PRP Records

Probable Primes Top 10000

(205869 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 (> 30000) Who ? When ?
725113^57733+1864312Lelio R Paula07/2013
72522^213621+7270764307Enzo Doria04/2016
725310^64305+13679164306Patrick De Geest05/2011
725410^64305-964305Alexander Gramolin01/2011
7255V(307652)64295Serge Batalov03/2015
72564*10^64286-8964287Robert Price08/2017
7257(2^213546-5)/222164281Lelio R Paula04/2012
72582^213438-5869564252Lelio R Paula10/2011
72592^213367-10564230Lelio R Paula08/2011
7260595^23148+23148^59564225Norbert Schneider07/2016
72613^134601+868064221Lelio R Paula05/2013
7262(26*10^64220+61)/364221Robert Price06/2017
7263500^23793+23793^50064217Norbert Schneider08/2016
7264179^28504-264216Lelio R Paula10/2017
72662^213314-45564214Yves Minet02/2012
726539^40359-3864214Norbert Schneider05/2014
72672^213292-1608564208Enzo Doria04/2013
72682^213274-7764202Lelio R Paula08/2011
726919^50203+7864198Lelio R Paula08/2013
7270(44*10^64192-233)/964193Robert Price10/2017
72712^213240-11286564192Enzo Doria06/2014
72722^213190-11239164177Enzo Doria06/2014
7273(9913*2^213184-1)/965764175Lelio R Paula04/2015
727414^55991+2764173Lelio R Paula07/2013
72752^213158-11258164167Enzo Doria06/2014
72762^213148+9164164Lelio R Paula08/2011
7277(96^32369+1)/9764163Paul Bourdelais08/2017
72796^82439+12564151Lelio R Paula07/2013
72787*2^213102+964151Lelio R Paula04/2014
7280L(306854)+F(306855)64129Henri Lifchitz01/2007
7281610^23017+23017^61064110Norbert Schneider07/2016
72822^212950-6487564105Lelio R Paula10/2011
7283(266*10^64102-17)/364104Robert Price06/2016
7284p(13679)#/2+6464097Robert Price03/2017
728519^50119+9464090Lelio R Paula08/2013
72862^212880-14764084Lelio R Paula08/2011
728711^61523-459064070Enzo Doria01/2013
72885^91663+3864070Lelio R Paula05/2013
72895^91650+5264061Lelio R Paula05/2013
72902^212770+6964051Lelio R Paula08/2011
7291(3^134227+1)/464042Paul Bourdelais11/2007
7292(2*10^64041-17)/364041Robert Price08/2014
7293(15^54449+1)/1664036Paul Bourdelais03/2010
7294(29*10^64027+91)/364028Robert Price03/2016
7295(lucasV(1,2,425405)+2)/(17*89)64027Mike Oakes03/2017
729616878!+16878#-164022D. Gazzoni Filho & Lucas Teixeira05/2005
72972^212663+5364018Lelio R Paula08/2011
7298(4*10^64014+197)/364015Robert Price03/2017
729910^63986+6363987Robert Price01/2011
730010^63986-3155763986Patrick De Geest05/2013
730131487!2-2^3148763982Robert Price09/2015
7302(21*2^212522-1)/141632363971Lelio R Paula01/2014
73035^91517+9863968Lelio R Paula04/2013
7304(19*10^63960-43)/363961Robert Price10/2017
7305(62*10^63954-17)/963955Robert Price09/2015
73075^91493-4^9149363951Predrag Minovic04/2004
7306V(364793)63951Serge Batalov03/2015
731019^50004+5863943Lelio R Paula05/2013
73085*6^82172-763943Lelio R Paula09/2014
7309(56*10^63942+223)/963943Robert Price07/2016
731119^50000-2463938Lelio R Paula05/2013
7312(23*2^212374-1)/2701963928Lelio R Paula01/2014
7313(9*2^212355-1)/76163924Lelio R Paula01/2014
73152^212344-18363922Lelio R Paula08/2011
7314(58695*2^212336-1)/37963922Lelio R Paula04/2015
731610^63916+7963917Robert Price01/2011
731710^63916-7682363916Patrick De Geest05/2013
73182^212295-2563908Lelio R Paula08/2011
73202^212285-238363905Yves Minet10/2013
7319267^26336+26336^26763905Norbert Schneider09/2014
7321(-lucasV(1,2,424552)-2)/160163899Mike Oakes03/2017
732219^49962+6063890Lelio R Paula05/2013
73233^133906-11305663890Enzo Doria07/2014
7324(lucasV(1,2,424451)+2)/363886Mike Oakes03/2017
73253*6^82092+563881Lelio R Paula09/2014
732615441^13706+13706^1544163879Hans Havermann02/2017
73272^212154-77635163865Paul Bourdelais03/2013
732835^41359+263862Lelio R Paula05/2013
7329(61*10^63857-43)/963858Robert Price09/2015
7330(2^212131-3)/48563856Lelio R Paula04/2012
73312^212112-45999563853Enzo Doria06/2015
733215^54290+5863850Lelio R Paula05/2013
73333*2^212097-763849Lelio R Paula04/2014
733455^36683-5463842Norbert Schneider08/2014
7335(509203*2^212056-1)/363841Lelio R Paula04/2015
7336(3^133805-7)/17263839Lelio R Paula04/2012
73372^212049+14963834Lelio R Paula08/2011
73385^91318-1863829Lelio R Paula04/2013
733918468^2857+2857^1846863824Hans Havermann03/2017
7340(2^212024-5)/111163823Lelio R Paula04/2012
73412^211961+1291563807Lelio R Paula02/2013
7342(3^133707-7)/578063791Lelio R Paula04/2012
7343(44*10^63790-161)/963791Robert Price11/2017
7344747^22198+22198^74763782Norbert Schneider07/2016
73452^211800-1716963759Enzo Doria05/2013
7346(85*10^63757-1)/363759Robert Price07/2017
7347(14*10^63747-11)/363748Erik Branger09/2014
734891*19^49848+663746Curtis Bright05/2015
734918855^2402+2402^1885563741Hans Havermann03/2017
7350(142*10^63734-7)/963736Robert Price02/2017
73512^211699-11163728Lelio R Paula08/2011
735211^61192-555063725Enzo Doria01/2013
7353(11*10^63718+7)/963719Serge Batalov06/2011
73546^81872-1363709Lelio R Paula04/2013
73553^133522+9863707Lelio R Paula05/2013
73572^211607-6163701Lelio R Paula08/2011
73565^91135+863701Lelio R Paula04/2013
735811^61157-27063689Enzo Doria07/2012
736010^63685+114514191963686Marisa Kirisame03/2015
735910^63685+10383763686Patrick De Geest03/2016
736110^63685-13079763685Patrick De Geest03/2016
73622^211547+1155*21154763682Henri Lifchitz02/2005
73632^211543+4563681Lelio R Paula08/2011
73642^211534+4363679Lelio R Paula08/2011
736511^61140-6063671Enzo Doria07/2012
73662^211491-11232163666Enzo Doria06/2014
736719085^2164+2164^1908563654Hans Havermann03/2017
7368(2^211430-5)/85963644Lelio R Paula04/2012
73692^211401-9163639Lelio R Paula08/2011
7370(6883*2^211378-1)/6963634Lelio R Paula04/2015
7371(F(152232)^3-F(152231)^3)/F(152230)63629Wayne Halsdorf03/2012
7372(29*2^211384-1)/5012262163627Lelio R Paula01/2014
73732^211333+1501563618Lelio R Paula01/2013
737433^41889-3263610Norbert Schneider03/2014
737513^57093+1863599Lelio R Paula05/2013
7376(5*2^211219-1)/963583Lelio R Paula01/2014
7377(107*10^63576-17)/963578Robert Price02/2017
737823^46687-102063575Enzo Doria08/2012
7379(67607*2^211188+1)/523431963573Lelio R Paula06/2014
7380(3^133243+7)/1072663570Lelio R Paula04/2012
7381(7*2^211181+1)/274563570Lelio R Paula06/2012
7383(20^48859-1)/1963566Paul Bourdelais03/2010
73822*3^133227+563566Lelio R Paula04/2014
73842^211155+11363564Lelio R Paula08/2011
73852^211134+34563558Lelio R Paula09/2011
73862^211121+1638563554Lelio R Paula09/2011
738716996^5483+5483^1699663549Hans Havermann02/2017
7388(2^211079+9)/36428363536Lelio R Paula03/2012
73893*10^63522+1363523Robert Price08/2017
739015852^10157+10157^1585263516Hans Havermann02/2017
73912^210948-1587363502Enzo Doria04/2013
73927^75136+663498Lelio R Paula04/2013
73932^210928+1291563496Lelio R Paula02/2013
73947*10^63493+3963494Robert Price07/2016
73952^210909+13563490Lelio R Paula08/2011
7396(3*2^210832+1)/763467Lelio R Paula07/2012
73978*7^75098-363467Lelio R Paula09/2014
739817683^3882+3882^1768363466Hans Havermann03/2017
7400Pell-LucasQ(165799)/263464Eric W. Weisstein11/2006
73992^210820-1690563464Enzo Doria05/2013
74015^90795-3663463Lelio R Paula04/2013
74022^210816-1319763462Enzo Doria10/2012
74032^210750+13363443Lelio R Paula08/2011
7404291^25742+25742^29163426Norbert Schneider09/2014
7405(3^132908+8)/27985963408Lelio R Paula04/2012
74066^81480-13963404Lelio R Paula04/2013
74072^210576-17363390Lelio R Paula08/2011
740818^50497+5563388Lelio R Paula05/2013
74092^210545+1163381Lelio R Paula08/2011
74102^210543+6363380Lelio R Paula08/2011
741183^33016+8263361Norbert Schneider04/2015
74122^210464+9876533163356Jason Earls12/2008
74137*10^63351+963352Dmitry Domanov11/2010
7414p(13534)#/2+51263348Robert Price05/2017
74151741^19546+19546^174163345Serge Batalov05/2014
741610^63336+1981963337Patrick De Geest12/2013
741710^63336-12288363336Patrick De Geest12/2013
7418(19^49523-2^49523)/1763327Robert Price09/2013
7419(2^210378+47)/9551693163323Lelio R Paula03/2012
742031191!2+25663316Robert Price01/2015
742116458^7031+7031^1645863315Hans Havermann01/2017
7422(lucasV(1,2,420636)-2)/(7*31^2*210319)63303Mike Oakes03/2017
7423(2^210283+7)/169114563296Lelio R Paula03/2012
74242^210217+129963282Lelio R Paula09/2011
7425(2^210221-3)/26963281Lelio R Paula04/2012
7426Phi(193404,10)/386809/812296963268Maksym Voznyy10/2011
742796^31913-9563261Norbert Schneider04/2016
74283^132572+28063253Lelio R Paula04/2013
74293^132570-2^(132570-1)63252Robert Price01/2016
743011^60734-492063248Enzo Doria01/2013
74322^210061+2163235Donovan Johnson06/2006
743118^50375+9563235Lelio R Paula05/2013
743385^32773-263233Lelio R Paula08/2013
7434(-lucasV(1,2,420115)-2)/(3*5^3)63232Mike Oakes02/2017
7435(2^210054-1017)/67163230Lelio R Paula04/2012
74363*2^210022+563224Lelio R Paula04/2014
743715^53756+3263222Lelio R Paula05/2013
743917^51380+2263221Lelio R Paula05/2013
7438(lucasV(1,2,420045)+2)/25763221Mike Oakes02/2017
744043^38700+4263216Norbert Schneider06/2014
74415^90431-9663209Lelio R Paula04/2013
7442(172*10^63202-1)/963204Serge Batalov12/2014
7443(43*10^63200+83)/963201Robert Price08/2017
74442^209914-1600563191Enzo Doria04/2013
74453*6^81190-563179Lelio R Paula09/2014
74462^209820+425763163Lelio R Paula10/2011
744899^31648+263158Lelio R Paula05/2013
744716976^5253+5253^1697663158Hans Havermann01/2017
74492^209790+6763154Lelio R Paula08/2011
74502^209759+9019563144Lelio R Paula02/2013
7451145823#+21150763142Arkadiusz Wesolowski03/2013
74532^209707+51363129Lelio R Paula10/2011
7452(3^132314-8)/1763129Lelio R Paula04/2012
7454(2*10^63117+7)/963117Erik Branger03/2011
74559*2^209654-763114Lelio R Paula04/2014
745611^60598-1463107Lelio R Paula05/2013
745715103^15078+15078^1510363106Hans Havermann01/2017
745815346^12941+12941^1534663103Hans Havermann01/2017
74603^132253+7663101Lelio R Paula04/2013
7459(56*10^63100+403)/963101Robert Price10/2017
746117549^3936+3936^1754963090Hans Havermann01/2017
7462(55459*2^209553+1)/42363084Lelio R Paula06/2014
7463(331^25033-1)/33063077Eric Chen09/2017
746420^48480+3163074Lelio R Paula06/2013
7465(26*10^63073-23)/363074Robert Price08/2016
74662^209499+7625363066Enzo Doria04/2016
746711^60546-1134063053Enzo Doria12/2012
74682^209426+5788963044Yves Minet02/2010
7469(22699*2^209405+1)/2163041Lelio R Paula06/2014
74705^90189+5463040Lelio R Paula04/2013
7471(22*10^63034-73)/363035Robert Price09/2017
7472(314021^11467+1)/31402263029Faysal YAtim05/2008
7473V(301486)63007Henri Lifchitz05/2003
7474(31*2^209298+1)/9563005Lelio R Paula08/2012
7475(27*2^209245+1)/562990Lelio R Paula08/2012
74766^80946-5^(80946-1)62989Robert Price05/2016
7477467^23596+23596^46762986Norbert Schneider08/2016
7478(7*2^209212-1)/362980Lelio R Paula01/2014
7479(27*2^209206-1)/1162978Lelio R Paula01/2014
74801456^19909+19909^145662976Serge Batalov05/2014
7482(3^131964-5)/18521239662955Lelio R Paula04/2012
748135^40772-146662955Enzo Doria03/2013
74835^90064-1370662953Enzo Doria02/2013
7484(22*10^62926+257)/962927Robert Price11/2017
7485(13*10^62914+401)/962915Robert Price10/2017
74862^208993+10762914Lelio R Paula08/2011
74872^208993+7762914Lelio R Paula08/2011
7488189^27636-262913Lelio R Paula10/2017
7489(2^208948-7)/26162898Lelio R Paula03/2012
7490(151*10^62879-1)/362881Robert Price04/2017
749115^53464-8262879Lelio R Paula05/2013
74922^208843-11292162869Enzo Doria06/2014
74932^208779+8162849Henri Lifchitz01/2007
7494(21181*2^208780+1)/899383884162844Lelio R Paula06/2014
7495(73*10^62824+17)/962825Robert Price10/2015
74963^131670-8262823Lelio R Paula04/2013
749719^49128-9062823Lelio R Paula05/2013
749811^60314-441062811Enzo Doria01/2013
7499(17*2^208614-1)/5362799Lelio R Paula01/2014
75002^208594+9362794Donovan Johnson06/2008


Find by discoverer :


Created by  Henri Lifchitz & Renaud Lifchitz : October, 26 2000, last modification: April, 22 2018 09:48 (Time in France)

Go back
Valid XHTML 1.0!    Valid CSS!