PRP Records

Probable Primes Top 10000

(193013 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 ?
72512^210576-17363390Lelio R Paula08/2011
725218^50497+5563388Lelio R Paula05/2013
72532^210545+1163381Lelio R Paula08/2011
72542^210543+6363380Lelio R Paula08/2011
725583^33016+8263361Norbert Schneider04/2015
72562^210464+9876533163356Jason Earls12/2008
72577*10^63351+963352Dmitry Domanov11/2010
7258p(13534)#/2+51263348Robert Price05/2017
72591741^19546+19546^174163345Serge Batalov05/2014
726010^63336+1981963337Patrick De Geest12/2013
726110^63336-12288363336Patrick De Geest12/2013
7262(19^49523-2^49523)/1763327Robert Price09/2013
7263(2^210378+47)/9551693163323Lelio R Paula03/2012
726431191!2+25663316Robert Price01/2015
726516458^7031+7031^1645863315Hans Havermann01/2017
7266(lucasV(1,2,420636)-2)/(7*31^2*210319)63303Mike Oakes03/2017
7267(2^210283+7)/169114563296Lelio R Paula03/2012
72682^210217+129963282Lelio R Paula09/2011
7269(2^210221-3)/26963281Lelio R Paula04/2012
7270Phi(193404,10)/386809/812296963268Maksym Voznyy10/2011
727196^31913-9563261Norbert Schneider04/2016
72723^132572+28063253Lelio R Paula04/2013
72733^132570-2^(132570-1)63252Robert Price01/2016
727411^60734-492063248Enzo Doria01/2013
72762^210061+2163235Donovan Johnson06/2006
727518^50375+9563235Lelio R Paula05/2013
727785^32773-263233Lelio R Paula08/2013
7278(-lucasV(1,2,420115)-2)/(3*5^3)63232Mike Oakes02/2017
7279(2^210054-1017)/67163230Lelio R Paula04/2012
72803*2^210022+563224Lelio R Paula04/2014
728115^53756+3263222Lelio R Paula05/2013
728317^51380+2263221Lelio R Paula05/2013
7282(lucasV(1,2,420045)+2)/25763221Mike Oakes02/2017
728443^38700+4263216Norbert Schneider06/2014
72855^90431-9663209Lelio R Paula04/2013
7286(172*10^63202-1)/963204Serge Batalov12/2014
7287(43*10^63200+83)/963201Robert Price08/2017
72882^209914-1600563191Enzo Doria04/2013
72893*6^81190-563179Lelio R Paula09/2014
72902^209820+425763163Lelio R Paula10/2011
729199^31648+263158Lelio R Paula05/2013
729216976^5253+5253^1697663158Hans Havermann01/2017
72932^209790+6763154Lelio R Paula08/2011
72942^209759+9019563144Lelio R Paula02/2013
7295145823#+21150763142Arkadiusz Wesolowski03/2013
72962^209707+51363129Lelio R Paula10/2011
7297(3^132314-8)/1763129Lelio R Paula04/2012
7298(2*10^63117+7)/963117Erik Branger03/2011
72999*2^209654-763114Lelio R Paula04/2014
730011^60598-1463107Lelio R Paula05/2013
730115103^15078+15078^1510363106Hans Havermann01/2017
730215346^12941+12941^1534663103Hans Havermann01/2017
73033^132253+7663101Lelio R Paula04/2013
7304(56*10^63100+403)/963101Robert Price10/2017
730517549^3936+3936^1754963090Hans Havermann01/2017
7306(55459*2^209553+1)/42363084Lelio R Paula06/2014
7307(331^25033-1)/33063077Eric Chen09/2017
730920^48480+3163074Lelio R Paula06/2013
7308(26*10^63073-23)/363074Robert Price08/2016
73102^209499+7625363066Enzo Doria04/2016
731111^60546-1134063053Enzo Doria12/2012
73122^209426+5788963044Yves Minet02/2010
7313(22699*2^209405+1)/2163041Lelio R Paula06/2014
73145^90189+5463040Lelio R Paula04/2013
7315(22*10^63034-73)/363035Robert Price09/2017
7316(314021^11467+1)/31402263029Faysal YAtim05/2008
7317V(301486)63007Henri Lifchitz05/2003
7318(31*2^209298+1)/9563005Lelio R Paula08/2012
7319(27*2^209245+1)/562990Lelio R Paula08/2012
73206^80946-5^(80946-1)62989Robert Price05/2016
7321467^23596+23596^46762986Norbert Schneider08/2016
7322(7*2^209212-1)/362980Lelio R Paula01/2014
7323(27*2^209206-1)/1162978Lelio R Paula01/2014
73241456^19909+19909^145662976Serge Batalov05/2014
7326(3^131964-5)/18521239662955Lelio R Paula04/2012
732535^40772-146662955Enzo Doria03/2013
73275^90064-1370662953Enzo Doria02/2013
7328(22*10^62926+257)/962927Robert Price11/2017
7329(13*10^62914+401)/962915Robert Price10/2017
73302^208993+10762914Lelio R Paula08/2011
73312^208993+7762914Lelio R Paula08/2011
7332189^27636-262913Lelio R Paula10/2017
7333(2^208948-7)/26162898Lelio R Paula03/2012
7334(151*10^62879-1)/362881Robert Price04/2017
733515^53464-8262879Lelio R Paula05/2013
73362^208843-11292162869Enzo Doria06/2014
73372^208779+8162849Henri Lifchitz01/2007
7338(21181*2^208780+1)/899383884162844Lelio R Paula06/2014
7339(73*10^62824+17)/962825Robert Price10/2015
73403^131670-8262823Lelio R Paula04/2013
734119^49128-9062823Lelio R Paula05/2013
734211^60314-441062811Enzo Doria01/2013
7343(17*2^208614-1)/5362799Lelio R Paula01/2014
73442^208594+9362794Donovan Johnson06/2008
7345(-lucasV(1,2,417184)+2)/(3*104297)62788Mike Oakes02/2017
7346(2^208534+7)/905962772Lelio R Paula03/2012
7347(13^56333+1)/1462751Paul Bourdelais03/2010
734810^62750+5762751Robert Price01/2011
734910^62750-26742962750Patrick De Geest01/2013
73502^208427-6962743Lelio R Paula08/2011
73512^208421-11177562741Enzo Doria05/2014
73522^208404-11207962736Enzo Doria06/2014
73532^208343-222162718Yves Minet08/2013
73542^208335+51362716Lelio R Paula10/2011
7356(2^208328+47)/362713Lelio R Paula03/2012
735511^60220-204062713Enzo Doria12/2012
73572^208292+8162703Henri Lifchitz10/2005
735815013^15012-1501262698Henri Lifchitz10/2014
73592^208271-11274762696Enzo Doria06/2014
736011^60202-438062694Enzo Doria01/2013
7361(3^131403-4)/15762693Lelio R Paula04/2012
73622^208127-12666762653Paul Bourdelais01/2012
736371^33843+262653Lelio R Paula05/2013
7364(3^131325+7)/106685062652Lelio R Paula04/2012
73652^208019+11962620Lelio R Paula08/2011
7366(-lucasV(1,2,416078)+2)/(11*190717)62620Mike Oakes02/2017
736711^60126-1137062615Enzo Doria12/2012
73682^207976-248962608Yves Minet07/2014
7369(22699*2^207945+1)/28170962597Lelio R Paula06/2014
73704*21^47335+20562588Curtis Bright05/2015
737115^53210+862580Lelio R Paula05/2013
73722^207865+2962574Henri Lifchitz08/2005
737315^53199-3862567Lelio R Paula05/2013
7374(F(24947)^13-F(24946)^13)/F(24945)62560Wayne Halsdorf03/2012
73752^207782+5890562549Lelio R Paula10/2011
7376(2^207748-3)/843762535Lelio R Paula03/2012
7377(2^207711+5)/1362527Lelio R Paula03/2012
7378(268*10^62523-1)/362525Robert Price10/2017
737910^62523+6362524Robert Price01/2011
738010^62523-29237362523Patrick De Geest01/2013
73812^207691+1155*20769162522Henri Lifchitz02/2005
7382(lucasV(1,2,415410)+2)/(17*653)62522Mike Oakes02/2017
73832^207626-11215762502Enzo Doria06/2014
73843^130987+5262497Lelio R Paula04/2013
73858*6^80299-762486Lelio R Paula09/2014
738611^59997-267062481Enzo Doria12/2012
738793^31740+262480Lelio R Paula05/2013
7388(10^62451+119)/362451Serge Batalov12/2014
7389(2^207443+47)/764562443Lelio R Paula03/2012
73902^207364+11562423Lelio R Paula08/2011
73913^130815-4662415Lelio R Paula04/2013
7392(F(182)^1657-F(181)^1657)/F(180)62409Wayne Halsdorf03/2012
739320^47968-948362408Enzo Doria03/2013
7394(10^62402+101)/362402Robert Price04/2016
7395(13*2^207264-1)/362394Lelio R Paula01/2014
7396(79*10^62387-61)/962388Robert Price10/2015
73975^89244+3*2^8924462379Mike Oakes02/2010
73986^80160-1362377Lelio R Paula04/2013
7399(7*10^62362+53)/362363Robert Price10/2017
7400(1000121^10391+1)/100012262341Faysal YAtim07/2008
7401(17*10^62328-11)/362329Robert Price07/2015
74022^207023+1171562321Lelio R Paula09/2011
7403(265*10^62298+11)/362300Robert Price03/2017
74042^206947-6962298Lelio R Paula08/2011
74052^206938+2983562295Lelio R Paula02/2013
74062^206911-72687762287Paul Bourdelais03/2013
7407(6883*2^206884-1)/362282Lelio R Paula04/2015
74082^206892-11281762281Enzo Doria06/2014
7409(7*10^62278+113)/362279Robert Price10/2017
74103^130523+4662276Lelio R Paula04/2013
74112^206872-11345362275Enzo Doria07/2014
74122^206840-9362266Lelio R Paula08/2011
7413(1017*2^206815-1)/63562258Lelio R Paula04/2015
741496^31406+9562256Norbert Schneider03/2016
7415(2^206824+7)/64621362255Lelio R Paula03/2012
74162^206765-94168362243Paul Bourdelais11/2012
7417(6^79987-1)/562242Paul Bourdelais11/2007
74182^206755-157962240Yves Minet03/2013
741911^59764-582062238Enzo Doria01/2013
74205*10^62233+362234Dmitry Domanov11/2010
74218*3^130421+762228Lelio R Paula04/2014
742219^48661+1062226Lelio R Paula05/2013
7424(17*2^206705+1)/562225Lelio R Paula08/2012
74232^206705-11263562225Enzo Doria06/2014
74253^130403+868062219Lelio R Paula04/2013
742611^59740-711062213Enzo Doria01/2013
74282^206596-16762192Lelio R Paula08/2011
74272^206597+1891562192Lelio R Paula02/2013
74296^79918+13762189Lelio R Paula04/2013
7430lucasU(2408,1,18390)-lucasU(2408,1,18389)62186Mike Oakes05/2009
74312^206574+61362185Jason Earls04/2008
74323^130328+8062183Lelio R Paula04/2013
7433(lucasV(1,2,413270)-2)/(11^2*23*443*1871*2003*37571*687961)62181Mike Oakes02/2017
74342^206550+7681962178Enzo Doria05/2016
743511^59703-2462175Lelio R Paula05/2013
74362^206524+7578162170Enzo Doria04/2016
74372^206506+42762165Henri Lifchitz01/2005
74382^206465+769562153Lelio R Paula02/2013
74392^206464-164962152Yves Minet03/2013
74405^88917+5662151Lelio R Paula04/2013
74412^206444-11156962146Enzo Doria05/2014
74425^88908-4262145Lelio R Paula04/2013
744318^49495-2962130Lelio R Paula05/2013
74443*6^79842-562130Lelio R Paula09/2014
74457*10^62127-1762128Robert Price01/2017
74462^206373+841562125Lelio R Paula02/2013
744720^47745-958362118Enzo Doria03/2013
744841^38516-262118Lelio R Paula08/2013
74492^206332-5869562113Lelio R Paula09/2011
745011^59639-126062108Enzo Doria11/2012
74512^206232-1589362083Enzo Doria04/2013
7452(115*10^62073-1)/362075Serge Batalov12/2014
74532^206206+7579962075Enzo Doria04/2016
7454(74*10^62072+43)/962073Robert Price10/2015
74552^206194-18562071Lelio R Paula08/2011
74566^79757-10362064Lelio R Paula04/2013
7457p(13285)#/2-6462063Robert Price04/2017
7458(29*10^62030-41)/362031Robert Price07/2016
745920^47675-8162027Lelio R Paula06/2013
74603^129972+9862013Lelio R Paula04/2013
74612^205962+362001Donovan Johnson02/2006
74622^205933-205933^261993Henri Lifchitz05/2005
7463(68*10^61991+7)/361993Robert Price03/2016
746420^47641-66361983Enzo Doria03/2013
74653^129861+266061960Lelio R Paula04/2013
7466(55459*2^205800+1)/134561954Lelio R Paula06/2014
746718^49354-9761953Lelio R Paula05/2013
7468(209*10^61947-17)/361949Robert Price05/2017
747014*10^61937+108961939Jens K. Andersen11/2007
7469(11*2^205758-1)/5361939Lelio R Paula01/2014
747120^47600+6361930Lelio R Paula06/2013
7472(16384!+1185)/(3*5*79*10705361)61926Makoto Morimoto09/2017
747344117!3+24361918Robert Price09/2014
7474(31*2^205677-1)/5961915Lelio R Paula01/2014
7475(lucasV(1,2,411332)-2)/(13*97*137*929*40507)61900Mike Oakes02/2017
747620^47575-8161897Lelio R Paula06/2013
7477(58695*2^205593-1)/72761892Lelio R Paula04/2015
747887^31909+8661889Norbert Schneider10/2015
74792^205568+14161883Lelio R Paula08/2011
748010^61868+5892761869Patrick De Geest12/2012
748110^61868-3961868Robert Price05/2011
74825^88505-8861863Lelio R Paula04/2013
7483(-lucasV(1,2,411034)-2)/1463961863Mike Oakes02/2017
748513^55528-9861856Lelio R Paula05/2013
7484(55^35543-1)/5461856Paul Bourdelais08/2017
748630535!2-861844Robert Price06/2015
748711^59371-120061829Enzo Doria11/2012
74887*2^205370-561824Lelio R Paula04/2014
7489(47*10^61821+403)/961822Robert Price04/2017
74902^205275+769561794Lelio R Paula02/2013
74912^205269+1291561793Lelio R Paula02/2013
7492(47*2^205265+1)/3561792Lelio R Paula04/2015
749319^48309+4061776Lelio R Paula05/2013
7494(424*10^61770-1)/961772Robert Price11/2017
74952^205192-407961769Yves Minet06/2011
74962^205184+1609561767Lelio R Paula09/2011
749720^47472-342361763Enzo Doria03/2013
7498(17*10^61760-89)/961761Robert Price11/2017
74992^205149-179561757Lelio R Paula09/2011
75002^205110-1761745Lelio R Paula08/2011


Find by discoverer :


Created by  Henri Lifchitz & Renaud Lifchitz : October, 26 2000, last modification: December, 09 2017 09:21 (Time in France)

Go back
Valid XHTML 1.0!    Valid CSS!