PRP Records

Probable Primes Top 10000

(252538 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 ?
65019998*2^245696+373966Donovan Johnson10/2004
650213^66400-8073966Lelio R Paula01/2015
6503(2^245704+9)/2573963Lelio R Paula07/2012
650511^71023-717073963Enzo Doria01/2013
65043*10^73962+1373963Robert Price08/2017
6506(31*2^245660-1)/11419573948Lelio R Paula01/2014
65072^245629-279781373942Eric Chen03/2016
65082^245557-15373921Lelio R Paula03/2012
6509(77*10^73917-59)/973918Robert Price11/2017
65102^245525+186988173911Enzo Doria06/2016
65112^245522+15973910Lelio R Paula03/2012
6512(13*10^73891-43)/373892Robert Price08/2017
651319^57783-5673891Lelio R Paula01/2015
65147*10^73888+7973889Robert Price02/2017
65156^94948+17428173884Mike Oakes02/2011
651611^70939-486073876Enzo Doria01/2013
65172^245372+5461573865Lelio R Paula05/2013
65182^245362-14373862Lelio R Paula03/2012
65197^87396+6^(87396-1)73859Robert Price03/2016
6520(22*10^73853-37)/373854Robert Price05/2017
65215^105646-1424673844Enzo Doria02/2013
65232^245290-4173840Lelio R Paula03/2012
65222^245290-9439573840Lelio R Paula05/2013
65248*5^105600-773813Lelio R Paula10/2014
65257*5^105573-473794Lelio R Paula10/2014
652618^58742-480573738Enzo Doria03/2013
652713^66179+6673720Lelio R Paula01/2015
6528(82*10^73714-1)/973715Robert Price12/2014
6529(29*2^244856-1)/18612173706Lelio R Paula01/2014
6530(13*2^244840-1)/279973702Lelio R Paula01/2014
6531(13*10^73701+17)/373702Robert Price06/2015
6532(2^244787-1017)/2841173684Lelio R Paula07/2012
6533(3^154421-4)/2373677Lelio R Paula06/2012
65348*7^87170+573669Lelio R Paula10/2014
6535(29*10^73659-113)/373660Robert Price11/2017
6536Phi(40100,-40100)73651Henri Lifchitz06/2013
6537(4*10^73647-19)/373648Robert Price06/2017
65382^244618-229773638Yves Minet10/2009
65393*5^105344+873633Lelio R Paula10/2014
65405^105334-1409673626Enzo Doria02/2013
6541(2^244584-7)/1323707424303373614Lelio R Paula07/2012
65422^244465-11018573592Enzo Doria05/2014
65432^244443+4075573585Lelio R Paula05/2013
65442^244404+384173573Yves Minet03/2011
65452^244372-11062773564Enzo Doria05/2014
6546(3*2^244255+1)/24573527Lelio R Paula08/2012
6547(11*2^244245+1)/2373525Lelio R Paula08/2012
6548(15185*2^244187-1)/611173509Lelio R Paula04/2015
6549(91^37507+1)/9273476Paul Bourdelais08/2017
655018^58521+6573460Lelio R Paula01/2015
655113^65940+3673454Lelio R Paula01/2015
6552(625^26267+1)/62673437Richard Fischer12/2017
65535^105050-1473427Lelio R Paula08/2014
6554(((((((((((((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
655515^62410-4673400Lelio R Paula01/2015
65562^243733+186970773371Enzo Doria05/2016
655711^70439-543073355Enzo Doria01/2013
65582^243676-8773354Lelio R Paula03/2012
6559(101*10^73346-17)/373348Robert Price08/2016
65602^243621-11318573338Enzo Doria07/2014
6561(5*2^243610-1)/166973332Lelio R Paula01/2014
65622*5^104888-773314Lelio R Paula10/2014
6563(58695*2^243516-1)/98373308Lelio R Paula04/2015
6564(3^153648-2)/3342313809773299Lelio R Paula06/2012
656518^58376-525573278Enzo Doria03/2013
656611^70363+3273276Lelio R Paula02/2015
65672^243413+425773275Lelio R Paula05/2013
6568104824^5+5^10482473269Andrey Kulsha07/2010
65697^86689-6^8668973261Predrag Minovic09/2004
65702^243296+9019573240Lelio R Paula05/2013
6572p(15433)#/2-473218Robert Price12/2016
6571(59*10^73217-77)/973218Robert Price11/2017
65732^243127+7135573189Lelio R Paula05/2013
65742^243116-24941973186Paul Bourdelais03/2013
6575(58695*2^243085-1)/1173180Lelio R Paula04/2015
657611^70262-9873171Lelio R Paula02/2015
6577(2^243034+47)/72270330373152Lelio R Paula07/2012
6578(2^242966+47)/4688773136Lelio R Paula07/2012
6579(43^44773-1)/4273134Robert Price04/2014
65806^93980-15835973131Mike Oakes02/2011
65816^93915+5373081Lelio R Paula01/2015
6582(5*10^73079+211)/973079Robert Price12/2017
6583(74*10^73076+43)/973077Robert Price10/2015
6584(3^153125+2)/114495573054Lelio R Paula06/2012
65852^242632-11219973040Enzo Doria06/2014
6586V(351646)73029Serge Batalov03/2015
658718^58175-8573026Lelio R Paula01/2015
6588p(15395)#/2-473019Robert Price12/2016
6589(4^121271+3^121271)/773012Jean-Louis Charton03/2011
65908*6^93825-573011Lelio R Paula10/2014
6591(F(220)^1601-F(219)^1601)/F(218)73005Wayne Halsdorf08/2013
6592(73^39181+1)/7473005Paul Bourdelais08/2017
65936^93815+14373003Lelio R Paula01/2015
65946^93812+573000Wojciech Florek03/2006
659519^57078-6272989Lelio R Paula01/2015
6596(29*10^72985+91)/372986Robert Price03/2016
659711^70082-252072983Enzo Doria12/2012
65986^93773+13372970Lelio R Paula01/2015
65992^242328-5972948Lelio R Paula03/2012
66005^104358-1301672944Enzo Doria02/2013
6601(75*10^72941-57)/9972941Ray Chandler03/2011
660212^67585-9572937Lelio R Paula02/2015
66032^242230-11328572919Enzo Doria07/2014
6604(5*10^72916-11)/372917Erik Branger12/2013
66052^242220-11039972916Enzo Doria05/2014
66062^242205-11341372911Enzo Doria07/2014
6607(3^152809+3^76405+1)/772908Serge Batalov03/2014
66082^242175+7424372902Yves Minet03/2011
66092^242150+1765972895Lelio R Paula11/2009
661011^69982-234072879Enzo Doria12/2012
6611(23*2^242093+1)/1011772875Lelio R Paula08/2012
6612(67607*2^242043+1)/3326372863Lelio R Paula06/2014
66132^242032+8772859Lelio R Paula03/2012
66142^241968-11059572840Enzo Doria05/2014
6615(10^72821+71)/972821Robert Price11/2014
66162^241852-6487572805Lelio R Paula05/2013
6617F(348307)/2056289086590809372776Donovan Johnson07/2007
6618(67*10^72772+23)/972773Ray Chandler11/2010
6619(8*10^72759+67)/372760Robert Price01/2017
66202^241670+14572750Lelio R Paula03/2012
66215^104074+5272745Lelio R Paula08/2014
6622(3^152466-5)/72472742Lelio R Paula06/2012
662320^55908-4172738Lelio R Paula01/2015
6624(73*10^72735+53)/972736Robert Price10/2015
662510^72730+22401172731Patrick De Geest05/2013
662610^72730-9972730Robert Price05/2011
66273*10^72723+6772724Robert Price11/2017
6628(11^69833+3^69833)/1472723Robert Price03/2013
6629(10^72723-79)/372723Robert Price10/2017
6630(88*10^72711-43)/972712Robert Price11/2015
66313^152379+28072704Lelio R Paula01/2015
6632(25*10^72703-241)/972704Robert Price01/2017
6633(47*10^72696+133)/972697Robert Price04/2017
663417^59077-9072692Lelio R Paula01/2015
663565^40096+5872691Lelio R Paula01/2016
6636(29*2^241446-1)/24572682Lelio R Paula01/2014
663811^69783-3840000072672Enzo Doria01/2013
66372^241409-11290372672Enzo Doria06/2014
6639(3^152287+1)/472659Paul Bourdelais04/2008
66403^152249-5672642Lelio R Paula01/2015
664110^72631+3772632Robert Price01/2011
664210^72631-881372631Patrick De Geest05/2013
6643(19*2^241254+1)/10172624Lelio R Paula08/2012
6644(9^76103+8^76103)/1772620Robert Price12/2012
66452^241220-11233772615Enzo Doria06/2014
6646(82*10^72612+449)/972613Robert Price02/2017
66472^241169-1579372600Enzo Doria04/2013
66489*10^72595+1172596Robert Kinser01/2017
6649(25*2^241048+1)/8972563Lelio R Paula08/2012
6650(22*10^72560+17)/372561Robert Price09/2015
66512^241032-2372558Lelio R Paula02/2012
665234485*10^72550+2^241004-372555Gilbert Mozzo12/2012
66532^241004-372550M. Frind & P. Underwood07/2002
665497*10^72522-372524Robert Price01/2017
6655(68*10^72516+7)/372518Robert Price03/2016
6656(78557*2^240844+1)/6372505Lelio R Paula06/2014
665767^39701-6672497Norbert Schneider11/2014
6658(185*10^72484+7)/372486Robert Price02/2017
6660(293*27^50631-1736)/1372473Curtis Bright05/2015
6659103^36005-10272473Norbert Schneider10/2016
666115^61616+8872467Lelio R Paula01/2015
666245^43831+272462Lelio R Paula05/2013
66632^240692-49238972456Paul Bourdelais03/2013
6664(646*10^72446-7)/972448Robert Price07/2016
66659*6^93083+772434Lelio R Paula10/2014
66662^240617-364572433Lelio R Paula05/2013
666711^69531-2400072410Enzo Doria12/2012
6668(22699*2^240396+1)/5572370Lelio R Paula06/2014
66696^92995+1372365Lelio R Paula01/2015
6670(11*10^72362-149)/372363Robert Price01/2017
6671(2^240381+3)/5165572358Lelio R Paula05/2012
66726^92974-5572348Lelio R Paula01/2015
66732^240295+1172337Lelio R Paula02/2012
6674(14*10^72326-53)/372327Robert Price12/2016
667515^61493-4672322Lelio R Paula01/2015
6676lucasU(46,1,43497)-lucasU(46,1,43496)72315Mike Oakes04/2009
66775*10^72302+972303Dmitry Domanov11/2010
6678(9787*2^240179-1)/26572303Lelio R Paula04/2015
667911^69419-312072293Enzo Doria12/2012
66804*10^72274-8372275Robert Price10/2017
668110^72267+3372268Robert Price01/2011
668210^72267-55394772267Patrick De Geest05/2013
668311^69389-138072262Enzo Doria12/2012
6684(16^60013-5^60013)/1172262Robert Price07/2013
66857^85507-3072262Lelio R Paula08/2014
6686(19*2^240026-1)/1572256Lelio R Paula02/2014
6687(3^151426-2)/66133772243Lelio R Paula06/2012
6688gcd(V(1296375),5*F(259275)*(F(259275)-1)+1)72227Serge Batalov04/2015
66892^239863-11226772206Enzo Doria06/2014
66902^239853-11485372203Enzo Doria05/2015
6691(4*10^72174+149)/972174Robert Price03/2017
6692(2^239671+9)/29613172143Lelio R Paula05/2012
66932^239651-11066572143Enzo Doria05/2014
6694(29*2^239650-1)/330572140Lelio R Paula01/2014
6695241^30280+30280^24172128Norbert Schneider11/2014
6696(68*10^72120-23)/972121Robert Price10/2015
6697(9^75571+8^75571)/1772112Robert Price12/2012
6698(15*2^239530-1)/17372105Lelio R Paula01/2014
66992^239513-11251972101Enzo Doria06/2014
6700(10^72097+149)/372097Serge Batalov12/2014
67012^239442-655572080Lelio R Paula05/2012
67022*5^103106+372069Lelio R Paula10/2014
67032^239402-19772068Lelio R Paula02/2012
67042^239356-11187572054Enzo Doria05/2014
6705(38*10^72050-119)/972051Robert Price11/2016
67062^239339+1501572049Lelio R Paula01/2013
6707159^32728+272048Lelio R Paula05/2013
670815^61259-3872047Lelio R Paula01/2015
670992^36683-91^3668372038Robert Price08/2015
67102^239280+5461572031Lelio R Paula05/2012
6712(47*2^239267+1)/7772027Lelio R Paula04/2015
6711(85*10^72025-1)/372027Robert Price07/2017
67132^239236-9730572018Lelio R Paula05/2012
6714144^33361-14372006Norbert Schneider11/2018
67152^239169+5971998Lelio R Paula02/2012
6717lucasU(2010,1,21796)-lucasU(2010,1,21795)71994Mike Oakes05/2009
6716(15*2^239171-1)/10630171994Lelio R Paula01/2014
6718(29^49211-1)/2871965Robert Price04/2012
6719(299*10^71963+1)/371965Robert Price11/2017
6721L(344293)71953Renaud Lifchitz09/2003
6720V(344293)71953Serge Batalov03/2015
67226*10^71951+771952Dmitry Domanov11/2010
67233^150798+4071949Lelio R Paula01/2015
67242^238961+9571935Lelio R Paula02/2012
67252^238936-40771927Yves Minet02/2012
67262^238923-2863571923Lelio R Paula05/2012
672710^71910+2511971911Patrick De Geest05/2016
672810^71910-80171910Robert Price04/2016
67292^238845-11265171900Enzo Doria06/2014
67302^238792-11124571884Enzo Doria05/2014
67316*7^85059+571884Lelio R Paula10/2014
67322^238752-11058971872Enzo Doria05/2014
673312^66581+771853Lelio R Paula07/2014
6734(7*2^238691+1)/4122971850Lelio R Paula06/2012
67354*3^150568-571840Lelio R Paula04/2014
67366^92301+6771825Lelio R Paula01/2015
67372^238568+9876533171817Jason Earls01/2009
67382^238541-11272371808Enzo Doria06/2014
67392^238529-1594971805Enzo Doria04/2013
67409*5^102721-871800Lelio R Paula10/2014
67412^238494-16571794Lelio R Paula02/2012
67422^238389-11090571763Enzo Doria05/2014
6743(145*10^71760-1)/971762Serge Batalov12/2014
67447^84913+506271760Mike Oakes02/2010
6745(F(11446)^31-F(11445)^31)/F(11444)71753Wayne Halsdorf03/2012
67462^238268-9730571726Lelio R Paula05/2012
6747gcd(V(1330365),5*F(266073)*(F(266073)-1)+1)71724Serge Batalov04/2015
67482^238235-11324771716Enzo Doria07/2014
67492*12^66450-5^6645071712Mike Oakes11/2010
6750(2^238213+lucasV(1,2,238213)+1)/471709Mike Oakes11/2016


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Created by  Henri Lifchitz & Renaud Lifchitz : October, 26 2000, last modification: February, 14 2019 10:37 (Time in France)

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