PRP Records

Probable Primes Top 10000

(255244 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 ?
8501(266*10^64102-17)/364104Robert Price06/2016
8502p(13679)#/2+6464097Robert Price03/2017
850319^50119+9464090Lelio R Paula08/2013
85042^212880-14764084Lelio R Paula08/2011
850511^61523-459064070Enzo Doria01/2013
85065^91663+3864070Lelio R Paula05/2013
85075^91650+5264061Lelio R Paula05/2013
85082^212770+6964051Lelio R Paula08/2011
8509(3^134227+1)/464042Paul Bourdelais11/2007
8510(2*10^64041-17)/364041Robert Price08/2014
8511(15^54449+1)/1664036Paul Bourdelais03/2010
8512(29*10^64027+91)/364028Robert Price03/2016
8513(lucasV(1,2,425405)+2)/(17*89)64027Mike Oakes03/2017
851416878!+16878#-164022D. Gazzoni Filho & Lucas Teixeira05/2005
851515862^10863+10863^1586264019Hans Havermann06/2019
85162^212663+5364018Lelio R Paula08/2011
8517(4*10^64014+197)/364015Robert Price03/2017
851885402!6-364014Robert Price08/2018
8519(140^29819+1)/14163994Richard Fischer05/2018
852015313^15094+15094^1531363991Hans Havermann06/2019
852110^63986+6363987Robert Price01/2011
852210^63986-3155763986Patrick De Geest05/2013
852315699^11900+11900^1569963983Hans Havermann07/2019
852431487!2-2^3148763982Robert Price09/2015
8525(21*2^212522-1)/141632363971Lelio R Paula01/2014
85265^91517+9863968Lelio R Paula04/2013
8527(19*10^63960-43)/363961Robert Price10/2017
8528(62*10^63954-17)/963955Robert Price09/2015
85305^91493-4^9149363951Predrag Minovic04/2004
8529V(364793)63951Serge Batalov03/2015
853119^50004+5863943Lelio R Paula05/2013
85325*6^82172-763943Lelio R Paula09/2014
8533(56*10^63942+223)/963943Robert Price07/2016
853419^50000-2463938Lelio R Paula05/2013
8535(23*2^212374-1)/2701963928Lelio R Paula01/2014
8536(9*2^212355-1)/76163924Lelio R Paula01/2014
85382^212344-18363922Lelio R Paula08/2011
8537(58695*2^212336-1)/37963922Lelio R Paula04/2015
853910^63916+7963917Robert Price01/2011
854010^63916-7682363916Patrick De Geest05/2013
85412^212295-2563908Lelio R Paula08/2011
85422^212285-238363905Yves Minet10/2013
8543267^26336+26336^26763905Norbert Schneider09/2014
8544(-lucasV(1,2,424552)-2)/160163899Mike Oakes03/2017
854619^49962+6063890Lelio R Paula05/2013
85453^133906-11305663890Enzo Doria07/2014
85477933^16384+7932^1638463889Richard Fischer09/2019
8548(lucasV(1,2,424451)+2)/363886Mike Oakes03/2017
85493*6^82092+563881Lelio R Paula09/2014
855015441^13706+13706^1544163879Hans Havermann02/2017
85512^212154-77635163865Paul Bourdelais03/2013
855235^41359+263862Lelio R Paula05/2013
8553(61*10^63857-43)/963858Robert Price09/2015
8554(2^212131-3)/48563856Lelio R Paula04/2012
85552^212112-45999563853Enzo Doria06/2015
855615^54290+5863850Lelio R Paula05/2013
85573*2^212097-763849Lelio R Paula04/2014
855855^36683-5463842Norbert Schneider08/2014
8559(509203*2^212056-1)/363841Lelio R Paula04/2015
8560(3^133805-7)/17263839Lelio R Paula04/2012
85612^212049+14963834Lelio R Paula08/2011
85625^91318-1863829Lelio R Paula04/2013
856318468^2857+2857^1846863824Hans Havermann03/2017
8564(2^212024-5)/111163823Lelio R Paula04/2012
85652^211961+1291563807Lelio R Paula02/2013
856613046^15503-15503^1304663803Norbert Schneider09/2019
8568(3^133707-7)/578063791Lelio R Paula04/2012
8567(44*10^63790-161)/963791Robert Price11/2017
8569747^22198+22198^74763782Norbert Schneider07/2016
85712^211800-1716963759Enzo Doria05/2013
8570(85*10^63757-1)/363759Robert Price07/2017
857285089!6-863757Robert Price08/2018
8573(14*10^63747-11)/363748Erik Branger09/2014
857491*19^49848+663746Curtis Bright05/2015
857518855^2402+2402^1885563741Hans Havermann03/2017
8576(142*10^63734-7)/963736Robert Price02/2017
85772^211699-11163728Lelio R Paula08/2011
857811^61192-555063725Enzo Doria01/2013
8579(11*10^63718+7)/963719Serge Batalov06/2011
85806^81872-1363709Lelio R Paula04/2013
85813^133522+9863707Lelio R Paula05/2013
85832^211607-6163701Lelio R Paula08/2011
85825^91135+863701Lelio R Paula04/2013
858411^61157-27063689Enzo Doria07/2012
858510^63685+114514191963686Marisa Kirisame03/2015
858610^63685+10383763686Patrick De Geest03/2016
858710^63685-13079763685Patrick De Geest03/2016
85882^211547+1155*21154763682Henri Lifchitz02/2005
85892^211543+4563681Lelio R Paula08/2011
85902^211534+4363679Lelio R Paula08/2011
859111^61140-6063671Enzo Doria07/2012
85922^211491-11232163666Enzo Doria06/2014
859319085^2164+2164^1908563654Hans Havermann03/2017
8594(2^211430-5)/85963644Lelio R Paula04/2012
85952^211401-9163639Lelio R Paula08/2011
8596(6883*2^211378-1)/6963634Lelio R Paula04/2015
8597(F(152232)^3-F(152231)^3)/F(152230)63629Wayne Halsdorf03/2012
8598(29*2^211384-1)/5012262163627Lelio R Paula01/2014
85992^211333+1501563618Lelio R Paula01/2013
860033^41889-3263610Norbert Schneider03/2014
860113^57093+1863599Lelio R Paula05/2013
8602(5*2^211219-1)/963583Lelio R Paula01/2014
8603(107*10^63576-17)/963578Robert Price02/2017
860423^46687-102063575Enzo Doria08/2012
8605(67607*2^211188+1)/523431963573Lelio R Paula06/2014
8606(3^133243+7)/1072663570Lelio R Paula04/2012
8607(7*2^211181+1)/274563570Lelio R Paula06/2012
8608(20^48859-1)/1963566Paul Bourdelais03/2010
86092*3^133227+563566Lelio R Paula04/2014
86102^211155+11363564Lelio R Paula08/2011
86112^211134+34563558Lelio R Paula09/2011
86122^211121+1638563554Lelio R Paula09/2011
861316996^5483+5483^1699663549Hans Havermann02/2017
8614(2^211079+9)/36428363536Lelio R Paula03/2012
86153*10^63522+1363523Robert Price08/2017
861615852^10157+10157^1585263516Hans Havermann02/2017
86172^210948-1587363502Enzo Doria04/2013
86187^75136+663498Lelio R Paula04/2013
86192^210928+1291563496Lelio R Paula02/2013
86207*10^63493+3963494Robert Price07/2016
86212^210909+13563490Lelio R Paula08/2011
8622(3*2^210832+1)/763467Lelio R Paula07/2012
86238*7^75098-363467Lelio R Paula09/2014
862417683^3882+3882^1768363466Hans Havermann03/2017
8626Pell-LucasQ(165799)/263464Eric W. Weisstein11/2006
86252^210820-1690563464Enzo Doria05/2013
86275^90795-3663463Lelio R Paula04/2013
862884731!6-4863463Robert Price08/2018
86292^210816-1319763462Enzo Doria10/2012
86302^210750+13363443Lelio R Paula08/2011
8631291^25742+25742^29163426Norbert Schneider09/2014
8632(3^132908+8)/27985963408Lelio R Paula04/2012
86336^81480-13963404Lelio R Paula04/2013
86342^210576-17363390Lelio R Paula08/2011
863518^50497+5563388Lelio R Paula05/2013
86362^210545+1163381Lelio R Paula08/2011
86372^210543+6363380Lelio R Paula08/2011
8638155^28929-15463365Norbert Schneider12/2018
863983^33016+8263361Norbert Schneider04/2015
86402^210464+9876533163356Jason Earls12/2008
86417*10^63351+963352Dmitry Domanov11/2010
864258483!4+463351Robert Price09/2019
8643p(13534)#/2+51263348Robert Price05/2017
86441741^19546+19546^174163345Serge Batalov05/2014
864510^63336+1981963337Patrick De Geest12/2013
864610^63336-12288363336Patrick De Geest12/2013
8647(19^49523-2^49523)/1763327Robert Price09/2013
8648(2^210378+47)/9551693163323Lelio R Paula03/2012
864931191!2+25663316Robert Price01/2015
865016458^7031+7031^1645863315Hans Havermann01/2017
8651(lucasV(1,2,420636)-2)/(7*31^2*210319)63303Mike Oakes03/2017
8652156^28864+15563303Norbert Schneider12/2018
8653(2^210283+7)/169114563296Lelio R Paula03/2012
86542^210217+129963282Lelio R Paula09/2011
8655(2^210221-3)/26963281Lelio R Paula04/2012
8656Phi(193404,10)/386809/812296963268Maksym Voznyy10/2011
865796^31913-9563261Norbert Schneider04/2016
86583^132572+28063253Lelio R Paula04/2013
86593^132570-2^(132570-1)63252Robert Price01/2016
866011^60734-492063248Enzo Doria01/2013
86622^210061+2163235Donovan Johnson06/2006
866118^50375+9563235Lelio R Paula05/2013
866385^32773-263233Lelio R Paula08/2013
8664(-lucasV(1,2,420115)-2)/(3*5^3)63232Mike Oakes02/2017
8665(2^210054-1017)/67163230Lelio R Paula04/2012
86663*2^210022+563224Lelio R Paula04/2014
866715^53756+3263222Lelio R Paula05/2013
866817^51380+2263221Lelio R Paula05/2013
8669(lucasV(1,2,420045)+2)/25763221Mike Oakes02/2017
867043^38700+4263216Norbert Schneider06/2014
86715^90431-9663209Lelio R Paula04/2013
8672(172*10^63202-1)/963204Serge Batalov12/2014
8673(43*10^63200+83)/963201Robert Price08/2017
86742^209914-1600563191Enzo Doria04/2013
86753*6^81190-563179Lelio R Paula09/2014
86762^209820+425763163Lelio R Paula10/2011
867799^31648+263158Lelio R Paula05/2013
867816976^5253+5253^1697663158Hans Havermann01/2017
86792^209790+6763154Lelio R Paula08/2011
8680145878#-p(145878)63152Henri Lifchitz12/2018
86812^209759+9019563144Lelio R Paula02/2013
8682145823#+21150763142Arkadiusz Wesolowski03/2013
86832^209707+51363129Lelio R Paula10/2011
8684(3^132314-8)/1763129Lelio R Paula04/2012
8685(2*10^63117+7)/963117Erik Branger03/2011
86869*2^209654-763114Lelio R Paula04/2014
868784304!6-963112Robert Price08/2018
868811^60598-1463107Lelio R Paula05/2013
868915103^15078+15078^1510363106Hans Havermann01/2017
869015346^12941+12941^1534663103Hans Havermann01/2017
86923^132253+7663101Lelio R Paula04/2013
8691(56*10^63100+403)/963101Robert Price10/2017
869317549^3936+3936^1754963090Hans Havermann01/2017
8694(55459*2^209553+1)/42363084Lelio R Paula06/2014
8695(331^25033-1)/33063077Eric Chen09/2017
869720^48480+3163074Lelio R Paula06/2013
8696(26*10^63073-23)/363074Robert Price08/2016
86982^209499+7625363066Enzo Doria04/2016
869911^60546-1134063053Enzo Doria12/2012
87002^209426+5788963044Yves Minet02/2010
8701(22699*2^209405+1)/2163041Lelio R Paula06/2014
87025^90189+5463040Lelio R Paula04/2013
8703(22*10^63034-73)/363035Robert Price09/2017
8704(314021^11467+1)/31402263029Faysal YAtim05/2008
8705V(301486)63007Henri Lifchitz05/2003
8706(31*2^209298+1)/9563005Lelio R Paula08/2012
8707(27*2^209245+1)/562990Lelio R Paula08/2012
87086^80946-5^(80946-1)62989Robert Price05/2016
8709467^23596+23596^46762986Norbert Schneider08/2016
8710(7*2^209212-1)/362980Lelio R Paula01/2014
8711(27*2^209206-1)/1162978Lelio R Paula01/2014
87121456^19909+19909^145662976Serge Batalov05/2014
8713(5^90107-1)/(4*2162569)62976Gord Palameta07/2019
8714(3^131964-5)/18521239662955Lelio R Paula04/2012
871535^40772-146662955Enzo Doria03/2013
87165^90064-1370662953Enzo Doria02/2013
8717(22*10^62926+257)/962927Robert Price11/2017
8718(13*10^62914+401)/962915Robert Price10/2017
87192^208993+10762914Lelio R Paula08/2011
87202^208993+7762914Lelio R Paula08/2011
8721189^27636-262913Lelio R Paula10/2017
8722(2^208948-7)/26162898Lelio R Paula03/2012
872315804^9545+9545^1580462897Hans Havermann06/2019
8724(151*10^62879-1)/362881Robert Price04/2017
872515^53464-8262879Lelio R Paula05/2013
872611018^15555-15555^1101862875Norbert Schneider11/2019
87272^208843-11292162869Enzo Doria06/2014
87282^208779+8162849Henri Lifchitz01/2007
8729159^28548+15862846Norbert Schneider12/2018
8730(21181*2^208780+1)/899383884162844Lelio R Paula06/2014
8731(73*10^62824+17)/962825Robert Price10/2015
87323^131670-8262823Lelio R Paula04/2013
873319^49128-9062823Lelio R Paula05/2013
873417687^3562+3562^1768762819Hans Havermann06/2019
873511^60314-441062811Enzo Doria01/2013
8736(17*2^208614-1)/5362799Lelio R Paula01/2014
87372^208594+9362794Donovan Johnson06/2008
8738(-lucasV(1,2,417184)+2)/(3*104297)62788Mike Oakes02/2017
8739(2^208534+7)/905962772Lelio R Paula03/2012
8741(13^56333+1)/1462751Paul Bourdelais03/2010
874010^62750+5762751Robert Price01/2011
874210^62750-26742962750Patrick De Geest01/2013
87432^208427-6962743Lelio R Paula08/2011
87442^208421-11177562741Enzo Doria05/2014
87452^208404-11207962736Enzo Doria06/2014
874615242^13041+13041^1524262726Hans Havermann06/2019
87472^208343-222162718Yves Minet08/2013
87482^208335+51362716Lelio R Paula10/2011
8749(2^208328+47)/362713Lelio R Paula03/2012
875011^60220-204062713Enzo Doria12/2012


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Created by  Henri Lifchitz & Renaud Lifchitz : October, 26 2000, last modification: November, 10 2019 12:07 (Time in France)

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