PRP Records

Probable Primes Top 10000

(271019 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 ?
675125*29^59147+2093686498Curtis Bright05/2015
67522^287298+187135986486Enzo Doria05/2016
6753118^41740-11786481Norbert Schneider08/2018
67543*10^86478+8986479Robert Price03/2017
67552^287272-7904986478Paul Bourdelais02/2012
6756(2^287259+2846)/286474Stefano Morozzi01/2020
6757906705*2*((10^86453-1)/9)+186459Danilo Nitsche01/2016
6758811824*2*((10^86453-1)/9)+186459Danilo Nitsche01/2016
6759779064*2*((10^86453-1)/9)+186459Danilo Nitsche01/2016
6760768385*2*((10^86453-1)/9)+186459Danilo Nitsche01/2016
6761700891*2*((10^86453-1)/9)+186459Danilo Nitsche01/2016
6762652320*2*((10^86453-1)/9)+186459Danilo Nitsche01/2016
6763377920*2*((10^86453-1)/9)+186458Danilo Nitsche01/2016
6764255060*2*((10^86453-1)/9)+186458Danilo Nitsche01/2016
6765187111*2*((10^86453-1)/9)+186458Danilo Nitsche01/2016
6766(10^86453-1)/986453Lew Baxter10/2000
6767(2^287172+658)/286448Stefano Morozzi01/2020
6768(2^287146+2542)/286440Stefano Morozzi01/2020
6769(2^287136+1726)/286437Stefano Morozzi01/2020
6770(2^287128+958)/286434Stefano Morozzi01/2020
677187^44563-86^4456386431Robert Price05/2015
67726^111057+6186420Lelio R Paula12/2015
67732^287057-10990986413Enzo Doria04/2014
67745^123608+2286399Lelio R Paula10/2015
6775(2^286970+618)/286387Stefano Morozzi01/2020
6776(2^286916+2646)/286371Stefano Morozzi01/2020
6777(2^286907+3690)/286368Stefano Morozzi01/2020
6778(31*10^86364-121)/986365Robert Price06/2016
6779(2^286868+2686)/286356Stefano Morozzi01/2020
67802^286859+7166386354Enzo Doria04/2016
6781(2^286845+1866)/286349Stefano Morozzi01/2020
67822^286740+2983586318Lelio R Paula10/2013
67832*10^86310+9^8631086311Mike Oakes05/2011
678411^82878-186086309Enzo Doria12/2012
67852223^25780+25780^222386285Norbert Schneider12/2019
67862^286547+1609586260Lelio R Paula10/2013
6787(58*10^86242+329)/986243Robert Price11/2017
67882^286455-11042786232Enzo Doria05/2014
6789(37*10^86230+53)/986231Robert Price05/2015
67908*3^180700+586217Lelio R Paula08/2014
67913^180697-4086215Lelio R Paula12/2015
6792(2^286383+3386)/286210Stefano Morozzi01/2020
6793(13*2^286318-1)/1325786188Lelio R Paula02/2014
6794(2^286295+1934)/286184Stefano Morozzi01/2020
6795(2^286251+3974)/286170Stefano Morozzi01/2020
67962^286165+7786145Lelio R Paula08/2012
67979*2^286140+786138Lelio R Paula08/2014
6798(2^286128+1762)/286133Stefano Morozzi01/2020
6799(29*2^286108-1)/200236786123Lelio R Paula02/2014
6800(2^286077+1122)/286118Stefano Morozzi01/2020
680110^86110+16111386111Patrick De Geest07/2013
680210^86110-6986110Robert Price05/2011
68032^286036-86968810586106Lelio R Paula07/2016
6804(2^285946+2358)/286079Stefano Morozzi01/2020
6806(77*10^86072+31)/986073Robert Price10/2015
6805(2^285926+3382)/286073Stefano Morozzi01/2020
68072^285923+34586072Lelio R Paula09/2013
680813^77266-9086070Lelio R Paula11/2015
68092^285910-45890386068Enzo Doria04/2015
68102^285904-12586066Lelio R Paula08/2012
6811(2^285882+2830)/286059Stefano Morozzi01/2020
68122^285836+6583586046Lelio R Paula09/2013
681321587^9670+9670^2158786034Hans Havermann08/2020
6814(2^285766+78557)/386024Lelio R Paula01/2013
6815(2^285732+2682)/286014Stefano Morozzi01/2020
6816(5*10^86011-107)/386012Robert Price01/2017
68176^110522+16386003Lelio R Paula12/2015
681841^53323-40^5332385999Robert Price07/2012
68192^285678-10961785998Enzo Doria04/2014
68206^110506-1667385991Enzo Doria02/2013
68212^285569-74185965Lelio R Paula09/2013
6822(32*10^85964+31)/985965Robert Price05/2015
6823133^40466+13285944Norbert Schneider02/2019
682423378^4743+4743^2337885939Hans Havermann08/2020
68256*10^85910-785911Dmitry Domanov11/2010
6826(412*10^85897-7)/985899Robert Price10/2017
68274*10^85881+6385882Robert Price06/2016
6828(2^285257+1514)/285871Stefano Morozzi01/2020
6829(2^285248+3738)/285868Stefano Morozzi01/2020
6830(10^85864+53)/985864Robert Price01/2015
68322^285230+34585863Lelio R Paula09/2013
683121774^8777+8777^2177485863Hans Havermann08/2020
6833(5*10^85855-473)/985855Robert Price12/2017
68342^285199+7568385854Enzo Doria04/2016
6835(76*10^85847-211)/985848Robert Price10/2017
6836p(17832)#/2+51285845Robert Price05/2017
6837(16*10^85839+167)/385840Robert Price10/2017
683811^82426-123085838Enzo Doria11/2012
6839(14727^20593-1)/1472685830Serge Batalov08/2020
68402^285113-10988185828Enzo Doria04/2014
6841(2^285033+1670)/285804Stefano Morozzi01/2020
6842(2^285033+3854)/285804Stefano Morozzi01/2020
6843(2^285035+3194)/285804Stefano Morozzi01/2020
68445^122746-9285796Lelio R Paula10/2015
68452^285001-11346185794Enzo Doria08/2014
6847(11*10^85782-131)/385783Robert Price02/2017
6846(2^284963+2778)/285783Stefano Morozzi01/2020
6848(2^284960+3570)/285782Stefano Morozzi01/2020
6849(2^284937+1706)/285775Stefano Morozzi01/2020
68502^284913-11049185768Enzo Doria05/2014
68516^110220+4785768Lelio R Paula12/2015
6852(1966^26041-1)/196585765Serge Batalov08/2020
685320698^13909+13909^2069885758Hans Havermann07/2020
68543*6^110202-585755Lelio R Paula10/2014
6855(157^39047-1)/15685742Alexander Zhirkov06/2016
6856(3^179705+7)/25085739Lelio R Paula12/2012
6857(9127^21649-1)/912685734Serge Batalov08/2020
68582^284734-655585714Lelio R Paula09/2013
6859(10^85712+53)/985712Robert Price01/2015
68603*10^85703+1185704Robert Price11/2017
6861(6883*2^284668-1)/385697Lelio R Paula04/2015
686220728^13621+13621^2072885694Hans Havermann07/2020
686322126^7459+7459^2212685687Hans Havermann07/2020
6864(9311^21589-1)/931085683Serge Batalov08/2020
686520^65855+8385680Lelio R Paula01/2016
68666^110105+5385679Lelio R Paula12/2015
6867(10^85666-97)/385666Robert Kinser10/2017
68692^284567-760585664Lelio R Paula09/2013
68689*5^122555-285664Lelio R Paula10/2014
68705^122554-1485662Lelio R Paula10/2015
68719*5^122543+485655Lelio R Paula10/2014
68723^179489-2^(179489-1)85639Robert Price01/2016
6873(2^284487+1970)/285639Stefano Morozzi01/2020
6874(2^284477+1614)/285636Stefano Morozzi01/2020
687523693^4114+4114^2369385633Hans Havermann07/2020
687619690^19941+19941^1969085632Norbert Schneider03/2020
68772^284429+17785622Lelio R Paula08/2012
68782*3^179452+585621Lelio R Paula07/2014
687921036^11711+11711^2103685587Hans Havermann07/2020
6881(19^66919+3^66919)/2285572Robert Price07/2013
6880(2^284265+602)/285572Stefano Morozzi01/2020
688466^47023-6585561Norbert Schneider11/2014
6882(2^284226+3802)/285561Stefano Morozzi01/2020
6883(2^284228+2170)/285561Stefano Morozzi01/2020
68856^109943+1385553Lelio R Paula12/2015
68862^284183-474785548Yves Minet05/2019
6887(5637^22807-1)/563685547Serge Batalov08/2020
688820782^13071+13071^2078285546Hans Havermann08/2020
6889(2^284167-509203)/3456477585536Lelio R Paula01/2013
6890(2^284136+2262)/285534Stefano Morozzi01/2020
68912^284133-385533M. Frind & P. Underwood07/2002
68922^284113+31585527Lelio R Paula09/2013
6893(2^284098+3082)/285522Stefano Morozzi01/2020
6894(2^284070+1482)/285514Stefano Morozzi01/2020
6895(2^284068+2866)/285513Stefano Morozzi01/2020
6896(8721^21701-1)/872085511Serge Batalov08/2020
689722085^7438+7438^2208585502Hans Havermann07/2020
6898(28*10^85500+149)/385501Robert Price10/2017
6899(16*10^85495-19)/385496Robert Price03/2016
69002^284004+17785494Lelio R Paula08/2012
6901(16*10^85473-91)/385474Robert Price06/2016
690266*10^85468+785470Robert Price07/2020
69033^179120+2285462Robert Price12/2013
69042^283872-279224985454Enzo Doria03/2016
6905(4703^23269-1)/470285449Serge Batalov08/2020
6906(29*10^85438+259)/985439Robert Price04/2017
69072^283817+8287585438Lelio R Paula09/2013
6908(2^283815-5)/20185435Lelio R Paula01/2013
69092^283796-12585432Lelio R Paula08/2012
6910(10174^21319-1)/1017385432Serge Batalov08/2020
6911(29*2^283784-1)/1385428Lelio R Paula02/2014
691215^72592-2885375Lelio R Paula11/2015
69142^283604-5869585374Lelio R Paula09/2013
691321863^8034+8034^2186385374Hans Havermann08/2020
6916(44*10^85370-503)/985371Robert Price10/2017
6915(2^283597+1854)/285371Stefano Morozzi01/2020
6917496^31671+31671^49685369Norbert Schneider07/2017
6918(2^283578+478)/285366Stefano Morozzi01/2020
6919(15*2^283583-1)/10305185364Lelio R Paula02/2014
692015^72572+9285352Lelio R Paula11/2015
69212^283473-161585334Lelio R Paula09/2013
6922(2^283469+2934)/285333Stefano Morozzi01/2020
69232^283466-1585332Lelio R Paula08/2012
6924(2^283437+3446)/285323Stefano Morozzi01/2020
692519966^18761+18761^1996685320Hans Havermann07/2020
6926(2^283411+3894)/285315Stefano Morozzi01/2020
692711^81916-702085307Enzo Doria02/2013
69286^109626-785306Lelio R Paula11/2014
69292^283374-11032785305Enzo Doria05/2014
693033*10^85297+785299Robert Price07/2016
6931(6010^22573-1)/600985297Serge Batalov08/2020
69321137^27908+27908^113785281Norbert Schneider04/2020
693318^67933+4185275Lelio R Paula11/2015
69342^283271-10934185274Enzo Doria04/2014
6935(2^283266+3678)/285272Stefano Morozzi01/2020
693619688^19855-19855^1968885262Norbert Schneider03/2020
6937(2^283216+1926)/285257Stefano Morozzi01/2020
6938(25*10^85249-73)/385250Robert Price09/2016
69392*5^121959+385246Lelio R Paula10/2014
694019834^19834+894785235Henri Lifchitz11/2004
69412^283140+191585234Lelio R Paula09/2013
69423*10^85227-9785228Robert Price08/2017
6943(16*10^85221-31)/385222Robert Price03/2016
6944(2^283096+3186)/285221Stefano Morozzi01/2020
69452^283083+186938385217Enzo Doria05/2016
6946(24737*2^283051+1)/1785211Lelio R Paula06/2014
6947(2^283032+78557)/385201Lelio R Paula01/2013
69482^283026-10989385200Enzo Doria04/2014
6949(2^283012+78557)/12985193Lelio R Paula01/2013
6950(10^(2*42589+1)+72*10^42589-1)/985179Robert Price09/2017
69512^282860-10972785150Enzo Doria04/2014
6952(2^282847+13)/385145Stefano Morozzi03/2020
69532^282819+186941385138Enzo Doria05/2016
69543^178428+285132Ray Chandler07/2011
695519985^18162+18162^1998585120Hans Havermann07/2020
6956(22699*2^282742+1)/7385117Lelio R Paula06/2014
6957(16^70687+5^70687)/2185115Robert Price07/2013
6958(2^282732+738)/285111Stefano Morozzi01/2020
6959(2^282720+1590)/285107Stefano Morozzi01/2020
6960(3^178352-2)/785095Lelio R Paula12/2012
696122150^6939+6939^2215085085Hans Havermann07/2020
696211^81699-279085081Enzo Doria12/2012
69632^282612-9585075Lelio R Paula08/2012
69642^282609-406985074Yves Minet02/2018
696575^45366-285065Lelio R Paula08/2013
6966(2^282550+1918)/285056Stefano Morozzi01/2020
6967(2^282515+3786)/285046Stefano Morozzi01/2020
69682^282511+6985045Lelio R Paula08/2012
696969^46249+285045Lelio R Paula06/2013
6970(2^282488+2382)/285038Stefano Morozzi01/2020
6971(2^282489+1862)/285038Stefano Morozzi01/2020
69723^178226+1085036Robert Price10/2013
6973(2^282475+1050)/285034Stefano Morozzi01/2020
6974(182*10^85017+43)/985019Robert Price11/2017
6975(14*10^85010+73)/385011Robert Price04/2016
69769*2^282338-784994Lelio R Paula08/2014
6977(9913*2^282330-1)/157800384988Lelio R Paula04/2015
697820025^17504+17504^2002584969Hans Havermann07/2020
69792^282203+584952Lelio R Paula08/2012
69802^282184+1384946Lelio R Paula08/2012
698111^81568-240084945Enzo Doria12/2012
698211^81562-234084939Enzo Doria12/2012
6983(41*10^84927+31)/984928Robert Price05/2015
6984(3923^23629-1)/392284911Serge Batalov08/2020
6985(2^282053+1406)/284907Stefano Morozzi01/2020
6986(2*10^84904-17)/384904Robert Price08/2014
6987(4^141017+23)/384901Robert Price02/2017
69886^109100-1865384897Enzo Doria03/2013
69892^281973+102584883Lelio R Paula09/2013
69902^281951-10965184876Enzo Doria04/2014
699121618^8431+8431^2161884870Hans Havermann07/2020
699211^81491-543084865Enzo Doria01/2013
6993((1+sqrt(3)+sqrt(2))^79357-1)*((1+sqrt(3)-sqrt(2))^79357-1)*((1-sqrt(3)+sqrt(2))^79357-1)*((1-sqrt(384849Mike Oakes04/2009
6994(2^281827+650)/284839Stefano Morozzi01/2020
69952^281825-186148384838Enzo Doria03/2016
69962^281809-9730584833Lelio R Paula09/2013
69982^281780-11489384825Enzo Doria05/2015
6997(7654^21841-1)/765384825Serge Batalov08/2020
69993^177719+6484794Lelio R Paula12/2015
70002^281673-11122384793Enzo Doria05/2014


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Created by  Henri Lifchitz & Renaud Lifchitz : October, 26 2000, last modification: September, 29 2020 15:45 (Time in France)

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