PRP Records

Probable Primes Top 10000

(277034 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(2^285257+1514)/285871Stefano Morozzi01/2020
7252(2^285248+3738)/285868Stefano Morozzi01/2020
7253(10^85864+53)/985864Robert Price01/2015
72552^285230+34585863Lelio R Paula09/2013
725421774^8777+8777^2177485863Hans Havermann08/2020
7256(5*10^85855-473)/985855Robert Price12/2017
72572^285199+7568385854Enzo Doria04/2016
7258(76*10^85847-211)/985848Robert Price10/2017
7259p(17832)#/2+51285845Robert Price05/2017
7260(16*10^85839+167)/385840Robert Price10/2017
726111^82426-123085838Enzo Doria11/2012
7262(14727^20593-1)/1472685830Serge Batalov08/2020
72632^285113-10988185828Enzo Doria04/2014
7264(2^285033+1670)/285804Stefano Morozzi01/2020
7265(2^285033+3854)/285804Stefano Morozzi01/2020
7266(2^285035+3194)/285804Stefano Morozzi01/2020
72675^122746-9285796Lelio R Paula10/2015
72682^285001-11346185794Enzo Doria08/2014
7270(11*10^85782-131)/385783Robert Price02/2017
7269(2^284963+2778)/285783Stefano Morozzi01/2020
7271(2^284960+3570)/285782Stefano Morozzi01/2020
7272(2^284937+1706)/285775Stefano Morozzi01/2020
72732^284913-11049185768Enzo Doria05/2014
72746^110220+4785768Lelio R Paula12/2015
7275(1966^26041-1)/196585765Serge Batalov08/2020
727620698^13909+13909^2069885758Hans Havermann07/2020
72773*6^110202-585755Lelio R Paula10/2014
72789*10^85746+3785747Robert Price12/2020
7279(157^39047-1)/15685742Alexander Zhirkov06/2016
7280(3^179705+7)/25085739Lelio R Paula12/2012
7281(9127^21649-1)/912685734Serge Batalov08/2020
72822^284734-655585714Lelio R Paula09/2013
7283(10^85712+53)/985712Robert Price01/2015
72843*10^85703+1185704Robert Price11/2017
7285(6883*2^284668-1)/385697Lelio R Paula04/2015
728620728^13621+13621^2072885694Hans Havermann07/2020
728722126^7459+7459^2212685687Hans Havermann07/2020
7288(9311^21589-1)/931085683Serge Batalov08/2020
728920^65855+8385680Lelio R Paula01/2016
72906^110105+5385679Lelio R Paula12/2015
7291(10^85666-97)/385666Robert Kinser10/2017
72932^284567-760585664Lelio R Paula09/2013
72929*5^122555-285664Lelio R Paula10/2014
72945^122554-1485662Lelio R Paula10/2015
72959*5^122543+485655Lelio R Paula10/2014
72973^179489-2^(179489-1)85639Robert Price01/2016
7296(2^284487+1970)/285639Stefano Morozzi01/2020
7298(2^284477+1614)/285636Stefano Morozzi01/2020
729923693^4114+4114^2369385633Hans Havermann07/2020
730019690^19941+19941^1969085632Norbert Schneider03/2020
73012^284429+17785622Lelio R Paula08/2012
73022*3^179452+585621Lelio R Paula07/2014
730321036^11711+11711^2103685587Hans Havermann07/2020
7305(19^66919+3^66919)/2285572Robert Price07/2013
7304(2^284265+602)/285572Stefano Morozzi01/2020
730866^47023-6585561Norbert Schneider11/2014
7306(2^284226+3802)/285561Stefano Morozzi01/2020
7307(2^284228+2170)/285561Stefano Morozzi01/2020
73096^109943+1385553Lelio R Paula12/2015
73102^284183-474785548Yves Minet05/2019
7311(5637^22807-1)/563685547Serge Batalov08/2020
731220782^13071+13071^2078285546Hans Havermann08/2020
7313(2^284167-509203)/3456477585536Lelio R Paula01/2013
7314(2^284136+2262)/285534Stefano Morozzi01/2020
73152^284133-385533M. Frind & P. Underwood07/2002
73162^284113+31585527Lelio R Paula09/2013
7317(2^284098+3082)/285522Stefano Morozzi01/2020
7318(2^284070+1482)/285514Stefano Morozzi01/2020
7319(2^284068+2866)/285513Stefano Morozzi01/2020
7320(8721^21701-1)/872085511Serge Batalov08/2020
732122085^7438+7438^2208585502Hans Havermann07/2020
7322(28*10^85500+149)/385501Robert Price10/2017
7323(16*10^85495-19)/385496Robert Price03/2016
73242^284004+17785494Lelio R Paula08/2012
7325(16*10^85473-91)/385474Robert Price06/2016
732666*10^85468+785470Robert Price07/2020
73273^179120+2285462Robert Price12/2013
73282^283872-279224985454Enzo Doria03/2016
7329(4703^23269-1)/470285449Serge Batalov08/2020
7330(29*10^85438+259)/985439Robert Price04/2017
73312^283817+8287585438Lelio R Paula09/2013
7332(2^283815-5)/20185435Lelio R Paula01/2013
73332^283796-12585432Lelio R Paula08/2012
7334(10174^21319-1)/1017385432Serge Batalov08/2020
7335(29*2^283784-1)/1385428Lelio R Paula02/2014
733615^72592-2885375Lelio R Paula11/2015
73382^283604-5869585374Lelio R Paula09/2013
733721863^8034+8034^2186385374Hans Havermann08/2020
7340(44*10^85370-503)/985371Robert Price10/2017
7339(2^283597+1854)/285371Stefano Morozzi01/2020
7341496^31671+31671^49685369Norbert Schneider07/2017
7342(2^283578+478)/285366Stefano Morozzi01/2020
7343(15*2^283583-1)/10305185364Lelio R Paula02/2014
734415^72572+9285352Lelio R Paula11/2015
73452^283473-161585334Lelio R Paula09/2013
7346(2^283469+2934)/285333Stefano Morozzi01/2020
73472^283466-1585332Lelio R Paula08/2012
7348(2^283437+3446)/285323Stefano Morozzi01/2020
734919966^18761+18761^1996685320Hans Havermann07/2020
7350(2^283411+3894)/285315Stefano Morozzi01/2020
735111^81916-702085307Enzo Doria02/2013
73526^109626-785306Lelio R Paula11/2014
73532^283374-11032785305Enzo Doria05/2014
735433*10^85297+785299Robert Price07/2016
7355(6010^22573-1)/600985297Serge Batalov08/2020
73561137^27908+27908^113785281Norbert Schneider04/2020
735718^67933+4185275Lelio R Paula11/2015
73582^283271-10934185274Enzo Doria04/2014
7359(2^283266+3678)/285272Stefano Morozzi01/2020
736019688^19855-19855^1968885262Norbert Schneider03/2020
7361(2^283216+1926)/285257Stefano Morozzi01/2020
7362(25*10^85249-73)/385250Robert Price09/2016
73632*5^121959+385246Lelio R Paula10/2014
736419834^19834+894785235Henri Lifchitz11/2004
73652^283140+191585234Lelio R Paula09/2013
73663*10^85227-9785228Robert Price08/2017
7367(16*10^85221-31)/385222Robert Price03/2016
7368(2^283096+3186)/285221Stefano Morozzi01/2020
73692^283083+186938385217Enzo Doria05/2016
7370(24737*2^283051+1)/1785211Lelio R Paula06/2014
7371(2^283032+78557)/385201Lelio R Paula01/2013
73722^283026-10989385200Enzo Doria04/2014
7373(2^283012+78557)/12985193Lelio R Paula01/2013
7374(10^(2*42589+1)+72*10^42589-1)/985179Robert Price09/2017
73752^282860-10972785150Enzo Doria04/2014
7376(2^282847+13)/385145Stefano Morozzi03/2020
73772^282819+186941385138Enzo Doria05/2016
73783^178428+285132Ray Chandler07/2011
737919985^18162+18162^1998585120Hans Havermann07/2020
7380(22699*2^282742+1)/7385117Lelio R Paula06/2014
7381(16^70687+5^70687)/2185115Robert Price07/2013
7382(2^282732+738)/285111Stefano Morozzi01/2020
7383(2^282720+1590)/285107Stefano Morozzi01/2020
7384(3^178352-2)/785095Lelio R Paula12/2012
738522150^6939+6939^2215085085Hans Havermann07/2020
738611^81699-279085081Enzo Doria12/2012
73872^282612-9585075Lelio R Paula08/2012
73882^282609-406985074Yves Minet02/2018
738975^45366-285065Lelio R Paula08/2013
7390(2^282550+1918)/285056Stefano Morozzi01/2020
7391(2^282515+3786)/285046Stefano Morozzi01/2020
73922^282511+6985045Lelio R Paula08/2012
739369^46249+285045Lelio R Paula06/2013
7394(2^282488+2382)/285038Stefano Morozzi01/2020
7395(2^282489+1862)/285038Stefano Morozzi01/2020
73963^178226+1085036Robert Price10/2013
7397(2^282475+1050)/285034Stefano Morozzi01/2020
7398(182*10^85017+43)/985019Robert Price11/2017
7399(14*10^85010+73)/385011Robert Price04/2016
74009*2^282338-784994Lelio R Paula08/2014
7401(9913*2^282330-1)/157800384988Lelio R Paula04/2015
740220025^17504+17504^2002584969Hans Havermann07/2020
74032^282203+584952Lelio R Paula08/2012
74042^282184+1384946Lelio R Paula08/2012
740511^81568-240084945Enzo Doria12/2012
740611^81562-234084939Enzo Doria12/2012
7407(41*10^84927+31)/984928Robert Price05/2015
7408(3923^23629-1)/392284911Serge Batalov08/2020
7409(2^282053+1406)/284907Stefano Morozzi01/2020
7410(2*10^84904-17)/384904Robert Price08/2014
7411(4^141017+23)/384901Robert Price02/2017
74126^109100-1865384897Enzo Doria03/2013
74132^281973+102584883Lelio R Paula09/2013
74142^281951-10965184876Enzo Doria04/2014
741521618^8431+8431^2161884870Hans Havermann07/2020
741611^81491-543084865Enzo Doria01/2013
741710^84863-4000184863Robert Price01/2021
7418((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
7419(2^281827+650)/284839Stefano Morozzi01/2020
74202^281825-186148384838Enzo Doria03/2016
74212^281809-9730584833Lelio R Paula09/2013
74232^281780-11489384825Enzo Doria05/2015
7422(7654^21841-1)/765384825Serge Batalov08/2020
74243^177719+6484794Lelio R Paula12/2015
74262^281675-19984793Lelio R Paula08/2012
74252^281673-11122384793Enzo Doria05/2014
7427(4*10^84779+149)/984779Robert Price03/2017
7429129^40167-12884777Norbert Schneider01/2019
7428(2^281622+3970)/284777Stefano Morozzi01/2020
7430(72*10^84772-27)/984773Ray Chandler01/2011
743111^81398-63084768Enzo Doria11/2012
7432(25*2^281577-1)/2384764Lelio R Paula02/2014
743320320^14819+14819^2032084752Hans Havermann07/2020
74342^281500-45584740Yves Minet03/2012
743510^84725+114514191984726Marisa Kirisame03/2015
743610^84725+14204184726Patrick De Geest10/2015
743710^84725-13867784725Patrick De Geest02/2016
743876^45044+7584720Norbert Schneider02/2015
743954^48897-5384709Norbert Schneider08/2014
7440(9913*2^281377-1)/6584706Lelio R Paula04/2015
7441Phi(171124,10)/29946701/7761329021/5856034404184700Maksym Voznyy11/2015
74422^281337-11122384691Enzo Doria05/2014
74432^281308+5461584683Lelio R Paula09/2013
74447*5^121144-684677Lelio R Paula10/2014
7445(2^281270+3858)/284671Stefano Morozzi01/2020
7446(2^281252+47)/384665Lelio R Paula01/2013
744711^81297-315084663Enzo Doria12/2012
74482^281208-30384653Yves Minet02/2012
7449197^36892-284648Lelio R Paula10/2017
7450(21*2^281187+1)/248384644Lelio R Paula01/2013
745111^81247-8484611Lelio R Paula10/2015
7452(10876^20959-1)/1087584597Serge Batalov08/2020
74532067^25516+25516^206784595Norbert Schneider11/2019
745517^68747-6484590Lelio R Paula11/2015
7454(2^281002+3718)/284590Stefano Morozzi01/2020
74565^121018-1559684588Enzo Doria02/2013
74576^108702+784587Lelio R Paula11/2014
745810^84582+10067784583Patrick De Geest05/2016
745910^84582-800184582Robert Price03/2016
74601828^25929+25929^182884580Norbert Schneider12/2019
7461(2^280968+1446)/284580Stefano Morozzi01/2020
74623*5^121004-884579Lelio R Paula10/2014
74635^120996-8484573Lelio R Paula10/2015
7464(2^280896+1522)/284558Stefano Morozzi01/2020
7465(10223*2^280881+1)/6841984553Lelio R Paula06/2014
74662^280852+9768184545Yves Minet08/2004
74672^280848-120384544Lelio R Paula09/2013
74685^120946-2484538Lelio R Paula10/2015
74692^280810-211184533Yves Minet08/2013
747011^81161-516084521Enzo Doria01/2013
74712^280737-9384511Lelio R Paula08/2012
7472(2^280737+494)/284510Stefano Morozzi01/2020
7473(2^280717+1166)/284504Stefano Morozzi01/2020
74742^280698+31584499Lelio R Paula09/2013
74753^177099-34084498Lelio R Paula12/2015
7476(8201^21589-1)/820084493Serge Batalov08/2020
7477(5*10^84469-107)/384470Robert Price01/2017
7478(3^177002+7)/669602227216174484436Lelio R Paula12/2012
7479(2^280500-1017)/82384436Lelio R Paula01/2013
748024677^2640+2640^2467784435Hans Havermann07/2020
748114^73660-584424Lelio R Paula11/2015
7482(2^280405+746)/284411Stefano Morozzi01/2020
7484(19*10^84409-61)/384410Robert Price04/2017
748320862^11119+11119^2086284410Hans Havermann07/2020
74852^280388+11784406Lelio R Paula08/2012
74862^280389-56653384406Paul Bourdelais03/2013
748723423^4008+4008^2342384392Hans Havermann07/2020
7488(2^280340+3322)/284391Stefano Morozzi01/2020
7489(141584^16384+1)/6553784390Syoichiro Yamada06/2008
7490(1897^25741-1)/189684378Serge Batalov08/2020
7492119^40652+11884376Norbert Schneider09/2018
7491(2^280291+2274)/284376Stefano Morozzi01/2020
74932^280240-17384361Lelio R Paula08/2012
7494(184*10^84348-1)/384350Robert Price02/2017
749521068^10083+10083^2106884348Hans Havermann07/2020
74964*10^84346+9384347Robert Price01/2017
74977*2^280156-584337Lelio R Paula08/2014
7498(8760^21391-1)/875984331Serge Batalov08/2020
74998*7^99782-384327Lelio R Paula10/2014
75002^280116+13384324Lelio R Paula08/2012


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Created by  Henri Lifchitz & Renaud Lifchitz : October, 26 2000, last modification: January, 18 2021 19:57 (Time in France)

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