PRP Records

Probable Primes Top 10000

(202622 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 ?
8501(34*10^56392-7)/9/37/883/2388756384Makoto Morimoto04/2016
850220^43337-956383Lelio R Paula02/2013
8503(26*10^56371-173)/356372Robert Price10/2017
8504(F(1008)^269-F(1007)^269)/F(1006)56364Wayne Halsdorf08/2010
85062^187230+42756362Henri Lifchitz01/2005
850511^54121-948056362Enzo Doria02/2013
8507(21*2^187202-1)/4356354Lelio R Paula01/2014
85082^187173-9156345Lelio R Paula03/2011
8509(23*2^187174-1)/2071988356340Lelio R Paula01/2014
85102^187125-283356331Yves Minet09/2014
85119*7^66655-456331Lelio R Paula09/2014
851218^44874-9756330Lelio R Paula02/2013
851360*79^29679+1956322Serge Batalov03/2016
85145^80571+5656317Lelio R Paula10/2012
85155^80551-2256303Lelio R Paula10/2012
8516(76*10^56281+41)/956282Robert Price10/2015
8517(88*10^56271-43)/956272Robert Price11/2015
8518(5*10^56256-119)/356257Robert Price04/2016
85191508^17691+17691^150856230Serge Batalov05/2014
85203^117844-5856226Lelio R Paula10/2012
8521(19*10^56224+737)/956225Robert Price10/2017
852295^28427+256221Lelio R Paula05/2013
85232^186713+7681756207Enzo Doria05/2016
852416534^2505+2505^1653456196Hans Havermann06/2016
852514428^7849+7849^1442856195Hans Havermann06/2016
85262*10^56194-5156195Robert Price11/2017
852714898^5909+5909^1489856189Hans Havermann06/2016
852818^44758+9556184Lelio R Paula02/2013
85292^186555-74156159Lelio R Paula05/2011
8530(4*10^56156+173)/356157Robert Price01/2017
8532(3^117708+7)/44789656156Lelio R Paula03/2012
853115711^3752+3752^1571156156Hans Havermann06/2016
8533(23*2^186549-1)/242902556152Lelio R Paula01/2014
8534387^21694+21694^38756138Norbert Schneider08/2014
85352^186422+1723956119Yves Minet01/2010
85362^186418+424242956118Jason Earls10/2008
8537136^26300+13556113Norbert Schneider04/2015
85385*2^186392+956111Lelio R Paula03/2014
853914345^8152+8152^1434556108Hans Havermann07/2016
8540(5*2^186351-1)/3956097Lelio R Paula01/2014
85412^186319-54123756088Paul Bourdelais11/2012
85422*10^56083-4356084Robert Price07/2017
8543(16*10^56082-61)/956083Serge Batalov05/2009
8544(14*10^56080-143)/356081Robert Price01/2017
8545(265*10^56076+17)/356078Robert Price05/2016
85467^66346-5056069Lelio R Paula10/2012
854720^43094-3356067Lelio R Paula02/2013
854820^43090-138356062Enzo Doria03/2013
85493^117482+266056054Lelio R Paula10/2012
8550(22699*2^186193+1)/11156052Lelio R Paula05/2014
8551(68*10^56042+13)/956043Ray Chandler09/2010
85523*6^71992+5^7199256022Mike Oakes03/2010
855313691^12352+12352^1369156020Hans Havermann07/2016
8554(2^186095+7)/7556019Lelio R Paula02/2012
8555247^23412+23412^24756018Norbert Schneider08/2014
85561839^17156+17156^183956008Serge Batalov05/2014
855713736^11949+11949^1373656007Hans Havermann04/2016
8558(5*2^186036-1)/1156003Lelio R Paula01/2014
8559(299*10^55998-17)/356000Robert Price01/2017
8560p(12103)#/2-12855994Robert Price05/2017
85632^186003-17433755993Gary Barnes09/2009
8561(2^186010+78557)/12355993Lelio R Paula05/2012
856220^43037-9355993Lelio R Paula02/2013
856416375^2626+2626^1637555991Hans Havermann03/2016
856515631^3816+3816^1563155985Hans Havermann03/2016
856621^42335-255977Lelio R Paula08/2013
8567Phi(64736,139)55959Enzo Doria07/2012
856815215^4762+4762^1521555958Hans Havermann03/2016
856919317^788+788^1931755953Anatoly F. Selevich12/2006
857013582^13165+13165^1358255950Hans Havermann08/2016
8571(78557*2^185842+1)/18955947Lelio R Paula06/2014
857215^47562-8655938Lelio R Paula02/2013
85734*10^55932+9155933Robert Price11/2017
85743^117222+455930Lelio R Paula03/2012
857524^40519-23^4051955925Robert Price07/2012
857613636^12623+12623^1363655924Hans Havermann07/2016
85772^185767-9955922Lelio R Paula03/2011
8578(19*2^185750-1)/1555917Lelio R Paula01/2014
858015^47542-5855914Lelio R Paula02/2013
857952211!4+255914Robert Price08/2017
858120^42973-558355910Enzo Doria03/2013
85824*10^55906+2155907Robert Price08/2016
85832^185713-11155906Lelio R Paula03/2011
858413^50174+8855891Lelio R Paula01/2013
858514569^6846+6846^1456955879Hans Havermann08/2016
8586Pell-LucasQ(145969)/255874Eric W. Weisstein08/2006
85873^117087-8055865Lelio R Paula10/2012
8588(7*10^55851-43)/955851Robert Price10/2014
85892^185519-16955847Lelio R Paula03/2011
85907^66074+1055840Lelio R Paula10/2012
8591(19*10^55833-49)/355834Robert Price02/2017
8592(2*10^55834-59)/355834Robert Price05/2017
859312^51732+555829Lelio R Paula01/2013
85943*2^185429+755821Lelio R Paula03/2014
8595(60^31393+1)/6155820Paul Bourdelais08/2017
8597(9787*2^185420-1)/38155819Lelio R Paula04/2015
859614427^7396+7396^1442755819Hans Havermann08/2016
859810^55811+2155812Robert Price01/2011
859910^55811-7410355811Patrick De Geest12/2012
860011^53591-153055810Enzo Doria11/2012
8601(5^79841-5^39921+1)/1533415955800Lelio R Paula09/2017
86022^185355-214555798Lelio R Paula03/2011
860314531^6912+6912^1453155794Hans Havermann07/2016
86042^185327-161555789Lelio R Paula03/2011
86052^185280-1277955775Enzo Doria10/2012
860615504^3955+3955^1550455771Hans Havermann07/2016
8607(2*10^55762-59)/355762Robert Price05/2017
86085^79770-4455757Lelio R Paula10/2012
860918^44416-8555755Lelio R Paula02/2013
86102^185208-45999555754Enzo Doria06/2015
86112^185200+118555751Lelio R Paula03/2011
8612(536*10^55748-23)/955750Robert Price11/2017
86137^65964+6^(65964-1)55747Robert Price03/2016
86142^185151-23715755737Gary Barnes09/2009
8615110017^11055-10255734Enzo Doria07/2012
861614754^5987+5987^1475455729Hans Havermann07/2016
861740090!3-955711Robert Price09/2014
86189*10^55707+8955708Robert Price11/2016
86192^185023-225755698Yves Minet06/2009
862018628^977+977^1862855696Anatoly F. Selevich01/2007
86212^185006-9355693Lelio R Paula03/2011
86222^185003-251555692Yves Minet07/2014
86233*10^55679+3755680Robert Price10/2017
86246^71524-1955657Lelio R Paula10/2012
86252^184872-219555653Yves Minet08/2013
8626507^20572+20572^50755648Norbert Schneider06/2016
8627(86*10^55645-311)/955646Robert Price10/2017
8628134^26151-13355626Norbert Schneider03/2015
862915340^4221+4221^1534055614Hans Havermann07/2016
863027743!2+255612Robert Price01/2013
863120^42744+8155612Lelio R Paula02/2013
863214609^6406+6406^1460955611Hans Havermann07/2016
86332^184724-11288355608Enzo Doria06/2014
863413507^13074+13074^1350755601Hans Havermann07/2016
86352^184689+12955597Lelio R Paula03/2011
8636(9179*2^184672-1)/19355594Lelio R Paula03/2015
8637(22*10^55592-19)/355593Robert Price02/2017
8638Phi(59984,89)55582Enzo Doria05/2012
863911^53368+1655578Lelio R Paula01/2013
864020^42717-192355577Enzo Doria03/2013
8641117^26870+26870^11755573Serge Batalov05/2014
864212^51488+5555565Lelio R Paula01/2013
8643(44*10^55558-17)/955559Robert Price06/2015
8644(2*10^55559-23)/355559Robert Price09/2017
864510^55555+3285755556Patrick De Geest06/2010
864610^55555-13672155555Patrick De Geest06/2010
8647(11*2^184541-1)/35155551Lelio R Paula01/2014
864820^42696-204355549Enzo Doria03/2013
8649(35*10^55547-737)/955548Robert Price11/2017
8650(2*10^55544+1)/355544Serge Batalov06/2009
8651(-lucasV(1,2,369056)+2)/(3*89*109*457)55542Mike Oakes04/2017
86525003^15013-16055537Enzo Doria07/2012
865339^34896-255522Lelio R Paula08/2013
8654(6^71345-61)/555517Lelio R Paula05/2014
86552^184407-301955513Yves Minet10/2014
8656(43*10^55512-61)/955513Robert Price06/2015
865720^42667-84355512Enzo Doria03/2013
8658133^26134-13255505Norbert Schneider03/2015
8659(31*2^184378-1)/71155502Lelio R Paula01/2014
86609*7^65667-455497Lelio R Paula09/2014
86612^184342-17355493Lelio R Paula03/2011
866215^47182+9255491Lelio R Paula02/2013
86635^79378+655483Lelio R Paula10/2012
8664581^20068+20068^58155472Norbert Schneider06/2016
8665(2^184232+1)/25755457Donovan Johnson03/2005
866618^44177-141555455Enzo Doria03/2013
86672^184203-279786755451Enzo Doria04/2016
86682^184189+1755447Lelio R Paula03/2011
86692^184183+2612355445Yves Minet01/2010
8670Phi(77077,10)55441Ray Chandler05/2009
86712^184141-11325155432Enzo Doria07/2014
86722^184093-50461355418Gary Barnes09/2009
8673(lucasV(1,2,368167)+2)/(11*1103*1307*5647)55404Mike Oakes04/2017
86742^184044-11126955403Enzo Doria05/2014
867514051^8766+8766^1405155401Hans Havermann07/2016
867698^27819+27819^9855394Serge Batalov05/2014
8677(178*10^55390-7)/955392Robert Price08/2017
867858046^9+9^5804655390Andrey Kulsha02/2004
86797^65536+2*59232-255385Jiahao He07/2017
86802^183980+7524155384Enzo Doria04/2016
868110^55372+3755373Robert Price01/2011
868210^55372-4996755372Patrick De Geest12/2012
8683(13*10^55367+17)/355368Robert Price06/2015
86842*6^71150+755366Lelio R Paula09/2014
868519^43296-6255365Lelio R Paula02/2013
868619^43295+1055364Lelio R Paula02/2013
8687(29*10^55362-11)/955363Robert Price04/2015
8688(37*10^55359+53)/955360Robert Price05/2015
868919^43283+7255349Lelio R Paula02/2013
86902^183800-6555330Lelio R Paula03/2011
869121001^12801-11055329Enzo Doria07/2012
869233^36433-32^3643355325Robert Price04/2012
8693(17*2^183729+1)/14555308Lelio R Paula07/2012
86949^57952+8^(57952-1)55301Robert Price03/2016
869514872^5229+5229^1487255301Hans Havermann08/2016
869661^30972-255296Lelio R Paula08/2013
86972^183671-11253755291Enzo Doria06/2014
8698(2^183687+7)/49793974555287Lelio R Paula02/2012
86993^115873+5655286Lelio R Paula10/2012
870013^49629-8455284Lelio R Paula01/2013
87012^183632-555279Henri Lifchitz08/2005
870213981^8988+8988^1398155277Hans Havermann07/2016
8703(5*2^183585+1)/1355265Lelio R Paula07/2012
87042^183576+17155262Lelio R Paula03/2011
870513^49604+8255257Lelio R Paula01/2013
8706(11*10^55254+1)/355255Erik Branger03/2014
87073^115802-2655252Lelio R Paula10/2012
87082^183534-364555250Lelio R Paula01/2011
8709(15*2^183533-1)/11355249Lelio R Paula01/2014
87105^79032-1376655241Enzo Doria02/2013
87118*3^115759-755232Lelio R Paula03/2014
87126^70974-13755229Lelio R Paula10/2012
87132^183446-11307355223Enzo Doria07/2014
87142^183441+57729457555222Lelio R Paula03/2013
87155^79000-655219Lelio R Paula10/2012
87162^183413-90155213Yves Minet01/2012
871719^43168-5055202Lelio R Paula02/2013
87182^183340+1968355191Lelio R Paula02/2012
87196^70923+3555189Lelio R Paula10/2012
87202^183317-403555184Lelio R Paula01/2011
87212^183284-1555174Lelio R Paula03/2011
87222^183255+14955166Lelio R Paula02/2011
87234*10^55165+8755166Robert Price05/2016
8724(3^115574+4)/6303755139Lelio R Paula03/2012
87252^183165-11233355139Enzo Doria06/2014
8726(109^27061-1)/10855133Richard Fischer09/2017
87272^183142+85555132Lelio R Paula01/2011
8728(49*10^55129+383)/955130Robert Price04/2017
87292^183019+25525555095Lelio R Paula01/2011
8730(10^55084-19)/955084Robert Price10/2017
87313*10^55077+755078Erik Branger11/2013
8732(62*10^55075-71)/955076Robert Price09/2015
873327499!2-3255070Robert Price10/2015
873415307^3958+3958^1530755067Hans Havermann08/2016
873570^29836-6955051Norbert Schneider10/2012
873618^43854-8355049Lelio R Paula02/2013
87377^65126+5855038Lelio R Paula10/2012
87382^182827-161555037Lelio R Paula11/2009
87397*10^55030-955031Dmitry Domanov11/2010
87406^70702+2355017Lelio R Paula10/2012
8741(23*2^182753+1)/15155014Lelio R Paula07/2012
87422^182743-161555012Lelio R Paula11/2009
8743(24737*2^182736+1)/39955011Lelio R Paula05/2014
87443^115280-956855003Enzo Doria02/2013
87452^182656-1284954985Enzo Doria10/2012
87469*19^42995+1654981Curtis Bright05/2015
87472^182627+2842554977Lelio R Paula11/2009
87482^182597-11305354968Enzo Doria07/2014
8749(3^115213+2)/3090672554964Lelio R Paula03/2012
87502^182581-197554963Yves Minet09/2012


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Created by  Henri Lifchitz & Renaud Lifchitz : October, 26 2000, last modification: February, 19 2018 09:17 (Time in France)

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