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) !!!


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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(299*10^55998-17)/356000Robert Price01/2017
8502p(12103)#/2-12855994Robert Price05/2017
85042^186003-17433755993Gary Barnes09/2009
8503(2^186010+78557)/12355993Lelio R Paula05/2012
850520^43037-9355993Lelio R Paula02/2013
850616375^2626+2626^1637555991Hans Havermann03/2016
850715631^3816+3816^1563155985Hans Havermann03/2016
850821^42335-255977Lelio R Paula08/2013
8509Phi(64736,139)55959Enzo Doria07/2012
851015215^4762+4762^1521555958Hans Havermann03/2016
851119317^788+788^1931755953Anatoly F. Selevich12/2006
851213582^13165+13165^1358255950Hans Havermann08/2016
8513(78557*2^185842+1)/18955947Lelio R Paula06/2014
851415^47562-8655938Lelio R Paula02/2013
85154*10^55932+9155933Robert Price11/2017
85163^117222+455930Lelio R Paula03/2012
851724^40519-23^4051955925Robert Price07/2012
851813636^12623+12623^1363655924Hans Havermann07/2016
85192^185767-9955922Lelio R Paula03/2011
8520(19*2^185750-1)/1555917Lelio R Paula01/2014
852215^47542-5855914Lelio R Paula02/2013
852152211!4+255914Robert Price08/2017
852320^42973-558355910Enzo Doria03/2013
85244*10^55906+2155907Robert Price08/2016
85252^185713-11155906Lelio R Paula03/2011
852613^50174+8855891Lelio R Paula01/2013
852714569^6846+6846^1456955879Hans Havermann08/2016
8528Pell-LucasQ(145969)/255874Eric W. Weisstein08/2006
85293^117087-8055865Lelio R Paula10/2012
8530(7*10^55851-43)/955851Robert Price10/2014
85312^185519-16955847Lelio R Paula03/2011
85327^66074+1055840Lelio R Paula10/2012
8533(19*10^55833-49)/355834Robert Price02/2017
8534(2*10^55834-59)/355834Robert Price05/2017
853512^51732+555829Lelio R Paula01/2013
85363*2^185429+755821Lelio R Paula03/2014
8537(60^31393+1)/6155820Paul Bourdelais08/2017
8538(9787*2^185420-1)/38155819Lelio R Paula04/2015
853914427^7396+7396^1442755819Hans Havermann08/2016
854010^55811+2155812Robert Price01/2011
854110^55811-7410355811Patrick De Geest12/2012
854211^53591-153055810Enzo Doria11/2012
8543(5^79841-5^39921+1)/1533415955800Lelio R Paula09/2017
85442^185355-214555798Lelio R Paula03/2011
854514531^6912+6912^1453155794Hans Havermann07/2016
85462^185327-161555789Lelio R Paula03/2011
85472^185280-1277955775Enzo Doria10/2012
854815504^3955+3955^1550455771Hans Havermann07/2016
8549(2*10^55762-59)/355762Robert Price05/2017
85505^79770-4455757Lelio R Paula10/2012
855118^44416-8555755Lelio R Paula02/2013
85522^185208-45999555754Enzo Doria06/2015
85532^185200+118555751Lelio R Paula03/2011
8554(536*10^55748-23)/955750Robert Price11/2017
85557^65964+6^(65964-1)55747Robert Price03/2016
85562^185151-23715755737Gary Barnes09/2009
8557110017^11055-10255734Enzo Doria07/2012
855814754^5987+5987^1475455729Hans Havermann07/2016
855940090!3-955711Robert Price09/2014
85609*10^55707+8955708Robert Price11/2016
85612^185023-225755698Yves Minet06/2009
856218628^977+977^1862855696Anatoly F. Selevich01/2007
85632^185006-9355693Lelio R Paula03/2011
85642^185003-251555692Yves Minet07/2014
85653*10^55679+3755680Robert Price10/2017
85666^71524-1955657Lelio R Paula10/2012
85672^184872-219555653Yves Minet08/2013
8568507^20572+20572^50755648Norbert Schneider06/2016
8569(86*10^55645-311)/955646Robert Price10/2017
8570134^26151-13355626Norbert Schneider03/2015
857115340^4221+4221^1534055614Hans Havermann07/2016
857227743!2+255612Robert Price01/2013
857320^42744+8155612Lelio R Paula02/2013
857414609^6406+6406^1460955611Hans Havermann07/2016
85752^184724-11288355608Enzo Doria06/2014
857613507^13074+13074^1350755601Hans Havermann07/2016
85772^184689+12955597Lelio R Paula03/2011
8578(9179*2^184672-1)/19355594Lelio R Paula03/2015
8579(22*10^55592-19)/355593Robert Price02/2017
8580Phi(59984,89)55582Enzo Doria05/2012
858111^53368+1655578Lelio R Paula01/2013
858220^42717-192355577Enzo Doria03/2013
8583117^26870+26870^11755573Serge Batalov05/2014
858412^51488+5555565Lelio R Paula01/2013
8585(44*10^55558-17)/955559Robert Price06/2015
8586(2*10^55559-23)/355559Robert Price09/2017
858710^55555+3285755556Patrick De Geest06/2010
858810^55555-13672155555Patrick De Geest06/2010
8589(11*2^184541-1)/35155551Lelio R Paula01/2014
859020^42696-204355549Enzo Doria03/2013
8591(35*10^55547-737)/955548Robert Price11/2017
8592(2*10^55544+1)/355544Serge Batalov06/2009
8593(-lucasV(1,2,369056)+2)/(3*89*109*457)55542Mike Oakes04/2017
85945003^15013-16055537Enzo Doria07/2012
859539^34896-255522Lelio R Paula08/2013
8596(6^71345-61)/555517Lelio R Paula05/2014
85972^184407-301955513Yves Minet10/2014
8598(43*10^55512-61)/955513Robert Price06/2015
859920^42667-84355512Enzo Doria03/2013
8600133^26134-13255505Norbert Schneider03/2015
8601(31*2^184378-1)/71155502Lelio R Paula01/2014
86029*7^65667-455497Lelio R Paula09/2014
86032^184342-17355493Lelio R Paula03/2011
860415^47182+9255491Lelio R Paula02/2013
86055^79378+655483Lelio R Paula10/2012
8606581^20068+20068^58155472Norbert Schneider06/2016
8607(2^184232+1)/25755457Donovan Johnson03/2005
860818^44177-141555455Enzo Doria03/2013
86092^184203-279786755451Enzo Doria04/2016
86102^184189+1755447Lelio R Paula03/2011
86112^184183+2612355445Yves Minet01/2010
8612Phi(77077,10)55441Ray Chandler05/2009
86132^184141-11325155432Enzo Doria07/2014
86142^184093-50461355418Gary Barnes09/2009
8615(lucasV(1,2,368167)+2)/(11*1103*1307*5647)55404Mike Oakes04/2017
86162^184044-11126955403Enzo Doria05/2014
861714051^8766+8766^1405155401Hans Havermann07/2016
861898^27819+27819^9855394Serge Batalov05/2014
8619(178*10^55390-7)/955392Robert Price08/2017
862058046^9+9^5804655390Andrey Kulsha02/2004
86217^65536+2*59232-255385Jiahao He07/2017
86222^183980+7524155384Enzo Doria04/2016
862310^55372+3755373Robert Price01/2011
862410^55372-4996755372Patrick De Geest12/2012
8625(13*10^55367+17)/355368Robert Price06/2015
86262*6^71150+755366Lelio R Paula09/2014
862719^43296-6255365Lelio R Paula02/2013
862819^43295+1055364Lelio R Paula02/2013
8629(29*10^55362-11)/955363Robert Price04/2015
8630(37*10^55359+53)/955360Robert Price05/2015
863119^43283+7255349Lelio R Paula02/2013
86322^183800-6555330Lelio R Paula03/2011
863321001^12801-11055329Enzo Doria07/2012
863433^36433-32^3643355325Robert Price04/2012
8635(17*2^183729+1)/14555308Lelio R Paula07/2012
86369^57952+8^(57952-1)55301Robert Price03/2016
863714872^5229+5229^1487255301Hans Havermann08/2016
863861^30972-255296Lelio R Paula08/2013
86392^183671-11253755291Enzo Doria06/2014
8640(2^183687+7)/49793974555287Lelio R Paula02/2012
86413^115873+5655286Lelio R Paula10/2012
864213^49629-8455284Lelio R Paula01/2013
86432^183632-555279Henri Lifchitz08/2005
864413981^8988+8988^1398155277Hans Havermann07/2016
8645(5*2^183585+1)/1355265Lelio R Paula07/2012
86462^183576+17155262Lelio R Paula03/2011
864713^49604+8255257Lelio R Paula01/2013
8648(11*10^55254+1)/355255Erik Branger03/2014
86493^115802-2655252Lelio R Paula10/2012
86502^183534-364555250Lelio R Paula01/2011
8651(15*2^183533-1)/11355249Lelio R Paula01/2014
86525^79032-1376655241Enzo Doria02/2013
86538*3^115759-755232Lelio R Paula03/2014
86546^70974-13755229Lelio R Paula10/2012
86552^183446-11307355223Enzo Doria07/2014
86562^183441+57729457555222Lelio R Paula03/2013
86575^79000-655219Lelio R Paula10/2012
86582^183413-90155213Yves Minet01/2012
865919^43168-5055202Lelio R Paula02/2013
86602^183340+1968355191Lelio R Paula02/2012
86616^70923+3555189Lelio R Paula10/2012
86622^183317-403555184Lelio R Paula01/2011
86632^183284-1555174Lelio R Paula03/2011
86642^183255+14955166Lelio R Paula02/2011
86654*10^55165+8755166Robert Price05/2016
8666(3^115574+4)/6303755139Lelio R Paula03/2012
86672^183165-11233355139Enzo Doria06/2014
8668(109^27061-1)/10855133Richard Fischer09/2017
86692^183142+85555132Lelio R Paula01/2011
8670(49*10^55129+383)/955130Robert Price04/2017
86712^183019+25525555095Lelio R Paula01/2011
8672(10^55084-19)/955084Robert Price10/2017
86733*10^55077+755078Erik Branger11/2013
8674(62*10^55075-71)/955076Robert Price09/2015
867527499!2-3255070Robert Price10/2015
867615307^3958+3958^1530755067Hans Havermann08/2016
867770^29836-6955051Norbert Schneider10/2012
867818^43854-8355049Lelio R Paula02/2013
86797^65126+5855038Lelio R Paula10/2012
86802^182827-161555037Lelio R Paula11/2009
86817*10^55030-955031Dmitry Domanov11/2010
86826^70702+2355017Lelio R Paula10/2012
8683(23*2^182753+1)/15155014Lelio R Paula07/2012
86842^182743-161555012Lelio R Paula11/2009
8685(24737*2^182736+1)/39955011Lelio R Paula05/2014
86863^115280-956855003Enzo Doria02/2013
86872^182656-1284954985Enzo Doria10/2012
86889*19^42995+1654981Curtis Bright05/2015
86892^182627+2842554977Lelio R Paula11/2009
86902^182597-11305354968Enzo Doria07/2014
8691(3^115213+2)/3090672554964Lelio R Paula03/2012
86922^182581-197554963Yves Minet09/2012
8693(2*10^54960-179)/354960Robert Price11/2017
869427449!!-1654959Robert Price06/2015
8695(22*10^54958-73)/354959Robert Price09/2017
86964^91283-3^9128354958Jean-Louis Charton01/2004
86972^182565+10754958Lelio R Paula11/2009
86982^182560+205354957Lelio R Paula12/2010
86992^182451-18245154924Henri Lifchitz10/2004
87002^182444+8154922Henri Lifchitz10/2005
87012^182433+7410554918Enzo Doria04/2016
870220^42206-524354912Enzo Doria03/2013
87032^182394+8554907Lelio R Paula02/2011
87042^182374-11228754901Enzo Doria06/2014
8705(47^32833-33^32833)/1454899Serge Batalov12/2016
87062^182363-11316754897Enzo Doria07/2014
87072^182359-11222154896Enzo Doria06/2014
8708(F(1905)^139-F(1904)^139)/F(1903)54893Wayne Halsdorf05/2010
8709(17*2^182274+1)/146754869Lelio R Paula01/2012
871018^43698-554853Lelio R Paula02/2013
87112^182209-189354851Yves Minet09/2012
87122^182194-344354846Yves Minet12/2016
871315023^4468+4468^1502354836Hans Havermann08/2016
87142^182135+9014354829Yves Minet10/2010
87152^182119+7433354824Enzo Doria04/2016
871614289^6860+6860^1428954818Hans Havermann08/2016
87173^114892-114892^354818Norbert Schneider03/2017
87182^182070-4735554809Lelio R Paula01/2011
87193^114869+7654807Lelio R Paula10/2012
87208^60681-60681^854801Norbert Schneider12/2016
87211897^16710+16710^189754777Serge Batalov05/2014
8722Phi(61868,59)54776Enzo Doria04/2012
8723113^26679+254775Lelio R Paula05/2013
87243^114789-7454769Lelio R Paula10/2012
872515^46567+9854768Lelio R Paula02/2013
8726(2*10^54767-71)/354767Robert Price01/2017
8727(298*10^54765-7)/354767Robert Price06/2017
8728(21*2^181931-1)/16999754763Lelio R Paula01/2014
87302^181913+2954762Henri Lifchitz06/2005
8729(31*10^54761-121)/954762Robert Price06/2016
87312^181887+18954754Lelio R Paula02/2011
87322^181874+181874^2-154750Robert Price04/2014
8733(2^181865+9)/733954743Lelio R Paula02/2012
87345^78314-9254740Lelio R Paula10/2012
8735(163*10^54727-1)/954729Serge Batalov12/2014
873615^46531+7454725Lelio R Paula02/2013
8737277^22400-34854712Enzo Doria07/2012
87386^70302+10154706Lelio R Paula10/2012
87393^114622-1040854689Enzo Doria02/2013
8741(23*2^181674+1)/48954688Lelio R Paula01/2012
87402^181669-155154688Yves Minet08/2012
8742(57352^11491-1)/5735154676Serge Batalov04/2015
8743(31*2^181629-1)/1073472154671Lelio R Paula01/2014
8744(F(1048)^251-F(1047)^251)/F(1046)54668Wayne Halsdorf05/2010
874513^49073+4654665Lelio R Paula01/2013
8746(57042^11491-1)/5704154649Serge Batalov04/2015
874820^42000+7354644Lelio R Paula02/2013
8747(67607*2^181517+1)/165554644Lelio R Paula05/2014
874933*10^54634+754636Robert Price07/2016
875020^41988+6154628Lelio R Paula01/2013


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

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