PRP Records

Probable Primes Top 10000

(172213 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(34*10^104168-7)/9/13/551179104162Makoto Morimoto05/2016
25026^133854-17993104159Enzo Doria03/2013
25032^345990+1874239104154Enzo Doria06/2016
25042^345988-20373104153Enzo Doria06/2013
25053*5^148968+8104125Lelio R Paula11/2014
2506p(21253)#/2+8104113Robert Price01/2017
2507322^41507+41507^322104094Norbert Schneider12/2014
25086^133768-17423104092Enzo Doria03/2013
25092^345786-19557104092Enzo Doria05/2013
25102^345704-149104068Lelio R Paula09/2011
25116^133704-17273104042Enzo Doria02/2013
2512(3*2^345590-1)/23104033Lelio R Paula03/2014
2513(19*2^345590+1)/33859104030Lelio R Paula12/2013
25142^345547+11104021Lelio R Paula09/2011
25152^345504+723104008Lelio R Paula09/2011
25162^345498-20037104006Enzo Doria06/2013
251718^82854-37104005Lelio R Paula01/2017
25182^345486-109065104002Enzo Doria04/2014
25192^345487-1851507104002Enzo Doria08/2015
25202^345476+777103999Lelio R Paula09/2011
2521(5*2^345321-1)/3103953Lelio R Paula03/2014
2522(2^345267-9)/539049127103927Lelio R Paula12/2013
2523(78557*2^345163+1)/78589103905Lelio R Paula07/2014
25242^345106-112181103888Enzo Doria06/2014
25252^345079+99103880Lelio R Paula09/2011
252611^99736-1500103865Enzo Doria12/2012
25272^344842-20157103808Enzo Doria06/2013
2528(47*2^344822+1)/1071103801Lelio R Paula05/2015
25292^344802-20765103796Enzo Doria06/2013
25302^344794-3821103794Yves Minet05/2011
25312^344782-109103103790Enzo Doria04/2014
25323^217521-112292103784Enzo Doria06/2014
25332^344759-3505103783Lelio R Paula11/2016
25342^344735-147103776Lelio R Paula09/2011
2535(55459*2^344617+1)/3103745Lelio R Paula07/2014
25362^344607-108891103738Enzo Doria03/2014
25372^344541-19561103718Enzo Doria05/2013
2538(1017*2^344529-1)/569103714Lelio R Paula05/2015
2539(4*10^103703-1)/3103704Serge Batalov08/2009
25402^344444-455103688Yves Minet03/2012
25412^344317-109933103650Enzo Doria04/2014
25422^344309-1852033103648Enzo Doria08/2015
25432^344213-21253103619Enzo Doria06/2013
25442^344196-465103614Lelio R Paula11/2016
25452^344187-20001103611Enzo Doria06/2013
254620^79621-19^79621103590Jean-Louis Charton03/2011
2547Phi(155391,10)/1243129103586Maksym Voznyy09/2015
25482^344085-20365103580Enzo Doria06/2013
25495^148169+54103566Lelio R Paula11/2016
25502^344017-108795103560Enzo Doria03/2014
25512^343971-5077103546Lelio R Paula09/2011
25522^343899+141103524Lelio R Paula08/2011
25536^133029-67103517Lelio R Paula11/2016
2554(17*2^343877+1)/13625103515Lelio R Paula12/2013
2555(136*10^103474-1)/9103476Serge Batalov12/2014
25565^148014-24103458Lelio R Paula11/2016
25572^343604+9931103436Yves Minet01/2011
25582^343601-21189103435Enzo Doria06/2013
25592^343508-115229103407Enzo Doria06/2015
2560(509203*2^343491-1)/16147103403Lelio R Paula05/2015
25613^216685-113056103386Enzo Doria07/2014
256244^62903-43^62903103379Jean-Louis Charton08/2012
256311^99262-20103371Lelio R Paula12/2016
2564(509203*2^343357-1)/5103366Lelio R Paula05/2015
25652^343356-2791889103361Enzo Doria03/2016
2566Phi(104989,10)/2939693103350Maksym Voznyy09/2015
25672^343182-171103309Lelio R Paula08/2011
2568(23619^23619+23620^23620)/7187103294David Broadhurst09/2009
25692^343079-1835611103278Enzo Doria05/2015
25702^343063-1147103273Yves Minet06/2013
25719*6^132689+7103254Lelio R Paula11/2014
25722^342979-18085103247Enzo Doria05/2013
25732^342966-16995103244Lelio R Paula11/2016
25745^147650+16103203Lelio R Paula11/2016
2575gcd(Phi(852060,10),(10^42603+1)^3*(10^42603+1-10^21302)+(10^85206+10^42603)*(10^21302+1)+10^127809)103201Serge Batalov04/2015
25762^342817+2707067103199Enzo Doria03/2016
257743^63177-42103198Theodore Burton02/2007
25782^342805-21025103195Enzo Doria06/2013
25792^342714+12285103168Lelio R Paula11/2016
258018^82178-4481103156Enzo Doria03/2013
25812^342665-17349103153Enzo Doria05/2013
25822^342612+175103137Lelio R Paula08/2011
25835*2^342585-3103130Lelio R Paula09/2014
25842^342503-19209103104Enzo Doria05/2013
25852^342476+51103096Lelio R Paula08/2011
25862^342460-18885103091Enzo Doria05/2013
25877^121968+82103075Lelio R Paula10/2016
25882^342392-108863103071Enzo Doria03/2014
25893^216014+28103065Lelio R Paula11/2016
25902^342353-108879103059Enzo Doria03/2014
259110^103055+276081103056Patrick De Geest12/2016
259210^103055-53103055Lelio R Paula11/2016
25937^121933+4103046Lelio R Paula11/2014
259419^80560-68103017Lelio R Paula10/2016
25952^342209+76607103016Enzo Doria05/2016
2597328^40945+40945^328103013Norbert Schneider12/2014
259612^95454-91103013Lelio R Paula10/2016
259865^56809-64^56809102990Robert Price08/2013
25995^147338-6102985Lelio R Paula11/2014
26002^342084-112739102978Enzo Doria06/2014
26019*6^132330+7102974Lelio R Paula11/2014
26022^342034-16737102963Enzo Doria05/2013
2603(9787*2^342011-1)/25102959Lelio R Paula05/2015
2604(3^215802-5)/124343756102956Lelio R Paula12/2013
26052^341991-17421102950Enzo Doria05/2013
26062^341969-112225102943Enzo Doria06/2014
2607(9787*2^341864-1)/3102915Lelio R Paula05/2015
26082^341859+1869413102910Enzo Doria05/2016
260910^102909+61102910Lelio R Paula11/2016
261010^102909-67049102909Patrick De Geest12/2016
26112^341659+1836773102850Enzo Doria03/2016
26122^341608-110639102835Enzo Doria05/2014
261310^102824+49102825Lelio R Paula11/2016
261410^102824-168011102824Patrick De Geest12/2016
261511^98708-8102794Lelio R Paula10/2016
26162^341466+4429102792Lelio R Paula09/2011
26172^341460-107102790Lelio R Paula08/2011
2618(2^341388+47)/21014943102761Lelio R Paula12/2013
26192^341355+21102759Lelio R Paula08/2011
26202^341246+40755102726Lelio R Paula11/2016
2621(2^341256-5)/991699102723Lelio R Paula12/2013
26227^121547+78102720Lelio R Paula10/2016
26232^341223-461197102719Enzo Doria06/2015
26252^341190-20577102709Enzo Doria06/2013
2624(27*2^341212+1)/84674449102709Lelio R Paula12/2013
26266^131976-65102698Lelio R Paula10/2016
26272^341134+2533102692Henri Lifchitz09/2005
262813^92184-54102688Lelio R Paula10/2016
26292^341116-20873102687Enzo Doria06/2013
26302^341094-19953102680Enzo Doria06/2013
26312^341053+129102668Lelio R Paula08/2011
2632(31*2^341006-1)/3102655Lelio R Paula03/2014
26337^121471+94102655Lelio R Paula10/2016
26352^341004-173102653Lelio R Paula08/2011
263420^78901+3102653Lelio R Paula10/2016
26365^146853-52102646Lelio R Paula10/2016
26372^340969-216931102642Enzo Doria05/2014
26382^340952+1870021102637Enzo Doria05/2016
26395*2^340940-3102634Lelio R Paula08/2014
2640(6^131891+1)/7102631Paul Bourdelais01/2010
264175^54717+74102598Norbert Schneider01/2015
26422^340806-20393102593Enzo Doria06/2013
2643(2^340790+5)/138267102583Lelio R Paula12/2013
26446^131821+77102577Lelio R Paula10/2016
26452^340688-29102558Henri Lifchitz05/2005
26462^340685-109101102557Enzo Doria04/2014
264765^56567-64102552Norbert Schneider11/2014
26482^340547-108897102515Enzo Doria03/2014
26497^121268+82102484Lelio R Paula10/2016
2650(6883*2^340443-1)/162401102483Lelio R Paula05/2015
26512^340434-5955102481Lelio R Paula11/2016
2652(2^340381+47)/7102465Lelio R Paula12/2013
26532^340291-20301102438Enzo Doria06/2013
265412^94915+89102431Lelio R Paula10/2016
26552^340208-20373102413Enzo Doria06/2013
26566^131598-17273102404Enzo Doria02/2013
26572^340115-21181102385Enzo Doria06/2013
2658(55459*2^340090+1)/1591102379Lelio R Paula07/2014
265989^52511-88^52511102365Robert Price06/2015
26603^214539-112756102362Enzo Doria07/2014
26612^340000-19877102351Enzo Doria06/2013
26622^339990-114845102348Enzo Doria05/2015
2663(3^214516-2)/51383102346Lelio R Paula12/2013
266420^78661-99102341Lelio R Paula09/2016
26652^339951-19585102336Enzo Doria05/2013
2666(13*2^339943+1)/45102333Lelio R Paula12/2013
26672^339889+29327102317Yves Minet06/2010
26682^339834-109493102301Enzo Doria04/2014
2669(11^98221-5^98221)/6102286Robert Price01/2013
26703^214365+1820102279Lelio R Paula10/2016
2671(11*2^339705-1)/183102261Lelio R Paula03/2014
26722^339694-16995102259Lelio R Paula09/2016
26737^120985-38102245Lelio R Paula10/2016
267410^102244+122961102245Patrick De Geest12/2016
267510^102244-27102244Lelio R Paula09/2016
26767^120982-62102242Lelio R Paula10/2016
26774*6^131382-5102236Lelio R Paula11/2014
26782^339586-1091102226Yves Minet11/2012
267911^98161-3072000102225Enzo Doria12/2012
26809*7^120961-4102225Lelio R Paula11/2014
26815*3^214250+2102224Serge Batalov10/2010
268212^94713-59102213Lelio R Paula10/2016
268312^94705+89102204Lelio R Paula10/2016
26842^339407-177102172Lelio R Paula08/2011
26852^339355+65102157Lelio R Paula07/2011
2686(2^339323+47)/880715102141Lelio R Paula12/2013
26872^339168+21102100Lelio R Paula07/2011
26882^339167-108807102100Enzo Doria03/2014
26892^339156+163102097Lelio R Paula08/2011
2690(2^338982-7)/1754517102038Lelio R Paula12/2013
26912^338891-18885102017Enzo Doria05/2013
26922^338829-113239101998Enzo Doria07/2014
26932^338828-113297101998Enzo Doria07/2014
26942^338796+93101988Donovan Johnson06/2008
2695lucasU(1373,1,32502)-lucasU(1373,1,32501)101978Mike Oakes05/2009
26972^338682-19865101954Enzo Doria06/2013
2696(2^(112895*3+1)+243)/7101954Kevin Acres12/2013
26982^338568+37101920Lelio R Paula07/2011
26992^338559-1858777101917Enzo Doria04/2016
2700(9*2^338520+1)/365101904Lelio R Paula12/2013
27012^338497-17041101898Enzo Doria05/2013
27022^338475+54615101892Lelio R Paula10/2016
27032^338426-19797101877Enzo Doria06/2013
27042^338368-20369101859Enzo Doria06/2013
27052^338366+74179101859Enzo Doria04/2016
27062^338280-19745101833Enzo Doria06/2013
2707(3*2^338236-1)/347101818Lelio R Paula03/2014
27086^130841+103101815Lelio R Paula10/2016
27092^338122-20117101785Enzo Doria06/2013
2710(2^338139+5)/905333101785Lelio R Paula12/2013
271135^65917-7092101781Enzo Doria03/2013
27122^338010-19833101752Enzo Doria06/2013
27133^213215-76101730Lelio R Paula09/2016
27142^337930+63101728Lelio R Paula07/2011
27152^337920+1869661101725Enzo Doria05/2016
27162^337859-19645101706Enzo Doria05/2013
27172^337754+1869169101675Enzo Doria05/2016
2718(31*2^337677-1)/593101650Lelio R Paula03/2014
271911^97605-24101646Lelio R Paula10/2016
27208^112539-112539101633Robert Price01/2014
27212^337515-19869101603Enzo Doria06/2013
27222^337473+719101590Lelio R Paula08/2011
2723(2^337485-509203)/656647157101585Lelio R Paula12/2013
27242^337452-108815101584Enzo Doria03/2014
27252^337453+1185101584Lelio R Paula09/2016
27262^337410-113561101571Enzo Doria08/2014
27272^337387+855101564Lelio R Paula09/2016
27282^337367-17295101558Lelio R Paula09/2016
27292^337342-109035101551Enzo Doria04/2014
27302^337267-19101528Lelio R Paula07/2011
27312^337183-19989101503Enzo Doria06/2013
27322^337149+72425101492Enzo Doria04/2016
27332^337101-20241101478Enzo Doria06/2013
27342^337035-20001101458Enzo Doria06/2013
27352^337017-16995101453Lelio R Paula09/2016
27362^336979-115315101441Enzo Doria06/2015
27372^336970-20885101439Enzo Doria06/2013
27382^336958+79101435Lelio R Paula10/2009
27392^336942+169101430Lelio R Paula10/2009
2740(15185*2^336894-1)/7939101416Lelio R Paula05/2015
27412^336871+257463101409Tony Prest / Never Odd Or Even04/2016
27422^336871+318105101409Tony Prest / Never Odd Or Even04/2016
27432^336871+1010813101409Tony Prest / Never Odd Or Even04/2016
27442^336871+2302245101409Tony Prest / Never Odd Or Even04/2016
27452^336871+389273101409Tony Prest / Never Odd Or Even04/2016
27462^336871+1685475101409Tony Prest / Never Odd Or Even04/2016
27472^336871+1068119101409Tony Prest / Never Odd Or Even04/2016
27482^336871+586905101409Tony Prest / Never Odd Or Even04/2016
27492^336871+674571101409Tony Prest / Never Odd Or Even04/2016
27502^336871+707009101409Tony Prest / Never Odd Or Even04/2016


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Created by  Henri Lifchitz & Renaud Lifchitz : October, 26 2000, last modification: March, 26 2017 17:51 (Time in France)

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