PRP Records

Probable Primes Top 10000

(252675 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 (> 50000) Who ? When ?
32513^216685-113056103386Enzo Doria07/2014
325244^62903-43^62903103379Jean-Louis Charton08/2012
325311^99262-20103371Lelio R Paula12/2016
3254(509203*2^343357-1)/5103366Lelio R Paula05/2015
32562^343356-2791889103361Enzo Doria03/2016
3255(25*10^103360-241)/9103361Robert Price05/2018
3257Phi(104989,10)/2939693103350Maksym Voznyy09/2015
32582^343182-171103309Lelio R Paula08/2011
3259(23619^23619+23620^23620)/7187103294David Broadhurst09/2009
32602^343079-1835611103278Enzo Doria05/2015
32612^343063-1147103273Yves Minet06/2013
32629*6^132689+7103254Lelio R Paula11/2014
32632^342979-18085103247Enzo Doria05/2013
3264(16*10^103244-31)/3103245Robert Price03/2019
32652^342966-16995103244Lelio R Paula11/2016
3266(16*10^103214-31)/3103215Robert Price03/2019
3267(37*10^103211+611)/9103212Robert Price11/2018
32685^147650+16103203Lelio R Paula11/2016
3269gcd(Phi(852060,10),(10^42603+1)^3*(10^42603+1-10^21302)+(10^85206+10^42603)*(10^21302+1)+10^127809)103201Serge Batalov04/2015
32702^342817+2707067103199Enzo Doria03/2016
327143^63177-42103198Theodore Burton02/2007
32722^342805-21025103195Enzo Doria06/2013
32732^342714+12285103168Lelio R Paula11/2016
327418^82178-4481103156Enzo Doria03/2013
32752^342665-17349103153Enzo Doria05/2013
32762^342612+175103137Lelio R Paula08/2011
32775*2^342585-3103130Lelio R Paula09/2014
3278(16*10^103127+77)/3103128Robert Price03/2019
32792^342503-19209103104Enzo Doria05/2013
32802^342476+51103096Lelio R Paula08/2011
32812^342460-18885103091Enzo Doria05/2013
32827^121968+82103075Lelio R Paula10/2016
32832^342392-108863103071Enzo Doria03/2014
32843^216014+28103065Lelio R Paula11/2016
32852^342353-108879103059Enzo Doria03/2014
328610^103055+276081103056Patrick De Geest12/2016
328710^103055-53103055Lelio R Paula11/2016
32887^121933+4103046Lelio R Paula11/2014
328919^80560-68103017Lelio R Paula10/2016
32902^342209+76607103016Enzo Doria05/2016
3292328^40945+40945^328103013Norbert Schneider12/2014
329112^95454-91103013Lelio R Paula10/2016
329325833^9716+9716^25833103009Hans Havermann01/2019
329465^56809-64^56809102990Robert Price08/2013
32955^147338-6102985Lelio R Paula11/2014
32962^342084-112739102978Enzo Doria06/2014
32979*6^132330+7102974Lelio R Paula11/2014
32982^342034-16737102963Enzo Doria05/2013
3299(9787*2^342011-1)/25102959Lelio R Paula05/2015
3300(3^215802-5)/124343756102956Lelio R Paula12/2013
33012^341991-17421102950Enzo Doria05/2013
33022^341969-112225102943Enzo Doria06/2014
3303(9787*2^341864-1)/3102915Lelio R Paula05/2015
33052^341859+1869413102910Enzo Doria05/2016
330410^102909+61102910Lelio R Paula11/2016
330610^102909-67049102909Patrick De Geest12/2016
330723814^20935+20935^23814102898Hans Havermann02/2019
330828345^4264+4264^28345102888Hans Havermann02/2019
330925665^10204+10204^25665102886Hans Havermann02/2019
331026288^8181+8181^26288102860Hans Havermann02/2019
33112^341659+1836773102850Enzo Doria03/2016
33122^341608-110639102835Enzo Doria05/2014
331310^102824+49102825Lelio R Paula11/2016
331410^102824-168011102824Patrick De Geest12/2016
331511^98708-8102794Lelio R Paula10/2016
33162^341466+4429102792Lelio R Paula09/2011
33172^341460-107102790Lelio R Paula08/2011
3318(2^341388+47)/21014943102761Lelio R Paula12/2013
33192^341355+21102759Lelio R Paula08/2011
33202^341246+40755102726Lelio R Paula11/2016
3321(2^341256-5)/991699102723Lelio R Paula12/2013
33227^121547+78102720Lelio R Paula10/2016
33232^341223-461197102719Enzo Doria06/2015
332427838^4893+4893^27838102711Hans Havermann03/2019
33262^341190-20577102709Enzo Doria06/2013
3325(27*2^341212+1)/84674449102709Lelio R Paula12/2013
33276^131976-65102698Lelio R Paula10/2016
33282^341134+2533102692Henri Lifchitz09/2005
332913^92184-54102688Lelio R Paula10/2016
33302^341116-20873102687Enzo Doria06/2013
33312^341094-19953102680Enzo Doria06/2013
333223761^20950+20950^23761102676Hans Havermann03/2019
33332^341053+129102668Lelio R Paula08/2011
3334(31*2^341006-1)/3102655Lelio R Paula03/2014
33357^121471+94102655Lelio R Paula10/2016
33372^341004-173102653Lelio R Paula08/2011
333620^78901+3102653Lelio R Paula10/2016
33385^146853-52102646Lelio R Paula10/2016
33392^340969-216931102642Enzo Doria05/2014
3340122^49196+121102641Norbert Schneider10/2018
33412^340952+1870021102637Enzo Doria05/2016
33425*2^340940-3102634Lelio R Paula08/2014
3343(6^131891+1)/7102631Paul Bourdelais01/2010
334425876^9239+9239^25876102615Hans Havermann02/2019
3345(4*10^102612+83)/3102613Robert Price02/2018
334775^54717+74102598Norbert Schneider01/2015
3346(17*10^102597+13)/3102598Robert Price01/2019
33482^340806-20393102593Enzo Doria06/2013
3349(2^340790+5)/138267102583Lelio R Paula12/2013
33506^131821+77102577Lelio R Paula10/2016
33512^340688-29102558Henri Lifchitz05/2005
33522^340685-109101102557Enzo Doria04/2014
335365^56567-64102552Norbert Schneider11/2014
335426230^8121+8121^26230102550Hans Havermann03/2019
33552^340547-108897102515Enzo Doria03/2014
335625592^10119+10119^25592102500Hans Havermann02/2019
33577^121268+82102484Lelio R Paula10/2016
3358(6883*2^340443-1)/162401102483Lelio R Paula05/2015
33592^340434-5955102481Lelio R Paula11/2016
3360(2^340381+47)/7102465Lelio R Paula12/2013
3361111^50095+110102461Norbert Schneider04/2017
33622^340291-20301102438Enzo Doria06/2013
336312^94915+89102431Lelio R Paula10/2016
336424466^15349+15349^24466102417Hans Havermann03/2019
33652^340208-20373102413Enzo Doria06/2013
33666^131598-17273102404Enzo Doria02/2013
33672^340115-21181102385Enzo Doria06/2013
3368(55459*2^340090+1)/1591102379Lelio R Paula07/2014
336989^52511-88^52511102365Robert Price06/2015
33703^214539-112756102362Enzo Doria07/2014
33712^340000-19877102351Enzo Doria06/2013
33722^339990-114845102348Enzo Doria05/2015
3373(3^214516-2)/51383102346Lelio R Paula12/2013
337420^78661-99102341Lelio R Paula09/2016
33752^339951-19585102336Enzo Doria05/2013
3376(13*2^339943+1)/45102333Lelio R Paula12/2013
33772^339889+29327102317Yves Minet06/2010
337826348^7641+7641^26348102314Hans Havermann03/2019
33792^339834-109493102301Enzo Doria04/2014
3380(16*10^102299-19)/3102300Robert Price02/2019
3381(11^98221-5^98221)/6102286Robert Price01/2013
33823^214365+1820102279Lelio R Paula10/2016
338331978^1579+1579^31978102278Hans Havermann03/2019
3384(11*2^339705-1)/183102261Lelio R Paula03/2014
33852^339694-16995102259Lelio R Paula09/2016
3386122^49008+121102249Norbert Schneider10/2018
33877^120985-38102245Lelio R Paula10/2016
338810^102244+122961102245Patrick De Geest12/2016
338910^102244-27102244Lelio R Paula09/2016
33907^120982-62102242Lelio R Paula10/2016
33914*6^131382-5102236Lelio R Paula11/2014
33922^339586-1091102226Yves Minet11/2012
339311^98161-3072000102225Enzo Doria12/2012
33949*7^120961-4102225Lelio R Paula11/2014
33955*3^214250+2102224Serge Batalov10/2010
339612^94713-59102213Lelio R Paula10/2016
339712^94705+89102204Lelio R Paula10/2016
33982^339407-177102172Lelio R Paula08/2011
33994*10^102163-57102164Robert Price10/2018
34002^339355+65102157Lelio R Paula07/2011
3401(2^339323+47)/880715102141Lelio R Paula12/2013
34022^339168+21102100Lelio R Paula07/2011
34032^339167-108807102100Enzo Doria03/2014
34042^339156+163102097Lelio R Paula08/2011
34052^339081-4543102074Yves Minet03/2019
340624327^15668+15668^24327102053Hans Havermann02/2019
340725080^11711+11711^25080102041Hans Havermann02/2019
3408(2^338982-7)/1754517102038Lelio R Paula12/2013
34092^338891-18885102017Enzo Doria05/2013
34102^338829-113239101998Enzo Doria07/2014
34112^338828-113297101998Enzo Doria07/2014
34122^338796+93101988Donovan Johnson06/2008
3413lucasU(1373,1,32502)-lucasU(1373,1,32501)101978Mike Oakes05/2009
341425295^10744+10744^25295101969Hans Havermann01/2019
341525712^9243+9243^25712101969Hans Havermann01/2019
3416(71^55079-1)/70101964Paul Bourdelais08/2017
34172^338682-19865101954Enzo Doria06/2013
3418(2^(112895*3+1)+243)/7101954Kevin Acres12/2013
341928594^3673+3673^28594101939Hans Havermann02/2019
34202^338568+37101920Lelio R Paula07/2011
34212^338559-1858777101917Enzo Doria04/2016
3422(9*2^338520+1)/365101904Lelio R Paula12/2013
342324502^14419+14419^24502101903Hans Havermann01/2019
34242^338497-17041101898Enzo Doria05/2013
34252^338475+54615101892Lelio R Paula10/2016
34262^338426-19797101877Enzo Doria06/2013
34272^338368-20369101859Enzo Doria06/2013
34282^338366+74179101859Enzo Doria04/2016
342927088^5755+5755^27088101853Hans Havermann01/2019
34302^338280-19745101833Enzo Doria06/2013
3431(3*2^338236-1)/347101818Lelio R Paula03/2014
34326^130841+103101815Lelio R Paula10/2016
34332^338122-20117101785Enzo Doria06/2013
3434(2^338139+5)/905333101785Lelio R Paula12/2013
343535^65917-7092101781Enzo Doria03/2013
34362^338010-19833101752Enzo Doria06/2013
34373^213215-76101730Lelio R Paula09/2016
343823907^17998+17998^23907101730Hans Havermann01/2019
34392^337930+63101728Lelio R Paula07/2011
34402^337920+1869661101725Enzo Doria05/2016
344124116^16509+16509^24116101715Hans Havermann01/2019
34422^337859-19645101706Enzo Doria05/2013
34432^337754+1869169101675Enzo Doria05/2016
34443*10^101657-37101658Robert Price07/2018
3445(31*2^337677-1)/593101650Lelio R Paula03/2014
344611^97605-24101646Lelio R Paula10/2016
34478^112539-112539101633Robert Price01/2014
344825694^9003+9003^25694101605Hans Havermann12/2018
34492^337515-19869101603Enzo Doria06/2013
34502^337473+719101590Lelio R Paula08/2011
3451(2^337485-509203)/656647157101585Lelio R Paula12/2013
34522^337452-108815101584Enzo Doria03/2014
34532^337453+1185101584Lelio R Paula09/2016
34542^337410-113561101571Enzo Doria08/2014
34552^337387+855101564Lelio R Paula09/2016
34562^337367-17295101558Lelio R Paula09/2016
34572^337342-109035101551Enzo Doria04/2014
345823703^19238+19238^23703101548Hans Havermann12/2018
34592^337267-19101528Lelio R Paula07/2011
34602^337183-19989101503Enzo Doria06/2013
34612^337149+72425101492Enzo Doria04/2016
346224041^16642+16642^24041101483Hans Havermann12/2018
346333982^969+969^33982101482Hans Havermann12/2018
34642^337101-20241101478Enzo Doria06/2013
34652^337035-20001101458Enzo Doria06/2013
34662^337017-16995101453Lelio R Paula09/2016
34672^336979-115315101441Enzo Doria06/2015
34682^336970-20885101439Enzo Doria06/2013
34692^336958+79101435Lelio R Paula10/2009
34702^336942+169101430Lelio R Paula10/2009
3471(15185*2^336894-1)/7939101416Lelio R Paula05/2015
34724*10^101415-89101416Robert Price11/2018
34732^336871+257463101409Tony Prest / Never Odd Or Even04/2016
34742^336871+318105101409Tony Prest / Never Odd Or Even04/2016
34752^336871+1010813101409Tony Prest / Never Odd Or Even04/2016
34762^336871+2302245101409Tony Prest / Never Odd Or Even04/2016
34772^336871+389273101409Tony Prest / Never Odd Or Even04/2016
34782^336871+1685475101409Tony Prest / Never Odd Or Even04/2016
34792^336871+1068119101409Tony Prest / Never Odd Or Even04/2016
34802^336871+586905101409Tony Prest / Never Odd Or Even04/2016
34812^336871+674571101409Tony Prest / Never Odd Or Even04/2016
34822^336871+707009101409Tony Prest / Never Odd Or Even04/2016
34832^336871+1210299101409Tony Prest / Never Odd Or Even04/2016
34842^336871+1921185101409Tony Prest / Never Odd Or Even04/2016
34852^336871+2003973101409Tony Prest / Never Odd Or Even04/2016
34862^336871+2656475101409Tony Prest / Never Odd Or Even04/2016
34872^336871+2703023101409Tony Prest / Never Odd Or Even04/2016
34882^336871+2704545101409Tony Prest / Never Odd Or Even04/2016
34892^336871+2766801101409Tony Prest / Never Odd Or Even04/2016
34902^336871+2127735101409Tony Prest / Never Odd Or Even04/2016
3491(2^336871+821089)/3101408Tony Prest / Never Odd Or Even05/2016
3492(2^336871+119567)/5101408Tony Prest / Never Odd Or Even05/2016
3493(2^336871+398161)/3101408Tony Prest / Never Odd Or Even05/2016
3494(2^336871+625889)/7101408Tony Prest / Never Odd Or Even05/2016
349524097^16150+16150^24097101405Hans Havermann12/2018
34962^336842+94065101400Lelio R Paula09/2016
3497(2^336871+904417)/3/3/3/5/19/9287177/9690011663/29993043103101378Tony Prest / Never Odd Or Even04/2016
3498(2^336871+631971)/13/251/1601/294277/614362921/30324278867101377Tony Prest / Never Odd Or Even04/2016
3499(2^336871+1443541)/3/89/1655197/11018131/47972707/468862691879101374Tony Prest / Never Odd Or Even04/2016
3500(2^336871+689863)/3/11/109/137/1867/7151/20800501/29243857/127778489101373Tony Prest / Never Odd Or Even04/2016


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Created by  Henri Lifchitz & Renaud Lifchitz : October, 26 2000, last modification: April, 20 2019 09:21 (Time in France)

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