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) !!!


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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 (> 30000) Who ? When ?
85012^189671+13157097Lelio R Paula04/2011
8502(67607*2^189651+1)/4372757091Lelio R Paula05/2014
8503(29*2^189619-1)/39357080Lelio R Paula01/2014
85043^119587+8057058Lelio R Paula10/2012
85052^189502-11345357046Enzo Doria07/2014
85062^189455+15357032Lelio R Paula04/2011
850724^41317-41317^2457027Norbert Schneider07/2016
85082^189414-1757020Lelio R Paula03/2011
850924^41311+2357018Norbert Schneider12/2013
8510(4*10^56989-31)/956989Erik Branger05/2011
851111^54712-162056977Enzo Doria11/2012
85122^189237-11223156967Enzo Doria06/2014
851417^46285-4856952Lelio R Paula02/2013
85132^189188+7524156952Enzo Doria04/2016
85152^189181+9439556950Henri Lifchitz01/2005
85167001^14808-10856940Enzo Doria07/2012
85172^189147-11263956939Enzo Doria06/2014
8518(19*10^56933-43)/356934Robert Price10/2017
85192^189110-356928M. Frind & P. Underwood11/2002
85202^189069+1290956916Lelio R Paula04/2011
8521(13*10^56909+191)/356910Robert Price08/2017
8522(35*10^56898-17)/956899Serge Batalov02/2009
85232^189011-595556898Lelio R Paula04/2011
85246^73119-556898Lelio R Paula10/2012
852513^51076-9056896Lelio R Paula02/2013
85262^188997+5689756894Yves Minet02/2010
85275^81388-1376656888Enzo Doria02/2013
8528(156^25933+1)/15756873Eric Chen12/2017
852920^43713-640356872Enzo Doria03/2013
8530(71*10^56858-287)/956859Robert Price05/2017
85312^188857-25423356852Gary Barnes09/2009
853215^48338-8856850Lelio R Paula02/2013
853310^56849+13643756850Patrick De Geest07/2017
853410^56849-70156849Robert Price06/2017
8535(2^188788+78557)/356831Lelio R Paula05/2012
85362^188771+1609556826Lelio R Paula04/2011
85377*2^188742-956818Lelio R Paula03/2014
853812^52646-6556815Lelio R Paula02/2013
85395003^15358-15856813Enzo Doria07/2012
85402^188713+57729457556809Lelio R Paula03/2013
85412^188693-11209956803Enzo Doria05/2014
8542(7^67211+4^67211)/1156799Robert Price10/2012
85432^188678-9439556798Lelio R Paula09/2011
854420^43651-850356792Enzo Doria03/2013
85452^188657-237156792Yves Minet10/2013
8546(14^49549+5^49549)/1956789Robert Price05/2013
8547(45^34351-1)/4456788Robert Price05/2014
85487*10^56785-2356786Robert Price04/2016
8549(10^56781-31)/356781Serge Batalov12/2014
85507*10^56779+356780Erik Branger11/2009
855110^56765+25917956766Patrick De Geest09/2013
855210^56765-24949756765Patrick De Geest09/2013
8553t(188706)56764Robert Price04/2015
85542^188551-90432756760Paul Bourdelais11/2012
8556(64*10^56756+17)/956757Robert Price09/2015
8555131101#+14629156757Makoto Morimoto02/2016
85572^188539-11251956756Enzo Doria06/2014
85586^72927+10156749Lelio R Paula10/2012
855920^43617-160356748Enzo Doria03/2013
8560(3^118892-8)/9135892956718Lelio R Paula03/2012
8561(509203*2^188338-1)/356701Lelio R Paula03/2015
856220^43567-562356682Enzo Doria03/2013
85632^188234-11318356665Enzo Doria07/2014
8564(139^26437+1)/14056653Richard Fischer03/2018
8565(7*2^188215-1)/149731512556651Lelio R Paula01/2014
8566(1017*2^188171-1)/3556647Lelio R Paula03/2015
8567(34*10^56647-7)/9/37/26356644Makoto Morimoto04/2016
8568(2^188176-1017)/45381454356638Lelio R Paula02/2012
856933*10^56634+756636Robert Price07/2016
8570(F(31)^9241-F(30)^9241)/F(29)56634Wayne Halsdorf08/2010
857114^49413+3356634Lelio R Paula02/2013
85723^118680+11056625Lelio R Paula10/2012
8573(13*10^56624+161)/356625Robert Price04/2017
8574(3^118676-2)/751665326356613Lelio R Paula03/2012
8575(13*2^188062+1)/1756613Lelio R Paula07/2012
85762^188056-131356611Yves Minet08/2012
857720^43510-558356608Enzo Doria03/2013
85782^188032+1228556604Lelio R Paula03/2011
8579(19*10^56597-43)/356598Robert Price10/2017
8580(265*10^56588+17)/356590Robert Price05/2016
85812^187959+577556582Lelio R Paula03/2011
8582(5*2^187959+1)/5356581Lelio R Paula07/2012
85833*10^56575-1356576Robert Price11/2017
8584(11*2^187889-1)/35156559Lelio R Paula01/2014
8585(100049^11311+1)/10005056553Faysal YAtim09/2007
8586(19*10^56544-1)/956545Serge Batalov03/2009
858720^43447-892356526Enzo Doria03/2013
85882^187743-11217756517Enzo Doria06/2014
8589(F(5879)^47-F(5878)^47)/F(5877)56502Wayne Halsdorf08/2010
85905^80831-2256499Lelio R Paula10/2012
85915^80828-1316656497Enzo Doria02/2013
85927*2^187590-556472Lelio R Paula03/2014
85932^187555+7547356460Enzo Doria04/2016
85942^187541-28356456Yves Minet01/2012
8595(55*10^56453-1)/956454Serge Batalov03/2009
85962^187506-145156445Yves Minet08/2012
8597189^24794-256443Lelio R Paula10/2017
85986^72522+14356434Lelio R Paula10/2012
8599(15185*2^187452-1)/94956430Lelio R Paula03/2015
86002^187390+7956411Lelio R Paula03/2011
86012^187386+1290956409Lelio R Paula03/2011
86022^187382+61356408Jason Earls04/2008
8603(34*10^56392-7)/9/37/883/2388756384Makoto Morimoto04/2016
860420^43337-956383Lelio R Paula02/2013
8605(26*10^56371-173)/356372Robert Price10/2017
8606(F(1008)^269-F(1007)^269)/F(1006)56364Wayne Halsdorf08/2010
86082^187230+42756362Henri Lifchitz01/2005
860711^54121-948056362Enzo Doria02/2013
8609(21*2^187202-1)/4356354Lelio R Paula01/2014
86102^187173-9156345Lelio R Paula03/2011
8611(23*2^187174-1)/2071988356340Lelio R Paula01/2014
86122^187125-283356331Yves Minet09/2014
86139*7^66655-456331Lelio R Paula09/2014
861418^44874-9756330Lelio R Paula02/2013
861560*79^29679+1956322Serge Batalov03/2016
86165^80571+5656317Lelio R Paula10/2012
86175^80551-2256303Lelio R Paula10/2012
8618(76*10^56281+41)/956282Robert Price10/2015
8619(88*10^56271-43)/956272Robert Price11/2015
8620(5*10^56256-119)/356257Robert Price04/2016
86211508^17691+17691^150856230Serge Batalov05/2014
86223^117844-5856226Lelio R Paula10/2012
8623(19*10^56224+737)/956225Robert Price10/2017
862495^28427+256221Lelio R Paula05/2013
86252^186713+7681756207Enzo Doria05/2016
862616534^2505+2505^1653456196Hans Havermann06/2016
862714428^7849+7849^1442856195Hans Havermann06/2016
86282*10^56194-5156195Robert Price11/2017
862914898^5909+5909^1489856189Hans Havermann06/2016
863018^44758+9556184Lelio R Paula02/2013
86312^186555-74156159Lelio R Paula05/2011
8632(4*10^56156+173)/356157Robert Price01/2017
8634(3^117708+7)/44789656156Lelio R Paula03/2012
863315711^3752+3752^1571156156Hans Havermann06/2016
8635(23*2^186549-1)/242902556152Lelio R Paula01/2014
8636387^21694+21694^38756138Norbert Schneider08/2014
86372^186422+1723956119Yves Minet01/2010
86382^186418+424242956118Jason Earls10/2008
8639136^26300+13556113Norbert Schneider04/2015
86405*2^186392+956111Lelio R Paula03/2014
864114345^8152+8152^1434556108Hans Havermann07/2016
8642(5*2^186351-1)/3956097Lelio R Paula01/2014
86432^186319-54123756088Paul Bourdelais11/2012
86442*10^56083-4356084Robert Price07/2017
8645(16*10^56082-61)/956083Serge Batalov05/2009
8646(14*10^56080-143)/356081Robert Price01/2017
8647(265*10^56076+17)/356078Robert Price05/2016
86487^66346-5056069Lelio R Paula10/2012
864920^43094-3356067Lelio R Paula02/2013
865020^43090-138356062Enzo Doria03/2013
86513^117482+266056054Lelio R Paula10/2012
8652(22699*2^186193+1)/11156052Lelio R Paula05/2014
8653(68*10^56042+13)/956043Ray Chandler09/2010
86543*6^71992+5^7199256022Mike Oakes03/2010
865513691^12352+12352^1369156020Hans Havermann07/2016
8656(2^186095+7)/7556019Lelio R Paula02/2012
8657247^23412+23412^24756018Norbert Schneider08/2014
86581839^17156+17156^183956008Serge Batalov05/2014
865913736^11949+11949^1373656007Hans Havermann04/2016
8660(5*2^186036-1)/1156003Lelio R Paula01/2014
8661(299*10^55998-17)/356000Robert Price01/2017
8662p(12103)#/2-12855994Robert Price05/2017
86642^186003-17433755993Gary Barnes09/2009
8663(2^186010+78557)/12355993Lelio R Paula05/2012
866520^43037-9355993Lelio R Paula02/2013
866616375^2626+2626^1637555991Hans Havermann03/2016
866715631^3816+3816^1563155985Hans Havermann03/2016
866821^42335-255977Lelio R Paula08/2013
8669Phi(64736,139)55959Enzo Doria07/2012
867015215^4762+4762^1521555958Hans Havermann03/2016
867119317^788+788^1931755953Anatoly F. Selevich12/2006
867213582^13165+13165^1358255950Hans Havermann08/2016
8673(78557*2^185842+1)/18955947Lelio R Paula06/2014
867415^47562-8655938Lelio R Paula02/2013
86754*10^55932+9155933Robert Price11/2017
86763^117222+455930Lelio R Paula03/2012
867724^40519-23^4051955925Robert Price07/2012
867813636^12623+12623^1363655924Hans Havermann07/2016
86792^185767-9955922Lelio R Paula03/2011
8680(19*2^185750-1)/1555917Lelio R Paula01/2014
868215^47542-5855914Lelio R Paula02/2013
868152211!4+255914Robert Price08/2017
868320^42973-558355910Enzo Doria03/2013
86844*10^55906+2155907Robert Price08/2016
86852^185713-11155906Lelio R Paula03/2011
868613^50174+8855891Lelio R Paula01/2013
868714569^6846+6846^1456955879Hans Havermann08/2016
8688Pell-LucasQ(145969)/255874Eric W. Weisstein08/2006
86893^117087-8055865Lelio R Paula10/2012
8690(7*10^55851-43)/955851Robert Price10/2014
86912^185519-16955847Lelio R Paula03/2011
86927^66074+1055840Lelio R Paula10/2012
8693(19*10^55833-49)/355834Robert Price02/2017
8694(2*10^55834-59)/355834Robert Price05/2017
869512^51732+555829Lelio R Paula01/2013
86963*2^185429+755821Lelio R Paula03/2014
8697(60^31393+1)/6155820Paul Bourdelais08/2017
8698(9787*2^185420-1)/38155819Lelio R Paula04/2015
869914427^7396+7396^1442755819Hans Havermann08/2016
870010^55811+2155812Robert Price01/2011
870110^55811-7410355811Patrick De Geest12/2012
870211^53591-153055810Enzo Doria11/2012
8703(5^79841-5^39921+1)/1533415955800Lelio R Paula09/2017
87042^185355-214555798Lelio R Paula03/2011
870514531^6912+6912^1453155794Hans Havermann07/2016
87062^185327-161555789Lelio R Paula03/2011
87072^185280-1277955775Enzo Doria10/2012
870815504^3955+3955^1550455771Hans Havermann07/2016
8709(2*10^55762-59)/355762Robert Price05/2017
87105^79770-4455757Lelio R Paula10/2012
871118^44416-8555755Lelio R Paula02/2013
87122^185208-45999555754Enzo Doria06/2015
87132^185200+118555751Lelio R Paula03/2011
8714(536*10^55748-23)/955750Robert Price11/2017
87157^65964+6^(65964-1)55747Robert Price03/2016
87162^185151-23715755737Gary Barnes09/2009
8717110017^11055-10255734Enzo Doria07/2012
871814754^5987+5987^1475455729Hans Havermann07/2016
871940090!3-955711Robert Price09/2014
87209*10^55707+8955708Robert Price11/2016
87212^185023-225755698Yves Minet06/2009
872218628^977+977^1862855696Anatoly F. Selevich01/2007
87232^185006-9355693Lelio R Paula03/2011
87242^185003-251555692Yves Minet07/2014
87252^184992-7855755689Jorge Menendez02/2018
87263*10^55679+3755680Robert Price10/2017
87276^71524-1955657Lelio R Paula10/2012
87282^184872-219555653Yves Minet08/2013
8729507^20572+20572^50755648Norbert Schneider06/2016
8730(86*10^55645-311)/955646Robert Price10/2017
8731134^26151-13355626Norbert Schneider03/2015
873215340^4221+4221^1534055614Hans Havermann07/2016
873327743!2+255612Robert Price01/2013
873420^42744+8155612Lelio R Paula02/2013
873514609^6406+6406^1460955611Hans Havermann07/2016
87362^184724-11288355608Enzo Doria06/2014
873713507^13074+13074^1350755601Hans Havermann07/2016
87382^184689+12955597Lelio R Paula03/2011
8739(9179*2^184672-1)/19355594Lelio R Paula03/2015
8740(22*10^55592-19)/355593Robert Price02/2017
8741Phi(59984,89)55582Enzo Doria05/2012
874211^53368+1655578Lelio R Paula01/2013
874320^42717-192355577Enzo Doria03/2013
8744117^26870+26870^11755573Serge Batalov05/2014
874512^51488+5555565Lelio R Paula01/2013
8746(44*10^55558-17)/955559Robert Price06/2015
8747(2*10^55559-23)/355559Robert Price09/2017
874810^55555+3285755556Patrick De Geest06/2010
874910^55555-13672155555Patrick De Geest06/2010
8750(11*2^184541-1)/35155551Lelio R Paula01/2014


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

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