PRP Records

Probable Primes Top 10000

(224926 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 ?
62512^245629-279781373942Eric Chen03/2016
62522^245557-15373921Lelio R Paula03/2012
6253(77*10^73917-59)/973918Robert Price11/2017
62542^245525+186988173911Enzo Doria06/2016
62552^245522+15973910Lelio R Paula03/2012
6256(13*10^73891-43)/373892Robert Price08/2017
625719^57783-5673891Lelio R Paula01/2015
62587*10^73888+7973889Robert Price02/2017
62596^94948+17428173884Mike Oakes02/2011
626011^70939-486073876Enzo Doria01/2013
62612^245372+5461573865Lelio R Paula05/2013
62622^245362-14373862Lelio R Paula03/2012
62637^87396+6^(87396-1)73859Robert Price03/2016
6264(22*10^73853-37)/373854Robert Price05/2017
62655^105646-1424673844Enzo Doria02/2013
62672^245290-4173840Lelio R Paula03/2012
62662^245290-9439573840Lelio R Paula05/2013
62688*5^105600-773813Lelio R Paula10/2014
62697*5^105573-473794Lelio R Paula10/2014
627018^58742-480573738Enzo Doria03/2013
627113^66179+6673720Lelio R Paula01/2015
6272(82*10^73714-1)/973715Robert Price12/2014
6273(29*2^244856-1)/18612173706Lelio R Paula01/2014
6274(13*2^244840-1)/279973702Lelio R Paula01/2014
6275(13*10^73701+17)/373702Robert Price06/2015
6276(2^244787-1017)/2841173684Lelio R Paula07/2012
6277(3^154421-4)/2373677Lelio R Paula06/2012
62788*7^87170+573669Lelio R Paula10/2014
6279(29*10^73659-113)/373660Robert Price11/2017
6280Phi(40100,-40100)73651Henri Lifchitz06/2013
6281(4*10^73647-19)/373648Robert Price06/2017
62822^244618-229773638Yves Minet10/2009
62833*5^105344+873633Lelio R Paula10/2014
62845^105334-1409673626Enzo Doria02/2013
6285(2^244584-7)/1323707424303373614Lelio R Paula07/2012
62862^244465-11018573592Enzo Doria05/2014
62872^244443+4075573585Lelio R Paula05/2013
62882^244404+384173573Yves Minet03/2011
62892^244372-11062773564Enzo Doria05/2014
6290(3*2^244255+1)/24573527Lelio R Paula08/2012
6291(11*2^244245+1)/2373525Lelio R Paula08/2012
6292(15185*2^244187-1)/611173509Lelio R Paula04/2015
6293(91^37507+1)/9273476Paul Bourdelais08/2017
629418^58521+6573460Lelio R Paula01/2015
629513^65940+3673454Lelio R Paula01/2015
6296(625^26267+1)/62673437Richard Fischer12/2017
62975^105050-1473427Lelio R Paula08/2014
6298(((((((((((((30201^2-2)^2-2)^2-2)^2-2)^2-2)^2-2)^2-2)^2-2)^2-2)^2-2)^2-2)^2-2)^2-2)^2-273401Serge Batalov07/2016
629915^62410-4673400Lelio R Paula01/2015
63002^243733+186970773371Enzo Doria05/2016
630111^70439-543073355Enzo Doria01/2013
63022^243676-8773354Lelio R Paula03/2012
6303(101*10^73346-17)/373348Robert Price08/2016
63042^243621-11318573338Enzo Doria07/2014
6305(5*2^243610-1)/166973332Lelio R Paula01/2014
63062*5^104888-773314Lelio R Paula10/2014
6307(58695*2^243516-1)/98373308Lelio R Paula04/2015
6308(3^153648-2)/3342313809773299Lelio R Paula06/2012
630918^58376-525573278Enzo Doria03/2013
631011^70363+3273276Lelio R Paula02/2015
63112^243413+425773275Lelio R Paula05/2013
6312104824^5+5^10482473269Andrey Kulsha07/2010
63137^86689-6^8668973261Predrag Minovic09/2004
63142^243296+9019573240Lelio R Paula05/2013
6316p(15433)#/2-473218Robert Price12/2016
6315(59*10^73217-77)/973218Robert Price11/2017
63172^243127+7135573189Lelio R Paula05/2013
63182^243116-24941973186Paul Bourdelais03/2013
6319(58695*2^243085-1)/1173180Lelio R Paula04/2015
632011^70262-9873171Lelio R Paula02/2015
6321(2^243034+47)/72270330373152Lelio R Paula07/2012
6322(2^242966+47)/4688773136Lelio R Paula07/2012
6323(43^44773-1)/4273134Robert Price04/2014
63246^93980-15835973131Mike Oakes02/2011
63256^93915+5373081Lelio R Paula01/2015
6326(5*10^73079+211)/973079Robert Price12/2017
6327(74*10^73076+43)/973077Robert Price10/2015
6328(3^153125+2)/114495573054Lelio R Paula06/2012
63292^242632-11219973040Enzo Doria06/2014
6330V(351646)73029Serge Batalov03/2015
633118^58175-8573026Lelio R Paula01/2015
6332p(15395)#/2-473019Robert Price12/2016
6333(4^121271+3^121271)/773012Jean-Louis Charton03/2011
63348*6^93825-573011Lelio R Paula10/2014
6336(F(220)^1601-F(219)^1601)/F(218)73005Wayne Halsdorf08/2013
6335(73^39181+1)/7473005Paul Bourdelais08/2017
63376^93815+14373003Lelio R Paula01/2015
63386^93812+573000Wojciech Florek03/2006
633919^57078-6272989Lelio R Paula01/2015
6340(29*10^72985+91)/372986Robert Price03/2016
634111^70082-252072983Enzo Doria12/2012
63426^93773+13372970Lelio R Paula01/2015
63432^242328-5972948Lelio R Paula03/2012
63445^104358-1301672944Enzo Doria02/2013
6345(75*10^72941-57)/9972941Ray Chandler03/2011
634612^67585-9572937Lelio R Paula02/2015
63472^242230-11328572919Enzo Doria07/2014
6348(5*10^72916-11)/372917Erik Branger12/2013
63492^242220-11039972916Enzo Doria05/2014
63502^242205-11341372911Enzo Doria07/2014
6351(3^152809+3^76405+1)/772908Serge Batalov03/2014
63522^242175+7424372902Yves Minet03/2011
63532^242150+1765972895Lelio R Paula11/2009
635411^69982-234072879Enzo Doria12/2012
6355(23*2^242093+1)/1011772875Lelio R Paula08/2012
6356(67607*2^242043+1)/3326372863Lelio R Paula06/2014
63572^242032+8772859Lelio R Paula03/2012
63582^241968-11059572840Enzo Doria05/2014
6359(10^72821+71)/972821Robert Price11/2014
63602^241852-6487572805Lelio R Paula05/2013
6361F(348307)/2056289086590809372776Donovan Johnson07/2007
6362(67*10^72772+23)/972773Ray Chandler11/2010
6363(8*10^72759+67)/372760Robert Price01/2017
63642^241670+14572750Lelio R Paula03/2012
63655^104074+5272745Lelio R Paula08/2014
6366(3^152466-5)/72472742Lelio R Paula06/2012
636720^55908-4172738Lelio R Paula01/2015
6368(73*10^72735+53)/972736Robert Price10/2015
636910^72730+22401172731Patrick De Geest05/2013
637010^72730-9972730Robert Price05/2011
63713*10^72723+6772724Robert Price11/2017
6372(11^69833+3^69833)/1472723Robert Price03/2013
6373(10^72723-79)/372723Robert Price10/2017
6374(88*10^72711-43)/972712Robert Price11/2015
63753^152379+28072704Lelio R Paula01/2015
6376(25*10^72703-241)/972704Robert Price01/2017
6377(47*10^72696+133)/972697Robert Price04/2017
637817^59077-9072692Lelio R Paula01/2015
637965^40096+5872691Lelio R Paula01/2016
6380(29*2^241446-1)/24572682Lelio R Paula01/2014
638211^69783-3840000072672Enzo Doria01/2013
63812^241409-11290372672Enzo Doria06/2014
6383(3^152287+1)/472659Paul Bourdelais04/2008
63843^152249-5672642Lelio R Paula01/2015
638510^72631+3772632Robert Price01/2011
638610^72631-881372631Patrick De Geest05/2013
6387(19*2^241254+1)/10172624Lelio R Paula08/2012
6388(9^76103+8^76103)/1772620Robert Price12/2012
63892^241220-11233772615Enzo Doria06/2014
6390(82*10^72612+449)/972613Robert Price02/2017
63912^241169-1579372600Enzo Doria04/2013
63929*10^72595+1172596Robert Kinser01/2017
6393(25*2^241048+1)/8972563Lelio R Paula08/2012
6394(22*10^72560+17)/372561Robert Price09/2015
63952^241032-2372558Lelio R Paula02/2012
639634485*10^72550+2^241004-372555Gilbert Mozzo12/2012
63972^241004-372550M. Frind & P. Underwood07/2002
639897*10^72522-372524Robert Price01/2017
6399(68*10^72516+7)/372518Robert Price03/2016
6400(78557*2^240844+1)/6372505Lelio R Paula06/2014
640167^39701-6672497Norbert Schneider11/2014
6402(185*10^72484+7)/372486Robert Price02/2017
6404(293*27^50631-1736)/1372473Curtis Bright05/2015
6403103^36005-10272473Norbert Schneider10/2016
640515^61616+8872467Lelio R Paula01/2015
640645^43831+272462Lelio R Paula05/2013
64072^240692-49238972456Paul Bourdelais03/2013
6408(646*10^72446-7)/972448Robert Price07/2016
64099*6^93083+772434Lelio R Paula10/2014
64102^240617-364572433Lelio R Paula05/2013
641111^69531-2400072410Enzo Doria12/2012
6412(22699*2^240396+1)/5572370Lelio R Paula06/2014
64136^92995+1372365Lelio R Paula01/2015
6414(11*10^72362-149)/372363Robert Price01/2017
6415(2^240381+3)/5165572358Lelio R Paula05/2012
64166^92974-5572348Lelio R Paula01/2015
64172^240295+1172337Lelio R Paula02/2012
6418(14*10^72326-53)/372327Robert Price12/2016
641915^61493-4672322Lelio R Paula01/2015
6420lucasU(46,1,43497)-lucasU(46,1,43496)72315Mike Oakes04/2009
64225*10^72302+972303Dmitry Domanov11/2010
6421(9787*2^240179-1)/26572303Lelio R Paula04/2015
642311^69419-312072293Enzo Doria12/2012
64244*10^72274-8372275Robert Price10/2017
642510^72267+3372268Robert Price01/2011
642610^72267-55394772267Patrick De Geest05/2013
642711^69389-138072262Enzo Doria12/2012
6428(16^60013-5^60013)/1172262Robert Price07/2013
64297^85507-3072262Lelio R Paula08/2014
6430(19*2^240026-1)/1572256Lelio R Paula02/2014
6431(3^151426-2)/66133772243Lelio R Paula06/2012
6432gcd(V(1296375),5*F(259275)*(F(259275)-1)+1)72227Serge Batalov04/2015
64332^239863-11226772206Enzo Doria06/2014
64342^239853-11485372203Enzo Doria05/2015
6435(4*10^72174+149)/972174Robert Price03/2017
6437(2^239671+9)/29613172143Lelio R Paula05/2012
64362^239651-11066572143Enzo Doria05/2014
6438(29*2^239650-1)/330572140Lelio R Paula01/2014
6439241^30280+30280^24172128Norbert Schneider11/2014
6440(68*10^72120-23)/972121Robert Price10/2015
6441(9^75571+8^75571)/1772112Robert Price12/2012
6442(15*2^239530-1)/17372105Lelio R Paula01/2014
64432^239513-11251972101Enzo Doria06/2014
6444(10^72097+149)/372097Serge Batalov12/2014
64452^239442-655572080Lelio R Paula05/2012
64462*5^103106+372069Lelio R Paula10/2014
64472^239402-19772068Lelio R Paula02/2012
64482^239356-11187572054Enzo Doria05/2014
6449(38*10^72050-119)/972051Robert Price11/2016
64502^239339+1501572049Lelio R Paula01/2013
6451159^32728+272048Lelio R Paula05/2013
645215^61259-3872047Lelio R Paula01/2015
645392^36683-91^3668372038Robert Price08/2015
64542^239280+5461572031Lelio R Paula05/2012
6456(47*2^239267+1)/7772027Lelio R Paula04/2015
6455(85*10^72025-1)/372027Robert Price07/2017
64572^239236-9730572018Lelio R Paula05/2012
64582^239169+5971998Lelio R Paula02/2012
6460lucasU(2010,1,21796)-lucasU(2010,1,21795)71994Mike Oakes05/2009
6459(15*2^239171-1)/10630171994Lelio R Paula01/2014
6461(29^49211-1)/2871965Robert Price04/2012
6462(299*10^71963+1)/371965Robert Price11/2017
6464L(344293)71953Renaud Lifchitz09/2003
6463V(344293)71953Serge Batalov03/2015
64656*10^71951+771952Dmitry Domanov11/2010
64663^150798+4071949Lelio R Paula01/2015
64672^238961+9571935Lelio R Paula02/2012
64682^238936-40771927Yves Minet02/2012
64692^238923-2863571923Lelio R Paula05/2012
647010^71910+2511971911Patrick De Geest05/2016
647110^71910-80171910Robert Price04/2016
64722^238845-11265171900Enzo Doria06/2014
64732^238792-11124571884Enzo Doria05/2014
64746*7^85059+571884Lelio R Paula10/2014
64752^238752-11058971872Enzo Doria05/2014
647612^66581+771853Lelio R Paula07/2014
6477(7*2^238691+1)/4122971850Lelio R Paula06/2012
64784*3^150568-571840Lelio R Paula04/2014
64796^92301+6771825Lelio R Paula01/2015
64802^238568+9876533171817Jason Earls01/2009
64812^238541-11272371808Enzo Doria06/2014
64822^238529-1594971805Enzo Doria04/2013
64839*5^102721-871800Lelio R Paula10/2014
64842^238494-16571794Lelio R Paula02/2012
64852^238389-11090571763Enzo Doria05/2014
6486(145*10^71760-1)/971762Serge Batalov12/2014
64877^84913+506271760Mike Oakes02/2010
6488(F(11446)^31-F(11445)^31)/F(11444)71753Wayne Halsdorf03/2012
64892^238268-9730571726Lelio R Paula05/2012
6490gcd(V(1330365),5*F(266073)*(F(266073)-1)+1)71724Serge Batalov04/2015
64912^238235-11324771716Enzo Doria07/2014
64922*12^66450-5^6645071712Mike Oakes11/2010
6493(2^238213+lucasV(1,2,238213)+1)/471709Mike Oakes11/2016
64942^238199-11181771706Enzo Doria05/2014
6495lucasU(46,1,43125)+lucasU(46,1,43124)71696Mike Oakes04/2009
64962^238144+9876533171689Jason Earls01/2009
649718^57102-426571679Enzo Doria03/2013
6498(73*10^71670-1)/971671Robert Price01/2015
64992^238081+1155*23808171670Henri Lifchitz02/2005
65002^238067-11192571666Enzo Doria05/2014


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Created by  Henri Lifchitz & Renaud Lifchitz : October, 26 2000, last modification: October, 18 2018 22:22 (Time in France)

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