PRP Records

Probable Primes Top 10000

(172142 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 ?
65016^82670+3764330Lelio R Paula07/2013
6502(3^134839+4)/3231295964328Lelio R Paula04/2012
6503(22*10^64326+161)/364327Robert Price02/2017
650411^61767-405064324Enzo Doria12/2012
65052^213645-11485364314Enzo Doria05/2015
650613^57733+1864312Lelio R Paula07/2013
65072^213621+7270764307Enzo Doria04/2016
650810^64305+13679164306Patrick De Geest05/2011
650910^64305-964305Alexander Gramolin01/2011
6510V(307652)64295Serge Batalov03/2015
6511(2^213546-5)/222164281Lelio R Paula04/2012
65122^213438-5869564252Lelio R Paula10/2011
65132^213367-10564230Lelio R Paula08/2011
6514595^23148+23148^59564225Norbert Schneider07/2016
65153^134601+868064221Lelio R Paula05/2013
6516500^23793+23793^50064217Norbert Schneider08/2016
65172^213314-45564214Yves Minet02/2012
651839^40359-3864214Norbert Schneider05/2014
65192^213292-1608564208Enzo Doria04/2013
65202^213274-7764202Lelio R Paula08/2011
652119^50203+7864198Lelio R Paula08/2013
65222^213240-11286564192Enzo Doria06/2014
65232^213190-11239164177Enzo Doria06/2014
6524(9913*2^213184-1)/965764175Lelio R Paula04/2015
652514^55991+2764173Lelio R Paula07/2013
65262^213158-11258164167Enzo Doria06/2014
65272^213148+9164164Lelio R Paula08/2011
65296^82439+12564151Lelio R Paula07/2013
65287*2^213102+964151Lelio R Paula04/2014
6530L(306854)+F(306855)64129Henri Lifchitz01/2007
6531610^23017+23017^61064110Norbert Schneider07/2016
65322^212950-6487564105Lelio R Paula10/2011
6533(266*10^64102-17)/364104Robert Price06/2016
653419^50119+9464090Lelio R Paula08/2013
65352^212880-14764084Lelio R Paula08/2011
653611^61523-459064070Enzo Doria01/2013
65375^91663+3864070Lelio R Paula05/2013
65385^91650+5264061Lelio R Paula05/2013
65392^212770+6964051Lelio R Paula08/2011
6540(3^134227+1)/464042Paul Bourdelais11/2007
6541(2*10^64041-17)/364041Robert Price08/2014
6542(15^54449+1)/1664036Paul Bourdelais03/2010
6543(29*10^64027+91)/364028Robert Price03/2016
6544(lucasV(1,2,425405)+2)/(17*89)64027Mike Oakes03/2017
654516878!+16878#-164022D. Gazzoni Filho & Lucas Teixeira05/2005
65462^212663+5364018Lelio R Paula08/2011
6547(4*10^64014+197)/364015Robert Price03/2017
654810^63986+6363987Robert Price01/2011
654910^63986-3155763986Patrick De Geest05/2013
655031487!2-2^3148763982Robert Price09/2015
6551(21*2^212522-1)/141632363971Lelio R Paula01/2014
65525^91517+9863968Lelio R Paula04/2013
6553(62*10^63954-17)/963955Robert Price09/2015
65555^91493-4^9149363951Predrag Minovic04/2004
6554V(364793)63951Serge Batalov03/2015
655819^50004+5863943Lelio R Paula05/2013
65565*6^82172-763943Lelio R Paula09/2014
6557(56*10^63942+223)/963943Robert Price07/2016
655919^50000-2463938Lelio R Paula05/2013
6560(23*2^212374-1)/2701963928Lelio R Paula01/2014
6561(9*2^212355-1)/76163924Lelio R Paula01/2014
65632^212344-18363922Lelio R Paula08/2011
6562(58695*2^212336-1)/37963922Lelio R Paula04/2015
656410^63916+7963917Robert Price01/2011
656510^63916-7682363916Patrick De Geest05/2013
65662^212295-2563908Lelio R Paula08/2011
65682^212285-238363905Yves Minet10/2013
6567267^26336+26336^26763905Norbert Schneider09/2014
6569(-lucasV(1,2,424552)-2)/160163899Mike Oakes03/2017
657019^49962+6063890Lelio R Paula05/2013
65713^133906-11305663890Enzo Doria07/2014
6572(lucasV(1,2,424451)+2)/363886Mike Oakes03/2017
65733*6^82092+563881Lelio R Paula09/2014
657415441^13706+13706^1544163879Hans Havermann02/2017
65752^212154-77635163865Paul Bourdelais03/2013
657635^41359+263862Lelio R Paula05/2013
6577(61*10^63857-43)/963858Robert Price09/2015
6578(2^212131-3)/48563856Lelio R Paula04/2012
65792^212112-45999563853Enzo Doria06/2015
658015^54290+5863850Lelio R Paula05/2013
65813*2^212097-763849Lelio R Paula04/2014
658255^36683-5463842Norbert Schneider08/2014
6583(509203*2^212056-1)/363841Lelio R Paula04/2015
6584(3^133805-7)/17263839Lelio R Paula04/2012
65852^212049+14963834Lelio R Paula08/2011
65865^91318-1863829Lelio R Paula04/2013
658718468^2857+2857^1846863824Hans Havermann03/2017
6588(2^212024-5)/111163823Lelio R Paula04/2012
65892^211961+1291563807Lelio R Paula02/2013
6590(3^133707-7)/578063791Lelio R Paula04/2012
6591747^22198+22198^74763782Norbert Schneider07/2016
65922^211800-1716963759Enzo Doria05/2013
6593(14*10^63747-11)/363748Erik Branger09/2014
659491*19^49848+663746Curtis Bright05/2015
659518855^2402+2402^1885563741Hans Havermann03/2017
6596(142*10^63734-7)/963736Robert Price02/2017
65972^211699-11163728Lelio R Paula08/2011
659811^61192-555063725Enzo Doria01/2013
6599(11*10^63718+7)/963719Serge Batalov06/2011
66006^81872-1363709Lelio R Paula04/2013
66013^133522+9863707Lelio R Paula05/2013
66032^211607-6163701Lelio R Paula08/2011
66025^91135+863701Lelio R Paula04/2013
660411^61157-27063689Enzo Doria07/2012
660510^63685+114514191963686Marisa Kirisame03/2015
660610^63685+10383763686Patrick De Geest03/2016
660710^63685-13079763685Patrick De Geest03/2016
66082^211547+1155*21154763682Henri Lifchitz02/2005
66092^211543+4563681Lelio R Paula08/2011
66102^211534+4363679Lelio R Paula08/2011
661111^61140-6063671Enzo Doria07/2012
66122^211491-11232163666Enzo Doria06/2014
661319085^2164+2164^1908563654Hans Havermann03/2017
6614(2^211430-5)/85963644Lelio R Paula04/2012
66152^211401-9163639Lelio R Paula08/2011
6616(6883*2^211378-1)/6963634Lelio R Paula04/2015
6617(F(152232)^3-F(152231)^3)/F(152230)63629Wayne Halsdorf03/2012
6618(29*2^211384-1)/5012262163627Lelio R Paula01/2014
66192^211333+1501563618Lelio R Paula01/2013
662033^41889-3263610Norbert Schneider03/2014
662113^57093+1863599Lelio R Paula05/2013
6622(5*2^211219-1)/963583Lelio R Paula01/2014
6623(107*10^63576-17)/963578Robert Price02/2017
662423^46687-102063575Enzo Doria08/2012
6625(67607*2^211188+1)/523431963573Lelio R Paula06/2014
6626(3^133243+7)/1072663570Lelio R Paula04/2012
6627(7*2^211181+1)/274563570Lelio R Paula06/2012
6629(20^48859-1)/1963566Paul Bourdelais03/2010
66282*3^133227+563566Lelio R Paula04/2014
66302^211155+11363564Lelio R Paula08/2011
66312^211134+34563558Lelio R Paula09/2011
66322^211121+1638563554Lelio R Paula09/2011
663316996^5483+5483^1699663549Hans Havermann02/2017
6634(2^211079+9)/36428363536Lelio R Paula03/2012
663515852^10157+10157^1585263516Hans Havermann02/2017
66362^210948-1587363502Enzo Doria04/2013
66377^75136+663498Lelio R Paula04/2013
66382^210928+1291563496Lelio R Paula02/2013
66397*10^63493+3963494Robert Price07/2016
66402^210909+13563490Lelio R Paula08/2011
6641(3*2^210832+1)/763467Lelio R Paula07/2012
66428*7^75098-363467Lelio R Paula09/2014
664317683^3882+3882^1768363466Hans Havermann03/2017
6645Pell-LucasQ(165799)/263464Eric W. Weisstein11/2006
66442^210820-1690563464Enzo Doria05/2013
66465^90795-3663463Lelio R Paula04/2013
66472^210816-1319763462Enzo Doria10/2012
66482^210750+13363443Lelio R Paula08/2011
6649291^25742+25742^29163426Norbert Schneider09/2014
6650(3^132908+8)/27985963408Lelio R Paula04/2012
66516^81480-13963404Lelio R Paula04/2013
66522^210576-17363390Lelio R Paula08/2011
665318^50497+5563388Lelio R Paula05/2013
66542^210545+1163381Lelio R Paula08/2011
66552^210543+6363380Lelio R Paula08/2011
665683^33016+8263361Norbert Schneider04/2015
66572^210464+9876533163356Jason Earls12/2008
66587*10^63351+963352Dmitry Domanov11/2010
66591741^19546+19546^174163345Serge Batalov05/2014
666010^63336+1981963337Patrick De Geest12/2013
666110^63336-12288363336Patrick De Geest12/2013
6662(19^49523-2^49523)/1763327Robert Price09/2013
6663(2^210378+47)/9551693163323Lelio R Paula03/2012
666431191!2+25663316Robert Price01/2015
666516458^7031+7031^1645863315Hans Havermann01/2017
6666(lucasV(1,2,420636)-2)/(7*31^2*210319)63303Mike Oakes03/2017
6667(2^210283+7)/169114563296Lelio R Paula03/2012
66682^210217+129963282Lelio R Paula09/2011
6669(2^210221-3)/26963281Lelio R Paula04/2012
6670Phi(193404,10)/386809/812296963268Maksym Voznyy10/2011
667196^31913-9563261Norbert Schneider04/2016
66723^132572+28063253Lelio R Paula04/2013
66733^132570-2^(132570-1)63252Robert Price01/2016
667411^60734-492063248Enzo Doria01/2013
66762^210061+2163235Donovan Johnson06/2006
667518^50375+9563235Lelio R Paula05/2013
667785^32773-263233Lelio R Paula08/2013
6678(-lucasV(1,2,420115)-2)/(3*5^3)63232Mike Oakes02/2017
6679(2^210054-1017)/67163230Lelio R Paula04/2012
66803*2^210022+563224Lelio R Paula04/2014
668115^53756+3263222Lelio R Paula05/2013
668317^51380+2263221Lelio R Paula05/2013
6682(lucasV(1,2,420045)+2)/25763221Mike Oakes02/2017
668443^38700+4263216Norbert Schneider06/2014
66855^90431-9663209Lelio R Paula04/2013
6686(172*10^63202-1)/963204Serge Batalov12/2014
66872^209914-1600563191Enzo Doria04/2013
66883*6^81190-563179Lelio R Paula09/2014
66892^209820+425763163Lelio R Paula10/2011
669099^31648+263158Lelio R Paula05/2013
669116976^5253+5253^1697663158Hans Havermann01/2017
66922^209790+6763154Lelio R Paula08/2011
66932^209759+9019563144Lelio R Paula02/2013
6694145823#+21150763142Arkadiusz Wesolowski03/2013
66962^209707+51363129Lelio R Paula10/2011
6695(3^132314-8)/1763129Lelio R Paula04/2012
6697(2*10^63117+7)/963117Erik Branger03/2011
66989*2^209654-763114Lelio R Paula04/2014
669911^60598-1463107Lelio R Paula05/2013
670015103^15078+15078^1510363106Hans Havermann01/2017
670115346^12941+12941^1534663103Hans Havermann01/2017
67023^132253+7663101Lelio R Paula04/2013
670317549^3936+3936^1754963090Hans Havermann01/2017
6704(55459*2^209553+1)/42363084Lelio R Paula06/2014
670620^48480+3163074Lelio R Paula06/2013
6705(26*10^63073-23)/363074Robert Price08/2016
67072^209499+7625363066Enzo Doria04/2016
670811^60546-1134063053Enzo Doria12/2012
67092^209426+5788963044Yves Minet02/2010
6710(22699*2^209405+1)/2163041Lelio R Paula06/2014
67115^90189+5463040Lelio R Paula04/2013
6712(314021^11467+1)/31402263029Faysal YAtim05/2008
6713V(301486)63007Henri Lifchitz05/2003
6714(31*2^209298+1)/9563005Lelio R Paula08/2012
6715(27*2^209245+1)/562990Lelio R Paula08/2012
67166^80946-5^(80946-1)62989Robert Price05/2016
6717467^23596+23596^46762986Norbert Schneider08/2016
6718(7*2^209212-1)/362980Lelio R Paula01/2014
6719(27*2^209206-1)/1162978Lelio R Paula01/2014
67201456^19909+19909^145662976Serge Batalov05/2014
6721(3^131964-5)/18521239662955Lelio R Paula04/2012
672235^40772-146662955Enzo Doria03/2013
67235^90064-1370662953Enzo Doria02/2013
67242^208993+10762914Lelio R Paula08/2011
67252^208993+7762914Lelio R Paula08/2011
6726(2^208948-7)/26162898Lelio R Paula03/2012
672715^53464-8262879Lelio R Paula05/2013
67282^208843-11292162869Enzo Doria06/2014
67292^208779+8162849Henri Lifchitz01/2007
6730(21181*2^208780+1)/899383884162844Lelio R Paula06/2014
6731(73*10^62824+17)/962825Robert Price10/2015
67323^131670-8262823Lelio R Paula04/2013
673319^49128-9062823Lelio R Paula05/2013
673411^60314-441062811Enzo Doria01/2013
6735(17*2^208614-1)/5362799Lelio R Paula01/2014
67362^208594+9362794Donovan Johnson06/2008
6737(-lucasV(1,2,417184)+2)/(3*104297)62788Mike Oakes02/2017
6738(2^208534+7)/905962772Lelio R Paula03/2012
6739(13^56333+1)/1462751Paul Bourdelais03/2010
674010^62750+5762751Robert Price01/2011
674110^62750-26742962750Patrick De Geest01/2013
67422^208427-6962743Lelio R Paula08/2011
67432^208421-11177562741Enzo Doria05/2014
67442^208404-11207962736Enzo Doria06/2014
67452^208343-222162718Yves Minet08/2013
67462^208335+51362716Lelio R Paula10/2011
6747(2^208328+47)/362713Lelio R Paula03/2012
674811^60220-204062713Enzo Doria12/2012
67492^208292+8162703Henri Lifchitz10/2005
675015013^15012-1501262698Henri Lifchitz10/2014


Find by discoverer :


Created by  Henri Lifchitz & Renaud Lifchitz : October, 26 2000, last modification: March, 18 2017 12:02 (Time in France)

Go back
Valid XHTML 1.0!    Valid CSS!