PRP Records

Probable Primes Top 10000

(277054 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 ?
7251(2^285882+2830)/286059Stefano Morozzi01/2020
72522^285836+6583586046Lelio R Paula09/2013
725321587^9670+9670^2158786034Hans Havermann08/2020
7254(2^285766+78557)/386024Lelio R Paula01/2013
7255(2^285732+2682)/286014Stefano Morozzi01/2020
7256(5*10^86011-107)/386012Robert Price01/2017
72576^110522+16386003Lelio R Paula12/2015
725841^53323-40^5332385999Robert Price07/2012
72592^285678-10961785998Enzo Doria04/2014
72606^110506-1667385991Enzo Doria02/2013
72612^285569-74185965Lelio R Paula09/2013
7262(32*10^85964+31)/985965Robert Price05/2015
7263133^40466+13285944Norbert Schneider02/2019
726423378^4743+4743^2337885939Hans Havermann08/2020
72656*10^85910-785911Dmitry Domanov11/2010
7266(412*10^85897-7)/985899Robert Price10/2017
72674*10^85881+6385882Robert Price06/2016
7268(2^285257+1514)/285871Stefano Morozzi01/2020
7269(2^285248+3738)/285868Stefano Morozzi01/2020
7270(10^85864+53)/985864Robert Price01/2015
72722^285230+34585863Lelio R Paula09/2013
727121774^8777+8777^2177485863Hans Havermann08/2020
7273(5*10^85855-473)/985855Robert Price12/2017
72742^285199+7568385854Enzo Doria04/2016
7275(76*10^85847-211)/985848Robert Price10/2017
7276p(17832)#/2+51285845Robert Price05/2017
7277(16*10^85839+167)/385840Robert Price10/2017
727811^82426-123085838Enzo Doria11/2012
7279(14727^20593-1)/1472685830Serge Batalov08/2020
72802^285113-10988185828Enzo Doria04/2014
7281(2^285033+1670)/285804Stefano Morozzi01/2020
7282(2^285033+3854)/285804Stefano Morozzi01/2020
7283(2^285035+3194)/285804Stefano Morozzi01/2020
72845^122746-9285796Lelio R Paula10/2015
72852^285001-11346185794Enzo Doria08/2014
7287(11*10^85782-131)/385783Robert Price02/2017
7286(2^284963+2778)/285783Stefano Morozzi01/2020
7288(2^284960+3570)/285782Stefano Morozzi01/2020
7289(2^284937+1706)/285775Stefano Morozzi01/2020
72902^284913-11049185768Enzo Doria05/2014
72916^110220+4785768Lelio R Paula12/2015
7292(1966^26041-1)/196585765Serge Batalov08/2020
729320698^13909+13909^2069885758Hans Havermann07/2020
72943*6^110202-585755Lelio R Paula10/2014
72959*10^85746+3785747Robert Price12/2020
7296(157^39047-1)/15685742Alexander Zhirkov06/2016
7297(3^179705+7)/25085739Lelio R Paula12/2012
7298(9127^21649-1)/912685734Serge Batalov08/2020
72992^284734-655585714Lelio R Paula09/2013
7300(10^85712+53)/985712Robert Price01/2015
73013*10^85703+1185704Robert Price11/2017
7302(6883*2^284668-1)/385697Lelio R Paula04/2015
730320728^13621+13621^2072885694Hans Havermann07/2020
730422126^7459+7459^2212685687Hans Havermann07/2020
7305(9311^21589-1)/931085683Serge Batalov08/2020
730620^65855+8385680Lelio R Paula01/2016
73076^110105+5385679Lelio R Paula12/2015
7308(10^85666-97)/385666Robert Kinser10/2017
73102^284567-760585664Lelio R Paula09/2013
73099*5^122555-285664Lelio R Paula10/2014
73115^122554-1485662Lelio R Paula10/2015
73129*5^122543+485655Lelio R Paula10/2014
73143^179489-2^(179489-1)85639Robert Price01/2016
7313(2^284487+1970)/285639Stefano Morozzi01/2020
7315(2^284477+1614)/285636Stefano Morozzi01/2020
731623693^4114+4114^2369385633Hans Havermann07/2020
731719690^19941+19941^1969085632Norbert Schneider03/2020
73182^284429+17785622Lelio R Paula08/2012
73192*3^179452+585621Lelio R Paula07/2014
732021036^11711+11711^2103685587Hans Havermann07/2020
7322(19^66919+3^66919)/2285572Robert Price07/2013
7321(2^284265+602)/285572Stefano Morozzi01/2020
732566^47023-6585561Norbert Schneider11/2014
7323(2^284226+3802)/285561Stefano Morozzi01/2020
7324(2^284228+2170)/285561Stefano Morozzi01/2020
73266^109943+1385553Lelio R Paula12/2015
73272^284183-474785548Yves Minet05/2019
7328(5637^22807-1)/563685547Serge Batalov08/2020
732920782^13071+13071^2078285546Hans Havermann08/2020
7330(2^284167-509203)/3456477585536Lelio R Paula01/2013
7331(2^284136+2262)/285534Stefano Morozzi01/2020
73322^284133-385533M. Frind & P. Underwood07/2002
73332^284113+31585527Lelio R Paula09/2013
7334(2^284098+3082)/285522Stefano Morozzi01/2020
7335(2^284070+1482)/285514Stefano Morozzi01/2020
7336(2^284068+2866)/285513Stefano Morozzi01/2020
7337(8721^21701-1)/872085511Serge Batalov08/2020
733822085^7438+7438^2208585502Hans Havermann07/2020
7339(28*10^85500+149)/385501Robert Price10/2017
7340(16*10^85495-19)/385496Robert Price03/2016
73412^284004+17785494Lelio R Paula08/2012
7342(16*10^85473-91)/385474Robert Price06/2016
734366*10^85468+785470Robert Price07/2020
73443^179120+2285462Robert Price12/2013
73452^283872-279224985454Enzo Doria03/2016
7346(4703^23269-1)/470285449Serge Batalov08/2020
7347(29*10^85438+259)/985439Robert Price04/2017
73482^283817+8287585438Lelio R Paula09/2013
7349(2^283815-5)/20185435Lelio R Paula01/2013
73502^283796-12585432Lelio R Paula08/2012
7351(10174^21319-1)/1017385432Serge Batalov08/2020
7352(29*2^283784-1)/1385428Lelio R Paula02/2014
735315^72592-2885375Lelio R Paula11/2015
73552^283604-5869585374Lelio R Paula09/2013
735421863^8034+8034^2186385374Hans Havermann08/2020
7357(44*10^85370-503)/985371Robert Price10/2017
7356(2^283597+1854)/285371Stefano Morozzi01/2020
7358496^31671+31671^49685369Norbert Schneider07/2017
7359(2^283578+478)/285366Stefano Morozzi01/2020
7360(15*2^283583-1)/10305185364Lelio R Paula02/2014
736115^72572+9285352Lelio R Paula11/2015
73622^283473-161585334Lelio R Paula09/2013
7363(2^283469+2934)/285333Stefano Morozzi01/2020
73642^283466-1585332Lelio R Paula08/2012
7365(2^283437+3446)/285323Stefano Morozzi01/2020
736619966^18761+18761^1996685320Hans Havermann07/2020
7367(2^283411+3894)/285315Stefano Morozzi01/2020
736811^81916-702085307Enzo Doria02/2013
73696^109626-785306Lelio R Paula11/2014
73702^283374-11032785305Enzo Doria05/2014
737133*10^85297+785299Robert Price07/2016
7372(6010^22573-1)/600985297Serge Batalov08/2020
73731137^27908+27908^113785281Norbert Schneider04/2020
737418^67933+4185275Lelio R Paula11/2015
73752^283271-10934185274Enzo Doria04/2014
7376(2^283266+3678)/285272Stefano Morozzi01/2020
737719688^19855-19855^1968885262Norbert Schneider03/2020
7378(2^283216+1926)/285257Stefano Morozzi01/2020
7379(25*10^85249-73)/385250Robert Price09/2016
73802*5^121959+385246Lelio R Paula10/2014
738119834^19834+894785235Henri Lifchitz11/2004
73822^283140+191585234Lelio R Paula09/2013
73833*10^85227-9785228Robert Price08/2017
7384(16*10^85221-31)/385222Robert Price03/2016
7385(2^283096+3186)/285221Stefano Morozzi01/2020
73862^283083+186938385217Enzo Doria05/2016
7387(24737*2^283051+1)/1785211Lelio R Paula06/2014
7388(2^283032+78557)/385201Lelio R Paula01/2013
73892^283026-10989385200Enzo Doria04/2014
7390(2^283012+78557)/12985193Lelio R Paula01/2013
7391(10^(2*42589+1)+72*10^42589-1)/985179Robert Price09/2017
73922^282860-10972785150Enzo Doria04/2014
7393(2^282847+13)/385145Stefano Morozzi03/2020
73942^282819+186941385138Enzo Doria05/2016
73953^178428+285132Ray Chandler07/2011
739619985^18162+18162^1998585120Hans Havermann07/2020
7397(22699*2^282742+1)/7385117Lelio R Paula06/2014
7398(16^70687+5^70687)/2185115Robert Price07/2013
7399(2^282732+738)/285111Stefano Morozzi01/2020
7400(2^282720+1590)/285107Stefano Morozzi01/2020
7401(3^178352-2)/785095Lelio R Paula12/2012
740222150^6939+6939^2215085085Hans Havermann07/2020
740311^81699-279085081Enzo Doria12/2012
74042^282612-9585075Lelio R Paula08/2012
74052^282609-406985074Yves Minet02/2018
740675^45366-285065Lelio R Paula08/2013
7407(2^282550+1918)/285056Stefano Morozzi01/2020
7408(2^282515+3786)/285046Stefano Morozzi01/2020
74092^282511+6985045Lelio R Paula08/2012
741069^46249+285045Lelio R Paula06/2013
7411(2^282488+2382)/285038Stefano Morozzi01/2020
7412(2^282489+1862)/285038Stefano Morozzi01/2020
74133^178226+1085036Robert Price10/2013
7414(2^282475+1050)/285034Stefano Morozzi01/2020
7415(182*10^85017+43)/985019Robert Price11/2017
7416(14*10^85010+73)/385011Robert Price04/2016
74179*2^282338-784994Lelio R Paula08/2014
7418(9913*2^282330-1)/157800384988Lelio R Paula04/2015
741920025^17504+17504^2002584969Hans Havermann07/2020
74202^282203+584952Lelio R Paula08/2012
74212^282184+1384946Lelio R Paula08/2012
742211^81568-240084945Enzo Doria12/2012
742311^81562-234084939Enzo Doria12/2012
7424(41*10^84927+31)/984928Robert Price05/2015
7425(3923^23629-1)/392284911Serge Batalov08/2020
7426(2^282053+1406)/284907Stefano Morozzi01/2020
7427(2*10^84904-17)/384904Robert Price08/2014
7428(4^141017+23)/384901Robert Price02/2017
74296^109100-1865384897Enzo Doria03/2013
74302^281973+102584883Lelio R Paula09/2013
74312^281951-10965184876Enzo Doria04/2014
743221618^8431+8431^2161884870Hans Havermann07/2020
743311^81491-543084865Enzo Doria01/2013
743410^84863-4000184863Robert Price01/2021
7435((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
7436(2^281827+650)/284839Stefano Morozzi01/2020
74372^281825-186148384838Enzo Doria03/2016
74382^281809-9730584833Lelio R Paula09/2013
74402^281780-11489384825Enzo Doria05/2015
7439(7654^21841-1)/765384825Serge Batalov08/2020
74413^177719+6484794Lelio R Paula12/2015
74432^281675-19984793Lelio R Paula08/2012
74422^281673-11122384793Enzo Doria05/2014
7444(4*10^84779+149)/984779Robert Price03/2017
7446129^40167-12884777Norbert Schneider01/2019
7445(2^281622+3970)/284777Stefano Morozzi01/2020
7447(72*10^84772-27)/984773Ray Chandler01/2011
744811^81398-63084768Enzo Doria11/2012
7449(25*2^281577-1)/2384764Lelio R Paula02/2014
745020320^14819+14819^2032084752Hans Havermann07/2020
74512^281500-45584740Yves Minet03/2012
745210^84725+114514191984726Marisa Kirisame03/2015
745310^84725+14204184726Patrick De Geest10/2015
745410^84725-13867784725Patrick De Geest02/2016
745576^45044+7584720Norbert Schneider02/2015
745654^48897-5384709Norbert Schneider08/2014
7457(9913*2^281377-1)/6584706Lelio R Paula04/2015
7458Phi(171124,10)/29946701/7761329021/5856034404184700Maksym Voznyy11/2015
74592^281337-11122384691Enzo Doria05/2014
74602^281308+5461584683Lelio R Paula09/2013
74617*5^121144-684677Lelio R Paula10/2014
7462(2^281270+3858)/284671Stefano Morozzi01/2020
7463(2^281252+47)/384665Lelio R Paula01/2013
746411^81297-315084663Enzo Doria12/2012
74652^281208-30384653Yves Minet02/2012
7466197^36892-284648Lelio R Paula10/2017
7467(21*2^281187+1)/248384644Lelio R Paula01/2013
746811^81247-8484611Lelio R Paula10/2015
7469(10876^20959-1)/1087584597Serge Batalov08/2020
74702067^25516+25516^206784595Norbert Schneider11/2019
747217^68747-6484590Lelio R Paula11/2015
7471(2^281002+3718)/284590Stefano Morozzi01/2020
74735^121018-1559684588Enzo Doria02/2013
74746^108702+784587Lelio R Paula11/2014
747510^84582+10067784583Patrick De Geest05/2016
747610^84582-800184582Robert Price03/2016
74771828^25929+25929^182884580Norbert Schneider12/2019
7478(2^280968+1446)/284580Stefano Morozzi01/2020
74793*5^121004-884579Lelio R Paula10/2014
74805^120996-8484573Lelio R Paula10/2015
7481(2^280896+1522)/284558Stefano Morozzi01/2020
7482(10223*2^280881+1)/6841984553Lelio R Paula06/2014
74832^280852+9768184545Yves Minet08/2004
74842^280848-120384544Lelio R Paula09/2013
74855^120946-2484538Lelio R Paula10/2015
74862^280810-211184533Yves Minet08/2013
748711^81161-516084521Enzo Doria01/2013
74882^280737-9384511Lelio R Paula08/2012
7489(2^280737+494)/284510Stefano Morozzi01/2020
7490(2^280717+1166)/284504Stefano Morozzi01/2020
74912^280698+31584499Lelio R Paula09/2013
74923^177099-34084498Lelio R Paula12/2015
7493(8201^21589-1)/820084493Serge Batalov08/2020
7494(5*10^84469-107)/384470Robert Price01/2017
7495(3^177002+7)/669602227216174484436Lelio R Paula12/2012
7496(2^280500-1017)/82384436Lelio R Paula01/2013
749724677^2640+2640^2467784435Hans Havermann07/2020
749814^73660-584424Lelio R Paula11/2015
7499(2^280405+746)/284411Stefano Morozzi01/2020
750020862^11119+11119^2086284410Hans Havermann07/2020


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Created by  Henri Lifchitz & Renaud Lifchitz : October, 26 2000, last modification: January, 25 2021 11:23 (Time in France)

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