 (Time in France)

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