PRP Records

Probable Primes Top 10000

(183432 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 ?
7751(F(142164)^3-F(142163)^3)/F(142162)59421Wayne Halsdorf03/2012
77522^197392-11462959421Enzo Doria05/2015
77532^197355-15759410Lelio R Paula04/2011
77545^84992-8459407Lelio R Paula10/2012
77552*3^124504-559404Lelio R Paula04/2014
77562^197307-1916559396Enzo Doria05/2013
77572^197303+3276959395Lelio R Paula05/2011
77582*10^59394-6959395Robert Price07/2017
7759(53*10^59389+1)/959390Serge Batalov11/2010
77606^76316-3559386Lelio R Paula10/2012
77612^197259-292959381Yves Minet09/2014
7762lucasU(46,1,35715)-lucasU(46,1,35714)59377Mike Oakes04/2009
776317^48253-659373Lelio R Paula03/2013
77642^197156-1583759350Enzo Doria04/2013
77652^197149-1848159348Enzo Doria05/2013
77662^197142-1715759346Enzo Doria05/2013
7768(F(6)^65707-F(5)^65707)/F(4)59339Wayne Halsdorf04/2010
7767(8^65707-5^65707)/359339Robert Price12/2012
7769(2*14283^14283+1)/792549797559334David Broadhurst09/2010
77702^197012-11171959307Enzo Doria05/2014
77712^196975+51359296Lelio R Paula05/2011
7772(61*10^59294+119)/959295Robert Price09/2017
77732^196960+9759291Lelio R Paula04/2011
77749^62116+8^(62116-1)59274Robert Price03/2016
77752^196900-9730559273Lelio R Paula09/2011
77765*6^76155+759261Lelio R Paula09/2014
777715^50385-1459258Wojciech Florek06/2006
7778(136777#-1)/882358147759254Donovan Johnson05/2006
7779(2^196744-3)*6-759227Gilbert Mozzo05/2016
7780(67607*2^196696+1)/359216Lelio R Paula05/2014
77812^196696-11296759212Enzo Doria06/2014
778220^45508-422359208Enzo Doria03/2013
7783gcd(Phi(325820,10),(10^16291+1)^3*(10^16291+1-10^8146)+(10^32582+10^16291)*(10^8146+1)+10^48873)59201Serge Batalov04/2015
778414^51651-8159199Lelio R Paula03/2013
77852^196650-145159198Yves Minet08/2012
77862^196636-279779959194Enzo Doria04/2016
77871111*2^196610-55559189Henri Lifchitz04/2005
77883^124041+65859183Lelio R Paula10/2012
77892^196590-11179759180Enzo Doria05/2014
7790(10^59174-13)/359174Robert Price02/2017
7791(2*10^59174-113)/359174Robert Price09/2017
7792(9179*2^196533-1)/78359164Lelio R Paula04/2015
7793379*10^59152+959155Arkadiusz Wesolowski10/2011
779413^53095+4059145Lelio R Paula03/2013
77952*F(282999)-159144Henri Lifchitz12/2009
77964*7^69984+359144Lelio R Paula09/2014
7797(5*10^59142+1)/359143Erik Branger12/2013
77982^196463+571159142Lelio R Paula10/2011
77992^196453-9730559139Lelio R Paula09/2011
7800(28*10^59135+53)/959136Serge Batalov11/2008
7801(28*10^59133+113)/359134Robert Price03/2016
78022^196434+759133Lelio R Paula04/2011
7803(8*10^59127-29)/359128Robert Price05/2016
78042^196414+25559127Lelio R Paula05/2011
78055^84586-9259124Lelio R Paula10/2012
78062^196388-1717759119Enzo Doria05/2013
78073^123890+2059111Lelio R Paula10/2012
78082^196355-102177759109Paul Bourdelais11/2012
780911^56754-141059104Enzo Doria11/2012
7810(7*2^196297-1)/120040759087Lelio R Paula01/2014
7811(16*10^59062-19)/359063Robert Price03/2016
781235^38249-122859060Enzo Doria03/2013
78135^84475-1859046Lelio R Paula10/2012
78142^196123-1770159039Enzo Doria05/2013
781512^54702-3159034Lelio R Paula03/2013
78162^196101-17559033Lelio R Paula04/2011
78172^196085+577559028Lelio R Paula05/2011
78182^196034+1171559013Lelio R Paula05/2011
78192^196018-1848559008Enzo Doria05/2013
78202^195984-216358998Yves Minet08/2013
78213^123645-1658994Lelio R Paula10/2012
782239^37078-3858994Norbert Schneider05/2014
78232^195958-1685358990Enzo Doria05/2013
78242^195930-307158981Yves Minet10/2014
78252^195924+51358980Lelio R Paula05/2011
78262^195863+15558961Lelio R Paula04/2011
7827(28*10^58956+113)/358957Robert Price03/2016
782811^56612-930058956Enzo Doria02/2013
78292^195833-1717358952Enzo Doria05/2013
7830(27*2^195833-1)/5358952Lelio R Paula01/2014
7831(13*2^195821-1)/12242558945Lelio R Paula01/2014
7832139^27504-13858942Norbert Schneider10/2015
7833(418*10^58923+23)/958925Robert Price08/2017
78343^123495+4458923Lelio R Paula10/2012
78352^195737-1856558923Enzo Doria05/2013
783614^51407+4758920Lelio R Paula03/2013
78372^195691-9958909Lelio R Paula04/2011
78382^195667-185982758902Enzo Doria04/2016
78392^195642+7549958895Enzo Doria04/2016
78408*6^75678+558890Lelio R Paula09/2014
78422^195618+7318958887Enzo Doria04/2016
7841(3928^20480+1)/(3928^4096+1)58887Serge Batalov01/2017
7843t(197953)58881Robert Price12/2014
78442^195581-1610558876Enzo Doria04/2013
7845(8*10^58872+67)/358873Robert Price01/2017
78467*2^195542-558865Lelio R Paula03/2014
78472*10^58861+9^5886158862Mike Oakes04/2011
784811^56513-162058853Enzo Doria11/2012
78492^195496+16558851Lelio R Paula04/2011
78505^84187+6658845Lelio R Paula10/2012
7851(28*10^58843-43)/358844Robert Price04/2016
78522^195462-1756558840Enzo Doria05/2013
78532^195435+5927358832Yves Minet01/2011
78542^195424-1860558829Enzo Doria05/2013
78552^195385-11158817Lelio R Paula04/2011
78567*10^58815-8358816Robert Price09/2017
7857(47*2^195254+1)/26882158774Lelio R Paula03/2015
78582^195207-1810958764Enzo Doria05/2013
78592^195199-156758761Yves Minet08/2012
78602^195190+7375958759Enzo Doria04/2016
78619*7^69525-458757Lelio R Paula09/2014
78622^195170-1804558753Enzo Doria05/2013
78632^195166-16558751Lelio R Paula04/2011
7864(22699*2^195140+1)/17558746Lelio R Paula05/2014
78657*3^123109-258739Lelio R Paula04/2014
786618^46790+7758735Lelio R Paula03/2013
78682^195095-33729758730Gary Barnes09/2009
7867(14*10^58729+31)/958730Robert Price02/2015
786999^29424+9858720Norbert Schneider07/2013
7870(15185*2^195039-1)/21958715Lelio R Paula04/2015
78712^195001-6958702Lelio R Paula04/2011
78722^194978-48781158695Gary Barnes09/2009
7873163^26530+26530^16358690Serge Batalov05/2014
78742^194940-194940+158683Robert Price10/2014
7875(76*10^58669+41)/958670Robert Price10/2015
787614^51186+8758666Lelio R Paula03/2013
78772^194878-9730558665Lelio R Paula09/2011
78785^83927-1813658663Enzo Doria05/2014
7879(24737*2^194865+1)/108558662Lelio R Paula06/2014
78807^69411+4058660Lelio R Paula10/2012
78816^75382-7958659Lelio R Paula10/2012
78822^194854+2758657Lelio R Paula04/2011
78832^194801+2983558641Lelio R Paula10/2012
78842^194752+19558627Lelio R Paula04/2011
78857^69371-6^6937158626Predrag Minovic08/2004
78862^194747-11251958625Enzo Doria06/2014
7887(15*2^194737+1)/5958622Lelio R Paula07/2012
7888(23*2^194700+1)/358612Lelio R Paula02/2012
788910^58608+5527358609Patrick De Geest07/2017
789010^58608-80000158608Robert Price06/2017
789110^58608-6011958608Patrick De Geest07/2017
78925^83836+7658599Lelio R Paula10/2012
789318^46664+3158577Lelio R Paula03/2013
7894(34*10^58577-7)/9/19/46358574Makoto Morimoto04/2016
78952^194574+16558573Lelio R Paula04/2011
78982^194569-1221158572Enzo Doria06/2014
789610^58571+5^58571+2^5857158572Robert Price12/2016
789710^58571+20283758572Patrick De Geest02/2017
7899(10^58571+41)/358571Robert Price01/2017
790010^58571-34362958571Patrick De Geest02/2017
7901(43*10^58563-403)/958564Robert Price04/2017
790211^56235-795058563Enzo Doria02/2013
79032^194479-11323958545Enzo Doria07/2014
79042^194455-11224958537Enzo Doria06/2014
79052^194405-11191958522Enzo Doria05/2014
7906(4*10^58521-19)/358522Robert Price06/2017
7908(7^69247-4^69247)/358521Robert Price06/2012
79075*7^69246+858521Lelio R Paula09/2014
79092^194358-116758508Lelio R Paula05/2011
7910(2^194366+7)/137358507Lelio R Paula02/2012
7911(493*10^58486-7)/958488Robert Price07/2016
79123^122579-34058486Lelio R Paula10/2012
7913(11*10^58458-149)/358459Robert Price01/2017
7914(47*10^58456+133)/958457Robert Price04/2017
79152^194186+8558456Lelio R Paula04/2011
79163^122506-2^(122506-1)58451Robert Price01/2016
7917(74^31267-1)/7358444Paul Bourdelais08/2017
7918177^25998-258443Lelio R Paula10/2017
791915^49690-2658440Lelio R Paula03/2013
792010^58437+11072158438Patrick De Geest12/2012
792110^58437-1158437Robert Price05/2011
79222^194095+6958429Lelio R Paula04/2011
7923(29*10^58417-77)/358418Robert Price01/2017
79242^194034+17758411Lelio R Paula04/2011
7925789^20158+20158^78958400Norbert Schneider06/2016
792614^50949+7558395Lelio R Paula03/2013
79272^193974-11476158392Enzo Doria05/2015
79282^193965+558390Henri Lifchitz12/2002
7929(5*10^58384-29)/358385Robert Price02/2017
79303^122360+8058381Lelio R Paula10/2012
793110103^14577-11458373Enzo Doria07/2012
7932(22699*2^193883+1)/2158368Lelio R Paula06/2014
7933(31*2^193886+1)/14076558362Lelio R Paula07/2012
793411^56041-156058361Enzo Doria11/2012
7935(2^193881+9)/1769958360Lelio R Paula02/2012
79363^122313+5858359Lelio R Paula10/2012
79376^74996-11958359Lelio R Paula10/2012
7938(11*2^193859+1)/1358358Lelio R Paula07/2012
79392^193861-11225558358Enzo Doria06/2014
7940(22699*2^193854+1)/492758357Lelio R Paula06/2014
794118^46487+3758354Lelio R Paula03/2013
794217^47419+5458347Lelio R Paula03/2013
7943(31*2^193791+1)/358338Lelio R Paula02/2012
7944(27*2^193805-1)/98224958337Lelio R Paula01/2014
79453^122219-2^12221958314Mike Oakes09/2003
7946(199*10^58306+11)/358308Robert Price05/2017
79472^193674-1882558302Lelio R Paula05/2011
79485*10^58275+358276Dmitry Domanov11/2010
79492^193578-11291358273Enzo Doria06/2014
79502^193541+129958262Lelio R Paula05/2011
795110^58250+9358251Robert Price01/2011
795210^58250-17560758250Patrick De Geest12/2012
79532^193492+841558247Lelio R Paula10/2012
79542^193444+15758233Lelio R Paula04/2011
7955Phi(28754,28754)58231Henri Lifchitz08/2013
79562^193430-11188158229Enzo Doria05/2014
795710^58225+12457958226Patrick De Geest12/2012
795810^58225-9358225Robert Price05/2011
79592^193375-29558212Yves Minet05/2013
79602^193345+7726758203Enzo Doria05/2016
796121^44017-20^4401758201Robert Price05/2012
7962(17*2^193329-1)/958199Lelio R Paula01/2014
796317^47291+2058190Lelio R Paula03/2013
7964p(12528)#/2-12858170Robert Price05/2017
79652^193214-13558164Lelio R Paula04/2011
796619^45483-8058162Lelio R Paula03/2013
7967(4*10^58155+83)/358156Robert Price01/2017
796814^50739-1358154Lelio R Paula03/2013
7969(1017*2^193184-1)/482358154Lelio R Paula04/2015
7970(2*10^58151+457)/958151Robert Price01/2017
7971(9179*2^193183-1)/399926787958149Lelio R Paula04/2015
7972(19*2^193114-1)/118675558129Lelio R Paula01/2014
79742^193091-123758127Yves Minet08/2012
79739*7^68780-258127Lelio R Paula09/2014
79752^193083-86968810558124Lelio R Paula10/2012
79762^193058-4558117Lelio R Paula04/2011
7977(14016^14016+14017^14017)/(23*7103*19913)58115David Broadhurst09/2009
797811^55795-4258105Lelio R Paula03/2013
79793^121779-1658104Lelio R Paula10/2012
7980(13*10^58103+191)/358104Robert Price08/2017
79812^192986+19558095Lelio R Paula04/2011
79827^68740+2*3^6874058093Mike Oakes07/2010
7983(85*10^58091-1)/358093Robert Price07/2017
798412^53821+1158083Lelio R Paula02/2013
7985119^27979-11858072Norbert Schneider10/2013
7986(10223*2^192828+1)/24358049Lelio R Paula05/2014
79872^192808-112758041Yves Minet05/2013
7988(27*2^192803+1)/982758037Lelio R Paula07/2012
7989(2^192781+lucasV(1,2,192781)+1)/458033Mike Oakes11/2016
79902^192678+7294358002Enzo Doria04/2016
7991(13*10^57997-37)/357998Robert Price08/2017
79922^192657-318957996Yves Minet10/2014
79936^74525-14957992Lelio R Paula10/2012
799442^35723-4157988Norbert Schneider06/2014
7995(29*2^192625-1)/18357986Lelio R Paula01/2014
7996(3^121520-8)/384757977Lelio R Paula03/2012
7997(2^192596-5)/13957976Lelio R Paula02/2012
799810^57975+6783357976Patrick De Geest09/2013
799910^57975-4769357975Patrick De Geest09/2013
8000(F(7707)^37-F(7706)^37)/F(7705)57972Wayne Halsdorf03/2012


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Created by  Henri Lifchitz & Renaud Lifchitz : October, 26 2000, last modification: October, 17 2017 09:44 (Time in France)

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