PRP Records

Probable Primes Top 10000

(218736 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 ?
30012^344317-109933103650Enzo Doria04/2014
30022^344309-1852033103648Enzo Doria08/2015
30032^344213-21253103619Enzo Doria06/2013
30042^344196-465103614Lelio R Paula11/2016
30052^344187-20001103611Enzo Doria06/2013
3006(117191#+(355573#)/(117191#))/(200233679)103602Makoto Morimoto10/2017
300720^79621-19^79621103590Jean-Louis Charton03/2011
3008Phi(155391,10)/1243129103586Maksym Voznyy09/2015
30092^344085-20365103580Enzo Doria06/2013
30105^148169+54103566Lelio R Paula11/2016
30112^344017-108795103560Enzo Doria03/2014
30122^343971-5077103546Lelio R Paula09/2011
3013(7*10^103531+71)/3103532Robert Price05/2018
30142^343899+141103524Lelio R Paula08/2011
3015(2^343933+1)/(3*98294339989393)103520Gord Palameta08/2018
30166^133029-67103517Lelio R Paula11/2016
3017(17*2^343877+1)/13625103515Lelio R Paula12/2013
3018(136*10^103474-1)/9103476Serge Batalov12/2014
30195^148014-24103458Lelio R Paula11/2016
30202^343604+9931103436Yves Minet01/2011
30212^343601-21189103435Enzo Doria06/2013
30222^343508-115229103407Enzo Doria06/2015
3023(509203*2^343491-1)/16147103403Lelio R Paula05/2015
30243^216685-113056103386Enzo Doria07/2014
302544^62903-43^62903103379Jean-Louis Charton08/2012
302611^99262-20103371Lelio R Paula12/2016
3027(509203*2^343357-1)/5103366Lelio R Paula05/2015
30292^343356-2791889103361Enzo Doria03/2016
3028(25*10^103360-241)/9103361Robert Price05/2018
3030Phi(104989,10)/2939693103350Maksym Voznyy09/2015
30312^343182-171103309Lelio R Paula08/2011
3032(23619^23619+23620^23620)/7187103294David Broadhurst09/2009
30332^343079-1835611103278Enzo Doria05/2015
30342^343063-1147103273Yves Minet06/2013
30359*6^132689+7103254Lelio R Paula11/2014
30362^342979-18085103247Enzo Doria05/2013
30372^342966-16995103244Lelio R Paula11/2016
30385^147650+16103203Lelio R Paula11/2016
3039gcd(Phi(852060,10),(10^42603+1)^3*(10^42603+1-10^21302)+(10^85206+10^42603)*(10^21302+1)+10^127809)103201Serge Batalov04/2015
30402^342817+2707067103199Enzo Doria03/2016
304143^63177-42103198Theodore Burton02/2007
30422^342805-21025103195Enzo Doria06/2013
30432^342714+12285103168Lelio R Paula11/2016
304418^82178-4481103156Enzo Doria03/2013
30452^342665-17349103153Enzo Doria05/2013
30462^342612+175103137Lelio R Paula08/2011
30475*2^342585-3103130Lelio R Paula09/2014
30482^342503-19209103104Enzo Doria05/2013
30492^342476+51103096Lelio R Paula08/2011
30502^342460-18885103091Enzo Doria05/2013
30517^121968+82103075Lelio R Paula10/2016
30522^342392-108863103071Enzo Doria03/2014
30533^216014+28103065Lelio R Paula11/2016
30542^342353-108879103059Enzo Doria03/2014
305510^103055+276081103056Patrick De Geest12/2016
305610^103055-53103055Lelio R Paula11/2016
30577^121933+4103046Lelio R Paula11/2014
305819^80560-68103017Lelio R Paula10/2016
30592^342209+76607103016Enzo Doria05/2016
3061328^40945+40945^328103013Norbert Schneider12/2014
306012^95454-91103013Lelio R Paula10/2016
306265^56809-64^56809102990Robert Price08/2013
30635^147338-6102985Lelio R Paula11/2014
30642^342084-112739102978Enzo Doria06/2014
30659*6^132330+7102974Lelio R Paula11/2014
30662^342034-16737102963Enzo Doria05/2013
3067(9787*2^342011-1)/25102959Lelio R Paula05/2015
3068(3^215802-5)/124343756102956Lelio R Paula12/2013
30692^341991-17421102950Enzo Doria05/2013
30702^341969-112225102943Enzo Doria06/2014
3071(9787*2^341864-1)/3102915Lelio R Paula05/2015
30722^341859+1869413102910Enzo Doria05/2016
307310^102909+61102910Lelio R Paula11/2016
307410^102909-67049102909Patrick De Geest12/2016
30752^341659+1836773102850Enzo Doria03/2016
30762^341608-110639102835Enzo Doria05/2014
307710^102824+49102825Lelio R Paula11/2016
307810^102824-168011102824Patrick De Geest12/2016
307911^98708-8102794Lelio R Paula10/2016
30802^341466+4429102792Lelio R Paula09/2011
30812^341460-107102790Lelio R Paula08/2011
3082(2^341388+47)/21014943102761Lelio R Paula12/2013
30832^341355+21102759Lelio R Paula08/2011
30842^341246+40755102726Lelio R Paula11/2016
3085(2^341256-5)/991699102723Lelio R Paula12/2013
30867^121547+78102720Lelio R Paula10/2016
30872^341223-461197102719Enzo Doria06/2015
30892^341190-20577102709Enzo Doria06/2013
3088(27*2^341212+1)/84674449102709Lelio R Paula12/2013
30906^131976-65102698Lelio R Paula10/2016
30912^341134+2533102692Henri Lifchitz09/2005
309213^92184-54102688Lelio R Paula10/2016
30932^341116-20873102687Enzo Doria06/2013
30942^341094-19953102680Enzo Doria06/2013
30952^341053+129102668Lelio R Paula08/2011
3096(31*2^341006-1)/3102655Lelio R Paula03/2014
30977^121471+94102655Lelio R Paula10/2016
30992^341004-173102653Lelio R Paula08/2011
309820^78901+3102653Lelio R Paula10/2016
31005^146853-52102646Lelio R Paula10/2016
31012^340969-216931102642Enzo Doria05/2014
31022^340952+1870021102637Enzo Doria05/2016
31035*2^340940-3102634Lelio R Paula08/2014
3104(6^131891+1)/7102631Paul Bourdelais01/2010
3105(4*10^102612+83)/3102613Robert Price02/2018
310675^54717+74102598Norbert Schneider01/2015
31072^340806-20393102593Enzo Doria06/2013
3108(2^340790+5)/138267102583Lelio R Paula12/2013
31096^131821+77102577Lelio R Paula10/2016
31102^340688-29102558Henri Lifchitz05/2005
31112^340685-109101102557Enzo Doria04/2014
311265^56567-64102552Norbert Schneider11/2014
31132^340547-108897102515Enzo Doria03/2014
31147^121268+82102484Lelio R Paula10/2016
3115(6883*2^340443-1)/162401102483Lelio R Paula05/2015
31162^340434-5955102481Lelio R Paula11/2016
3117(2^340381+47)/7102465Lelio R Paula12/2013
3118111^50095+110102461Norbert Schneider04/2017
31192^340291-20301102438Enzo Doria06/2013
312012^94915+89102431Lelio R Paula10/2016
31212^340208-20373102413Enzo Doria06/2013
31226^131598-17273102404Enzo Doria02/2013
31232^340115-21181102385Enzo Doria06/2013
3124(55459*2^340090+1)/1591102379Lelio R Paula07/2014
312589^52511-88^52511102365Robert Price06/2015
31263^214539-112756102362Enzo Doria07/2014
31272^340000-19877102351Enzo Doria06/2013
31282^339990-114845102348Enzo Doria05/2015
3129(3^214516-2)/51383102346Lelio R Paula12/2013
313020^78661-99102341Lelio R Paula09/2016
31312^339951-19585102336Enzo Doria05/2013
3132(13*2^339943+1)/45102333Lelio R Paula12/2013
31332^339889+29327102317Yves Minet06/2010
31342^339834-109493102301Enzo Doria04/2014
3135(11^98221-5^98221)/6102286Robert Price01/2013
31363^214365+1820102279Lelio R Paula10/2016
3137(11*2^339705-1)/183102261Lelio R Paula03/2014
31382^339694-16995102259Lelio R Paula09/2016
31397^120985-38102245Lelio R Paula10/2016
314010^102244+122961102245Patrick De Geest12/2016
314110^102244-27102244Lelio R Paula09/2016
31427^120982-62102242Lelio R Paula10/2016
31434*6^131382-5102236Lelio R Paula11/2014
31442^339586-1091102226Yves Minet11/2012
314511^98161-3072000102225Enzo Doria12/2012
31469*7^120961-4102225Lelio R Paula11/2014
31475*3^214250+2102224Serge Batalov10/2010
314812^94713-59102213Lelio R Paula10/2016
314912^94705+89102204Lelio R Paula10/2016
31502^339407-177102172Lelio R Paula08/2011
31512^339355+65102157Lelio R Paula07/2011
3152(2^339323+47)/880715102141Lelio R Paula12/2013
31532^339168+21102100Lelio R Paula07/2011
31542^339167-108807102100Enzo Doria03/2014
31552^339156+163102097Lelio R Paula08/2011
3156(2^338982-7)/1754517102038Lelio R Paula12/2013
31572^338891-18885102017Enzo Doria05/2013
31582^338829-113239101998Enzo Doria07/2014
31592^338828-113297101998Enzo Doria07/2014
31602^338796+93101988Donovan Johnson06/2008
3161lucasU(1373,1,32502)-lucasU(1373,1,32501)101978Mike Oakes05/2009
3162(71^55079-1)/70101964Paul Bourdelais08/2017
31642^338682-19865101954Enzo Doria06/2013
3163(2^(112895*3+1)+243)/7101954Kevin Acres12/2013
31652^338568+37101920Lelio R Paula07/2011
31662^338559-1858777101917Enzo Doria04/2016
3167(9*2^338520+1)/365101904Lelio R Paula12/2013
31682^338497-17041101898Enzo Doria05/2013
31692^338475+54615101892Lelio R Paula10/2016
31702^338426-19797101877Enzo Doria06/2013
31712^338368-20369101859Enzo Doria06/2013
31722^338366+74179101859Enzo Doria04/2016
31732^338280-19745101833Enzo Doria06/2013
3174(3*2^338236-1)/347101818Lelio R Paula03/2014
31756^130841+103101815Lelio R Paula10/2016
31762^338122-20117101785Enzo Doria06/2013
3177(2^338139+5)/905333101785Lelio R Paula12/2013
317835^65917-7092101781Enzo Doria03/2013
31792^338010-19833101752Enzo Doria06/2013
31803^213215-76101730Lelio R Paula09/2016
31812^337930+63101728Lelio R Paula07/2011
31822^337920+1869661101725Enzo Doria05/2016
31832^337859-19645101706Enzo Doria05/2013
31842^337754+1869169101675Enzo Doria05/2016
31853*10^101657-37101658Robert Price07/2018
3186(31*2^337677-1)/593101650Lelio R Paula03/2014
318711^97605-24101646Lelio R Paula10/2016
31888^112539-112539101633Robert Price01/2014
31892^337515-19869101603Enzo Doria06/2013
31902^337473+719101590Lelio R Paula08/2011
3191(2^337485-509203)/656647157101585Lelio R Paula12/2013
31922^337452-108815101584Enzo Doria03/2014
31932^337453+1185101584Lelio R Paula09/2016
31942^337410-113561101571Enzo Doria08/2014
31952^337387+855101564Lelio R Paula09/2016
31962^337367-17295101558Lelio R Paula09/2016
31972^337342-109035101551Enzo Doria04/2014
31982^337267-19101528Lelio R Paula07/2011
31992^337183-19989101503Enzo Doria06/2013
32002^337149+72425101492Enzo Doria04/2016
32012^337101-20241101478Enzo Doria06/2013
32022^337035-20001101458Enzo Doria06/2013
32032^337017-16995101453Lelio R Paula09/2016
32042^336979-115315101441Enzo Doria06/2015
32052^336970-20885101439Enzo Doria06/2013
32062^336958+79101435Lelio R Paula10/2009
32072^336942+169101430Lelio R Paula10/2009
3208(15185*2^336894-1)/7939101416Lelio R Paula05/2015
32092^336871+257463101409Tony Prest / Never Odd Or Even04/2016
32102^336871+318105101409Tony Prest / Never Odd Or Even04/2016
32112^336871+1010813101409Tony Prest / Never Odd Or Even04/2016
32122^336871+2302245101409Tony Prest / Never Odd Or Even04/2016
32132^336871+389273101409Tony Prest / Never Odd Or Even04/2016
32142^336871+1685475101409Tony Prest / Never Odd Or Even04/2016
32152^336871+1068119101409Tony Prest / Never Odd Or Even04/2016
32162^336871+586905101409Tony Prest / Never Odd Or Even04/2016
32172^336871+674571101409Tony Prest / Never Odd Or Even04/2016
32182^336871+707009101409Tony Prest / Never Odd Or Even04/2016
32192^336871+1210299101409Tony Prest / Never Odd Or Even04/2016
32202^336871+1921185101409Tony Prest / Never Odd Or Even04/2016
32212^336871+2003973101409Tony Prest / Never Odd Or Even04/2016
32222^336871+2656475101409Tony Prest / Never Odd Or Even04/2016
32232^336871+2703023101409Tony Prest / Never Odd Or Even04/2016
32242^336871+2704545101409Tony Prest / Never Odd Or Even04/2016
32252^336871+2766801101409Tony Prest / Never Odd Or Even04/2016
32262^336871+2127735101409Tony Prest / Never Odd Or Even04/2016
3227(2^336871+821089)/3101408Tony Prest / Never Odd Or Even05/2016
3228(2^336871+119567)/5101408Tony Prest / Never Odd Or Even05/2016
3229(2^336871+398161)/3101408Tony Prest / Never Odd Or Even05/2016
3230(2^336871+625889)/7101408Tony Prest / Never Odd Or Even05/2016
32312^336842+94065101400Lelio R Paula09/2016
3232(2^336871+904417)/3/3/3/5/19/9287177/9690011663/29993043103101378Tony Prest / Never Odd Or Even04/2016
3233(2^336871+631971)/13/251/1601/294277/614362921/30324278867101377Tony Prest / Never Odd Or Even04/2016
3234(2^336871+1443541)/3/89/1655197/11018131/47972707/468862691879101374Tony Prest / Never Odd Or Even04/2016
3235(2^336871+689863)/3/11/109/137/1867/7151/20800501/29243857/127778489101373Tony Prest / Never Odd Or Even04/2016
3236(2^336871+219839)/191/643/3011/9479/117127/175750007/4578271757101373Tony Prest / Never Odd Or Even04/2016
3237(2^336871+272895)/19/661/977572033/95853078653/520779768241101373Tony Prest / Never Odd Or Even04/2016
3238(2^336871+1023429)/2311/415873/991889/3630648341/207732189179101373Tony Prest / Never Odd Or Even04/2016
323910^101369+203811101370Patrick De Geest11/2016
324010^101369-99101369Lelio R Paula09/2016
3241(2^336871+1832627)/5/5/23/181/4397/91373/3746673331/115602484097/279351383917101363Tony Prest / Never Odd Or Even04/2016
32422^336701-113563101358Enzo Doria08/2014
32432^336644-109023101340Enzo Doria04/2014
32442^336601-21081101327Enzo Doria06/2013
324520^77869+63101310Lelio R Paula09/2016
3246(13*2^336523-1)/19101304Lelio R Paula03/2014
32476^130179-137101299Lelio R Paula10/2016
3248(2^336506+lucasV(1,2,336506)+1)/2101299Mike Oakes11/2016
3249(24737*2^336485+1)/7285101293Lelio R Paula07/2014
3250(2^336448+9)/497405101276Lelio R Paula12/2013


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Created by  Henri Lifchitz & Renaud Lifchitz : October, 26 2000, last modification: August, 14 2018 21:45 (Time in France)

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