PRP Records

Probable Primes Top 10000

(280932 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) !!!


Submit your PRPs


See the Top discoverers
See the Latest PRPs
Search by form



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 ?
7751(2^285882+2830)/286059Stefano Morozzi01/2020
77522^285836+6583586046Lelio R Paula09/2013
775321587^9670+9670^2158786034Hans Havermann08/2020
7754(2^285766+78557)/386024Lelio R Paula01/2013
7755(2^285732+2682)/286014Stefano Morozzi01/2020
7756(5*10^86011-107)/386012Robert Price01/2017
77576^110522+16386003Lelio R Paula12/2015
775841^53323-40^5332385999Robert Price07/2012
77592^285678-10961785998Enzo Doria04/2014
77606^110506-1667385991Enzo Doria02/2013
77612^285569-74185965Lelio R Paula09/2013
7762(32*10^85964+31)/985965Robert Price05/2015
7763133^40466+13285944Norbert Schneider02/2019
776423378^4743+4743^2337885939Hans Havermann08/2020
77656*10^85910-785911Dmitry Domanov11/2010
7766(412*10^85897-7)/985899Robert Price10/2017
77674*10^85881+6385882Robert Price06/2016
7768(2^285257+1514)/285871Stefano Morozzi01/2020
7769(2^285248+3738)/285868Stefano Morozzi01/2020
7770(10^85864+53)/985864Robert Price01/2015
77722^285230+34585863Lelio R Paula09/2013
777121774^8777+8777^2177485863Hans Havermann08/2020
7773(5*10^85855-473)/985855Robert Price12/2017
77742^285199+7568385854Enzo Doria04/2016
7775(76*10^85847-211)/985848Robert Price10/2017
7776p(17832)#/2+51285845Robert Price05/2017
7777(16*10^85839+167)/385840Robert Price10/2017
777811^82426-123085838Enzo Doria11/2012
7779(14727^20593-1)/1472685830Serge Batalov08/2020
77802^285113-10988185828Enzo Doria04/2014
7781(2^285033+1670)/285804Stefano Morozzi01/2020
7782(2^285033+3854)/285804Stefano Morozzi01/2020
7783(2^285035+3194)/285804Stefano Morozzi01/2020
77845^122746-9285796Lelio R Paula10/2015
77852^285001-11346185794Enzo Doria08/2014
7787(11*10^85782-131)/385783Robert Price02/2017
7786(2^284963+2778)/285783Stefano Morozzi01/2020
7788(2^284960+3570)/285782Stefano Morozzi01/2020
7789(2^284937+1706)/285775Stefano Morozzi01/2020
77902^284913-11049185768Enzo Doria05/2014
77916^110220+4785768Lelio R Paula12/2015
7792(1966^26041-1)/196585765Serge Batalov08/2020
779320698^13909+13909^2069885758Hans Havermann07/2020
77943*6^110202-585755Lelio R Paula10/2014
77959*10^85746+3785747Robert Price12/2020
7796(157^39047-1)/15685742Alexander Zhirkov06/2016
7797(3^179705+7)/25085739Lelio R Paula12/2012
7798(9127^21649-1)/912685734Serge Batalov08/2020
77992^284734-655585714Lelio R Paula09/2013
7800(10^85712+53)/985712Robert Price01/2015
78013*10^85703+1185704Robert Price11/2017
7802(6883*2^284668-1)/385697Lelio R Paula04/2015
780320728^13621+13621^2072885694Hans Havermann07/2020
780422126^7459+7459^2212685687Hans Havermann07/2020
7805(9311^21589-1)/931085683Serge Batalov08/2020
780620^65855+8385680Lelio R Paula01/2016
78076^110105+5385679Lelio R Paula12/2015
78083*10^85672-7385673Robert Price02/2021
7809(10^85666-97)/385666Robert Kinser10/2017
78112^284567-760585664Lelio R Paula09/2013
78109*5^122555-285664Lelio R Paula10/2014
78125^122554-1485662Lelio R Paula10/2015
78139*5^122543+485655Lelio R Paula10/2014
78143^179489-2^(179489-1)85639Robert Price01/2016
7815(2^284487+1970)/285639Stefano Morozzi01/2020
7816(2^284477+1614)/285636Stefano Morozzi01/2020
781723693^4114+4114^2369385633Hans Havermann07/2020
781819690^19941+19941^1969085632Norbert Schneider03/2020
78192^284429+17785622Lelio R Paula08/2012
78202*3^179452+585621Lelio R Paula07/2014
782121036^11711+11711^2103685587Hans Havermann07/2020
7823(19^66919+3^66919)/2285572Robert Price07/2013
7822(2^284265+602)/285572Stefano Morozzi01/2020
782666^47023-6585561Norbert Schneider11/2014
7824(2^284226+3802)/285561Stefano Morozzi01/2020
7825(2^284228+2170)/285561Stefano Morozzi01/2020
78276^109943+1385553Lelio R Paula12/2015
78282^284183-474785548Yves Minet05/2019
7829(5637^22807-1)/563685547Serge Batalov08/2020
783020782^13071+13071^2078285546Hans Havermann08/2020
7831(2^284167-509203)/3456477585536Lelio R Paula01/2013
7832(2^284136+2262)/285534Stefano Morozzi01/2020
78332^284133-385533M. Frind & P. Underwood07/2002
78342^284113+31585527Lelio R Paula09/2013
7835(2^284098+3082)/285522Stefano Morozzi01/2020
7836(2^284070+1482)/285514Stefano Morozzi01/2020
7837(2^284068+2866)/285513Stefano Morozzi01/2020
7838(8721^21701-1)/872085511Serge Batalov08/2020
783922085^7438+7438^2208585502Hans Havermann07/2020
7840(28*10^85500+149)/385501Robert Price10/2017
7841(16*10^85495-19)/385496Robert Price03/2016
78422^284004+17785494Lelio R Paula08/2012
7843(16*10^85473-91)/385474Robert Price06/2016
784466*10^85468+785470Robert Price07/2020
78453^179120+2285462Robert Price12/2013
78462^283872-279224985454Enzo Doria03/2016
7847(4703^23269-1)/470285449Serge Batalov08/2020
7848(29*10^85438+259)/985439Robert Price04/2017
78492^283817+8287585438Lelio R Paula09/2013
7850(2^283815-5)/20185435Lelio R Paula01/2013
78512^283796-12585432Lelio R Paula08/2012
7852(10174^21319-1)/1017385432Serge Batalov08/2020
7853(29*2^283784-1)/1385428Lelio R Paula02/2014
785415^72592-2885375Lelio R Paula11/2015
78562^283604-5869585374Lelio R Paula09/2013
785521863^8034+8034^2186385374Hans Havermann08/2020
7858(44*10^85370-503)/985371Robert Price10/2017
7857(2^283597+1854)/285371Stefano Morozzi01/2020
7859496^31671+31671^49685369Norbert Schneider07/2017
7860(2^283578+478)/285366Stefano Morozzi01/2020
7861(15*2^283583-1)/10305185364Lelio R Paula02/2014
786215^72572+9285352Lelio R Paula11/2015
78632^283473-161585334Lelio R Paula09/2013
7864(2^283469+2934)/285333Stefano Morozzi01/2020
78652^283466-1585332Lelio R Paula08/2012
7866(2^283437+3446)/285323Stefano Morozzi01/2020
786719966^18761+18761^1996685320Hans Havermann07/2020
7868(2^283411+3894)/285315Stefano Morozzi01/2020
786911^81916-702085307Enzo Doria02/2013
78706^109626-785306Lelio R Paula11/2014
78712^283374-11032785305Enzo Doria05/2014
787233*10^85297+785299Robert Price07/2016
7873(6010^22573-1)/600985297Serge Batalov08/2020
78741137^27908+27908^113785281Norbert Schneider04/2020
787518^67933+4185275Lelio R Paula11/2015
78762^283271-10934185274Enzo Doria04/2014
7877(2^283266+3678)/285272Stefano Morozzi01/2020
787819688^19855-19855^1968885262Norbert Schneider03/2020
7879(2^283216+1926)/285257Stefano Morozzi01/2020
7880(25*10^85249-73)/385250Robert Price09/2016
78812*5^121959+385246Lelio R Paula10/2014
788219834^19834+894785235Henri Lifchitz11/2004
78832^283140+191585234Lelio R Paula09/2013
78843*10^85227-9785228Robert Price08/2017
7885(16*10^85221-31)/385222Robert Price03/2016
7886(2^283096+3186)/285221Stefano Morozzi01/2020
78872^283083+186938385217Enzo Doria05/2016
7888(24737*2^283051+1)/1785211Lelio R Paula06/2014
7889(2^283032+78557)/385201Lelio R Paula01/2013
78902^283026-10989385200Enzo Doria04/2014
7891(2^283012+78557)/12985193Lelio R Paula01/2013
7892(10^(2*42589+1)+72*10^42589-1)/985179Robert Price09/2017
78932^282860-10972785150Enzo Doria04/2014
7894(2^282847+13)/385145Stefano Morozzi03/2020
78952^282819+186941385138Enzo Doria05/2016
78963^178428+285132Ray Chandler07/2011
789719985^18162+18162^1998585120Hans Havermann07/2020
7898(22699*2^282742+1)/7385117Lelio R Paula06/2014
7899(16^70687+5^70687)/2185115Robert Price07/2013
7900(2^282732+738)/285111Stefano Morozzi01/2020
7901(2^282720+1590)/285107Stefano Morozzi01/2020
7902(3^178352-2)/785095Lelio R Paula12/2012
790322150^6939+6939^2215085085Hans Havermann07/2020
790411^81699-279085081Enzo Doria12/2012
79052^282612-9585075Lelio R Paula08/2012
79062^282609-406985074Yves Minet02/2018
790775^45366-285065Lelio R Paula08/2013
7908(2^282550+1918)/285056Stefano Morozzi01/2020
7909(2^282515+3786)/285046Stefano Morozzi01/2020
79102^282511+6985045Lelio R Paula08/2012
791169^46249+285045Lelio R Paula06/2013
7912(2^282488+2382)/285038Stefano Morozzi01/2020
7913(2^282489+1862)/285038Stefano Morozzi01/2020
79143^178226+1085036Robert Price10/2013
7915(2^282475+1050)/285034Stefano Morozzi01/2020
7916(182*10^85017+43)/985019Robert Price11/2017
7917(14*10^85010+73)/385011Robert Price04/2016
79189*2^282338-784994Lelio R Paula08/2014
7919(9913*2^282330-1)/157800384988Lelio R Paula04/2015
792020025^17504+17504^2002584969Hans Havermann07/2020
79212^282203+584952Lelio R Paula08/2012
79222^282184+1384946Lelio R Paula08/2012
792311^81568-240084945Enzo Doria12/2012
792411^81562-234084939Enzo Doria12/2012
7925(41*10^84927+31)/984928Robert Price05/2015
7926(3923^23629-1)/392284911Serge Batalov08/2020
7927(2^282053+1406)/284907Stefano Morozzi01/2020
7928(2*10^84904-17)/384904Robert Price08/2014
7929(4^141017+23)/384901Robert Price02/2017
79306^109100-1865384897Enzo Doria03/2013
79312^281973+102584883Lelio R Paula09/2013
79322^281951-10965184876Enzo Doria04/2014
793321618^8431+8431^2161884870Hans Havermann07/2020
793411^81491-543084865Enzo Doria01/2013
793510^84863+14105784864Patrick De Geest02/2021
793610^84863-4000184863Robert Price01/2021
7937((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
7938(2^281827+650)/284839Stefano Morozzi01/2020
79392^281825-186148384838Enzo Doria03/2016
79402^281809-9730584833Lelio R Paula09/2013
79422^281780-11489384825Enzo Doria05/2015
7941(7654^21841-1)/765384825Serge Batalov08/2020
79433^177719+6484794Lelio R Paula12/2015
79452^281675-19984793Lelio R Paula08/2012
79442^281673-11122384793Enzo Doria05/2014
7946(4*10^84779+149)/984779Robert Price03/2017
7948129^40167-12884777Norbert Schneider01/2019
7947(2^281622+3970)/284777Stefano Morozzi01/2020
7949(72*10^84772-27)/984773Ray Chandler01/2011
795011^81398-63084768Enzo Doria11/2012
7951(25*2^281577-1)/2384764Lelio R Paula02/2014
795220320^14819+14819^2032084752Hans Havermann07/2020
79532^281500-45584740Yves Minet03/2012
795410^84725+114514191984726Marisa Kirisame03/2015
795510^84725+14204184726Patrick De Geest10/2015
795610^84725-13867784725Patrick De Geest02/2016
795776^45044+7584720Norbert Schneider02/2015
795854^48897-5384709Norbert Schneider08/2014
7959(9913*2^281377-1)/6584706Lelio R Paula04/2015
7960Phi(171124,10)/29946701/7761329021/5856034404184700Maksym Voznyy11/2015
79612^281337-11122384691Enzo Doria05/2014
79622^281308+5461584683Lelio R Paula09/2013
79637*5^121144-684677Lelio R Paula10/2014
7964(2^281270+3858)/284671Stefano Morozzi01/2020
7965(2^281252+47)/384665Lelio R Paula01/2013
796611^81297-315084663Enzo Doria12/2012
79672^281208-30384653Yves Minet02/2012
7968197^36892-284648Lelio R Paula10/2017
7969(21*2^281187+1)/248384644Lelio R Paula01/2013
797011^81247-8484611Lelio R Paula10/2015
7971(10876^20959-1)/1087584597Serge Batalov08/2020
79722067^25516+25516^206784595Norbert Schneider11/2019
797417^68747-6484590Lelio R Paula11/2015
7973(2^281002+3718)/284590Stefano Morozzi01/2020
79755^121018-1559684588Enzo Doria02/2013
79766^108702+784587Lelio R Paula11/2014
797710^84582+10067784583Patrick De Geest05/2016
797810^84582-800184582Robert Price03/2016
79791828^25929+25929^182884580Norbert Schneider12/2019
7980(2^280968+1446)/284580Stefano Morozzi01/2020
79813*5^121004-884579Lelio R Paula10/2014
79825^120996-8484573Lelio R Paula10/2015
7983(2^280896+1522)/284558Stefano Morozzi01/2020
7984(10223*2^280881+1)/6841984553Lelio R Paula06/2014
79852^280852+9768184545Yves Minet08/2004
79862^280848-120384544Lelio R Paula09/2013
79875^120946-2484538Lelio R Paula10/2015
79882^280810-211184533Yves Minet08/2013
798911^81161-516084521Enzo Doria01/2013
79902^280737-9384511Lelio R Paula08/2012
7991(2^280737+494)/284510Stefano Morozzi01/2020
7992(2^280717+1166)/284504Stefano Morozzi01/2020
79932^280698+31584499Lelio R Paula09/2013
79943^177099-34084498Lelio R Paula12/2015
7995(8201^21589-1)/820084493Serge Batalov08/2020
7996(5*10^84469-107)/384470Robert Price01/2017
7997(3^177002+7)/669602227216174484436Lelio R Paula12/2012
7998(2^280500-1017)/82384436Lelio R Paula01/2013
799924677^2640+2640^2467784435Hans Havermann07/2020
800014^73660-584424Lelio R Paula11/2015


Find by discoverer :


Created by  Henri Lifchitz & Renaud Lifchitz : October, 26 2000, last modification: April, 13 2021 12:02 (Time in France)

Go back
Valid XHTML 1.0!    Valid CSS!