PRP Records

Probable Primes Top 10000

(253476 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 ?
850111^60546-1134063053Enzo Doria12/2012
85022^209426+5788963044Yves Minet02/2010
8503(22699*2^209405+1)/2163041Lelio R Paula06/2014
85045^90189+5463040Lelio R Paula04/2013
8505(22*10^63034-73)/363035Robert Price09/2017
8506(314021^11467+1)/31402263029Faysal YAtim05/2008
8507V(301486)63007Henri Lifchitz05/2003
8508(31*2^209298+1)/9563005Lelio R Paula08/2012
8509(27*2^209245+1)/562990Lelio R Paula08/2012
85106^80946-5^(80946-1)62989Robert Price05/2016
8511467^23596+23596^46762986Norbert Schneider08/2016
8512(7*2^209212-1)/362980Lelio R Paula01/2014
8513(27*2^209206-1)/1162978Lelio R Paula01/2014
85141456^19909+19909^145662976Serge Batalov05/2014
8515(5^90107-1)/(4*2162569)62976Gord Palameta07/2019
8517(3^131964-5)/18521239662955Lelio R Paula04/2012
851635^40772-146662955Enzo Doria03/2013
85185^90064-1370662953Enzo Doria02/2013
8519(22*10^62926+257)/962927Robert Price11/2017
8520(13*10^62914+401)/962915Robert Price10/2017
85212^208993+10762914Lelio R Paula08/2011
85222^208993+7762914Lelio R Paula08/2011
8523189^27636-262913Lelio R Paula10/2017
8524(2^208948-7)/26162898Lelio R Paula03/2012
852515804^9545+9545^1580462897Hans Havermann06/2019
8526(151*10^62879-1)/362881Robert Price04/2017
852715^53464-8262879Lelio R Paula05/2013
85282^208843-11292162869Enzo Doria06/2014
85292^208779+8162849Henri Lifchitz01/2007
8530159^28548+15862846Norbert Schneider12/2018
8531(21181*2^208780+1)/899383884162844Lelio R Paula06/2014
8532(73*10^62824+17)/962825Robert Price10/2015
85333^131670-8262823Lelio R Paula04/2013
853419^49128-9062823Lelio R Paula05/2013
853517687^3562+3562^1768762819Hans Havermann06/2019
853611^60314-441062811Enzo Doria01/2013
8537(17*2^208614-1)/5362799Lelio R Paula01/2014
85382^208594+9362794Donovan Johnson06/2008
8539(-lucasV(1,2,417184)+2)/(3*104297)62788Mike Oakes02/2017
8540(2^208534+7)/905962772Lelio R Paula03/2012
8542(13^56333+1)/1462751Paul Bourdelais03/2010
854110^62750+5762751Robert Price01/2011
854310^62750-26742962750Patrick De Geest01/2013
85442^208427-6962743Lelio R Paula08/2011
85452^208421-11177562741Enzo Doria05/2014
85462^208404-11207962736Enzo Doria06/2014
854715242^13041+13041^1524262726Hans Havermann06/2019
85482^208343-222162718Yves Minet08/2013
85492^208335+51362716Lelio R Paula10/2011
8551(2^208328+47)/362713Lelio R Paula03/2012
855011^60220-204062713Enzo Doria12/2012
85522^208292+8162703Henri Lifchitz10/2005
855315013^15012-1501262698Henri Lifchitz10/2014
85542^208271-11274762696Enzo Doria06/2014
855511^60202-438062694Enzo Doria01/2013
8556(3^131403-4)/15762693Lelio R Paula04/2012
855720349^1202+1202^2034962673Hans Havermann06/2019
85582^208127-12666762653Paul Bourdelais01/2012
855971^33843+262653Lelio R Paula05/2013
8560(3^131325+7)/106685062652Lelio R Paula04/2012
85622^208019+11962620Lelio R Paula08/2011
8561(-lucasV(1,2,416078)+2)/(11*190717)62620Mike Oakes02/2017
856311^60126-1137062615Enzo Doria12/2012
85642^207976-248962608Yves Minet07/2014
8565(22699*2^207945+1)/28170962597Lelio R Paula06/2014
85664*21^47335+20562588Curtis Bright05/2015
856715^53210+862580Lelio R Paula05/2013
856816529^6106+6106^1652962575Hans Havermann06/2019
85692^207865+2962574Henri Lifchitz08/2005
857015^53199-3862567Lelio R Paula05/2013
8571(F(24947)^13-F(24946)^13)/F(24945)62560Wayne Halsdorf03/2012
85722^207782+5890562549Lelio R Paula10/2011
8573(2^207748-3)/843762535Lelio R Paula03/2012
8574(2^207711+5)/1362527Lelio R Paula03/2012
8575(268*10^62523-1)/362525Robert Price10/2017
857610^62523+6362524Robert Price01/2011
857710^62523-29237362523Patrick De Geest01/2013
85792^207691+1155*20769162522Henri Lifchitz02/2005
8578(lucasV(1,2,415410)+2)/(17*653)62522Mike Oakes02/2017
85802^207626-11215762502Enzo Doria06/2014
85813^130987+5262497Lelio R Paula04/2013
85828*6^80299-762486Lelio R Paula09/2014
858311^59997-267062481Enzo Doria12/2012
858493^31740+262480Lelio R Paula05/2013
8585(10^62451+119)/362451Serge Batalov12/2014
8586(2^207443+47)/764562443Lelio R Paula03/2012
858716150^7347+7347^1615062438Hans Havermann06/2019
85882^207364+11562423Lelio R Paula08/2011
85893^130815-4662415Lelio R Paula04/2013
8590(F(182)^1657-F(181)^1657)/F(180)62409Wayne Halsdorf03/2012
859120^47968-948362408Enzo Doria03/2013
8592(10^62402+101)/362402Robert Price04/2016
8593(13*2^207264-1)/362394Lelio R Paula01/2014
8594(79*10^62387-61)/962388Robert Price10/2015
85955^89244+3*2^8924462379Mike Oakes02/2010
85966^80160-1362377Lelio R Paula04/2013
8597(7*10^62362+53)/362363Robert Price10/2017
8598(1000121^10391+1)/100012262341Faysal YAtim07/2008
8599(17*10^62328-11)/362329Robert Price07/2015
86002^207023+1171562321Lelio R Paula09/2011
8601(265*10^62298+11)/362300Robert Price03/2017
86022^206947-6962298Lelio R Paula08/2011
86032^206938+2983562295Lelio R Paula02/2013
86042^206911-72687762287Paul Bourdelais03/2013
8605(6883*2^206884-1)/362282Lelio R Paula04/2015
86062^206892-11281762281Enzo Doria06/2014
8607(7*10^62278+113)/362279Robert Price10/2017
86083^130523+4662276Lelio R Paula04/2013
86092^206872-11345362275Enzo Doria07/2014
86102^206840-9362266Lelio R Paula08/2011
8611(1017*2^206815-1)/63562258Lelio R Paula04/2015
861296^31406+9562256Norbert Schneider03/2016
8613(2^206824+7)/64621362255Lelio R Paula03/2012
86142^206765-94168362243Paul Bourdelais11/2012
8615(6^79987-1)/562242Paul Bourdelais11/2007
86162^206755-157962240Yves Minet03/2013
861711^59764-582062238Enzo Doria01/2013
86185*10^62233+362234Dmitry Domanov11/2010
86198*3^130421+762228Lelio R Paula04/2014
862019^48661+1062226Lelio R Paula05/2013
8621(17*2^206705+1)/562225Lelio R Paula08/2012
86222^206705-11263562225Enzo Doria06/2014
86233^130403+868062219Lelio R Paula04/2013
862411^59740-711062213Enzo Doria01/2013
862515113^13068+13068^1511362209Hans Havermann06/2019
86272^206596-16762192Lelio R Paula08/2011
86262^206597+1891562192Lelio R Paula02/2013
86286^79918+13762189Lelio R Paula04/2013
8629lucasU(2408,1,18390)-lucasU(2408,1,18389)62186Mike Oakes05/2009
86302^206574+61362185Jason Earls04/2008
86313^130328+8062183Lelio R Paula04/2013
8632(lucasV(1,2,413270)-2)/(11^2*23*443*1871*2003*37571*687961)62181Mike Oakes02/2017
86332^206550+7681962178Enzo Doria05/2016
863411^59703-2462175Lelio R Paula05/2013
86352^206524+7578162170Enzo Doria04/2016
86362^206506+42762165Henri Lifchitz01/2005
86372^206465+769562153Lelio R Paula02/2013
86382^206464-164962152Yves Minet03/2013
86395^88917+5662151Lelio R Paula04/2013
86402^206444-11156962146Enzo Doria05/2014
86415^88908-4262145Lelio R Paula04/2013
864218^49495-2962130Lelio R Paula05/2013
86433*6^79842-562130Lelio R Paula09/2014
86447*10^62127-1762128Robert Price01/2017
86452^206373+841562125Lelio R Paula02/2013
864620^47745-958362118Enzo Doria03/2013
864741^38516-262118Lelio R Paula08/2013
86482^206332-5869562113Lelio R Paula09/2011
864911^59639-126062108Enzo Doria11/2012
865014898^14719+14719^1489862094Hans Havermann06/2019
86512^206232-1589362083Enzo Doria04/2013
8652(115*10^62073-1)/362075Serge Batalov12/2014
86532^206206+7579962075Enzo Doria04/2016
8654(74*10^62072+43)/962073Robert Price10/2015
86552^206194-18562071Lelio R Paula08/2011
86566^79757-10362064Lelio R Paula04/2013
8657p(13285)#/2-6462063Robert Price04/2017
8658(29*10^62030-41)/362031Robert Price07/2016
865920^47675-8162027Lelio R Paula06/2013
86603^129972+9862013Lelio R Paula04/2013
86612^205962+362001Donovan Johnson02/2006
86622^205933-205933^261993Henri Lifchitz05/2005
8663(68*10^61991+7)/361993Robert Price03/2016
866420^47641-66361983Enzo Doria03/2013
866516737^5036+5036^1673761962Hans Havermann06/2019
86663^129861+266061960Lelio R Paula04/2013
8667(55459*2^205800+1)/134561954Lelio R Paula06/2014
866818^49354-9761953Lelio R Paula05/2013
8669(209*10^61947-17)/361949Robert Price05/2017
867014*10^61937+108961939Jens K. Andersen11/2007
8671(11*2^205758-1)/5361939Lelio R Paula01/2014
867220^47600+6361930Lelio R Paula06/2013
867320487^1054+1054^2048761929Hans Havermann06/2019
8674(16384!+1185)/(3*5*79*10705361)61926Makoto Morimoto09/2017
867515267^11374+11374^1526761922Hans Havermann06/2019
867644117!3+24361918Robert Price09/2014
8677(31*2^205677-1)/5961915Lelio R Paula01/2014
8678(lucasV(1,2,411332)-2)/(13*97*137*929*40507)61900Mike Oakes02/2017
867920^47575-8161897Lelio R Paula06/2013
8680(58695*2^205593-1)/72761892Lelio R Paula04/2015
868187^31909+8661889Norbert Schneider10/2015
86822^205568+14161883Lelio R Paula08/2011
868310^61868+5892761869Patrick De Geest12/2012
868410^61868-3961868Robert Price05/2011
86855^88505-8861863Lelio R Paula04/2013
8686(-lucasV(1,2,411034)-2)/1463961863Mike Oakes02/2017
868813^55528-9861856Lelio R Paula05/2013
8687(55^35543-1)/5461856Paul Bourdelais08/2017
868930535!2-861844Robert Price06/2015
869011^59371-120061829Enzo Doria11/2012
86917*2^205370-561824Lelio R Paula04/2014
8692(47*10^61821+403)/961822Robert Price04/2017
86932^205275+769561794Lelio R Paula02/2013
86942^205269+1291561793Lelio R Paula02/2013
8695(47*2^205265+1)/3561792Lelio R Paula04/2015
869619^48309+4061776Lelio R Paula05/2013
8697(424*10^61770-1)/961772Robert Price11/2017
86982^205192-407961769Yves Minet06/2011
86992^205184+1609561767Lelio R Paula09/2011
870020^47472-342361763Enzo Doria03/2013
8701(17*10^61760-89)/961761Robert Price11/2017
87022^205149-179561757Lelio R Paula09/2011
87032^205110-1761745Lelio R Paula08/2011
8704(373^24007+1)/37461737Eric Chen10/2017
870514734^14811-14811^1473461737Norbert Schneider06/2019
8706(2^205025-7)/2561718Lelio R Paula03/2012
870727^43117-26^4311761717Robert Price08/2012
87082^205016+3761716Lelio R Paula08/2011
8709gcd(V(738275),5*F(147655)*(F(147655)-1)+1)61715Serge Batalov04/2015
87101263^19898+19898^126361712Serge Batalov05/2014
8711135^28963-13461701Norbert Schneider04/2015
8712(33*2^204966+1)/23434161698Michael Porter01/2015
8713(7*10^61696+167)/361696Robert Kinser10/2017
8714(46*10^61693+17)/961694Robert Price06/2015
8715((((((((((2^3+3)^3+30)^3+6)^3+80)^3+12)^3+450)^3+894)^3+3636)^3+70756)^3+97220)^3+6676861684Phil Carmody09/2004
87161850^18879+18879^185061681Serge Batalov05/2014
87182^204891-100561679Lelio R Paula09/2011
8717151^28306-261679Lelio R Paula10/2017
8719(3^129271-5)/4150661674Lelio R Paula03/2012
872015937^7408+7408^1593761672Hans Havermann02/2017
87215^88216-1261661Lelio R Paula04/2013
872218185^2454+2454^1818561645Hans Havermann01/2017
87242^204767-1586561642Enzo Doria04/2013
8723(lucasV(1,2,409560)+2)/307961642Mike Oakes01/2017
87257*2^204751-961638Lelio R Paula04/2014
87274*10^61625+2161626Robert Price08/2016
872615369^10226+10226^1536961626Hans Havermann02/2017
87282^204702-1812561622Enzo Doria05/2013
87295*3^129146+861620Lelio R Paula04/2014
87302^204673+12961613Lelio R Paula08/2011
873118^49079+9761608Lelio R Paula05/2013
8732106^30416+10561602Norbert Schneider12/2016
87332^204590-3361588Lelio R Paula08/2011
87342^204586-11197561587Enzo Doria06/2014
87352^204580-1607761585Enzo Doria04/2013
87362^204574-1604161583Enzo Doria04/2013
873715^52358+5661578Lelio R Paula05/2013
8738(28*10^61574+11)/361575Robert Price11/2015
87392^204516-1749361566Enzo Doria05/2013
87404*5^88076-361564Lelio R Paula09/2014
874111^59110-252061557Enzo Doria12/2012
87422^204477-5869561554Lelio R Paula09/2011
874312^57026-7361542Lelio R Paula05/2013
8744(257^25537+1)/25861541Richard Fischer04/2018
874517^50013+9061539Lelio R Paula05/2013
874656^35201-55^3520161538Robert Price10/2013
87478*7^72810+561533Lelio R Paula09/2014
8749204^26641-203^2664161531Jean-Louis Charton08/2009
874843867!3-656161531Robert Price11/2015
875010^61525+6225761526Patrick De Geest12/2016


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Created by  Henri Lifchitz & Renaud Lifchitz : October, 26 2000, last modification: August, 25 2019 15:53 (Time in France)

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