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 ?
875120^42696-204355549Enzo Doria03/2013
8752(35*10^55547-737)/955548Robert Price11/2017
8753(2*10^55544+1)/355544Serge Batalov06/2009
8754(-lucasV(1,2,369056)+2)/(3*89*109*457)55542Mike Oakes04/2017
87555003^15013-16055537Enzo Doria07/2012
875639^34896-255522Lelio R Paula08/2013
8757(6^71345-61)/555517Lelio R Paula05/2014
87582^184407-301955513Yves Minet10/2014
8759(43*10^55512-61)/955513Robert Price06/2015
876020^42667-84355512Enzo Doria03/2013
8761133^26134-13255505Norbert Schneider03/2015
8762(31*2^184378-1)/71155502Lelio R Paula01/2014
87639*7^65667-455497Lelio R Paula09/2014
87642^184342-17355493Lelio R Paula03/2011
876515^47182+9255491Lelio R Paula02/2013
87665^79378+655483Lelio R Paula10/2012
8767581^20068+20068^58155472Norbert Schneider06/2016
8768(2^184232+1)/25755457Donovan Johnson03/2005
876918^44177-141555455Enzo Doria03/2013
87702^184203-279786755451Enzo Doria04/2016
87712^184189+1755447Lelio R Paula03/2011
87722^184183+2612355445Yves Minet01/2010
8773Phi(77077,10)55441Ray Chandler05/2009
87742^184141-11325155432Enzo Doria07/2014
87752^184093-50461355418Gary Barnes09/2009
8776(lucasV(1,2,368167)+2)/(11*1103*1307*5647)55404Mike Oakes04/2017
87772^184044-11126955403Enzo Doria05/2014
877814051^8766+8766^1405155401Hans Havermann07/2016
877998^27819+27819^9855394Serge Batalov05/2014
8780(178*10^55390-7)/955392Robert Price08/2017
878158046^9+9^5804655390Andrey Kulsha02/2004
87827^65536+2*59232-255385Jiahao He07/2017
87832^183980+7524155384Enzo Doria04/2016
878410^55372+3755373Robert Price01/2011
878510^55372-4996755372Patrick De Geest12/2012
8786(13*10^55367+17)/355368Robert Price06/2015
87872*6^71150+755366Lelio R Paula09/2014
878819^43296-6255365Lelio R Paula02/2013
878919^43295+1055364Lelio R Paula02/2013
8790(29*10^55362-11)/955363Robert Price04/2015
8791(37*10^55359+53)/955360Robert Price05/2015
879219^43283+7255349Lelio R Paula02/2013
87932^183800-6555330Lelio R Paula03/2011
879421001^12801-11055329Enzo Doria07/2012
879533^36433-32^3643355325Robert Price04/2012
8796(17*2^183729+1)/14555308Lelio R Paula07/2012
87989^57952+8^(57952-1)55301Robert Price03/2016
879714872^5229+5229^1487255301Hans Havermann08/2016
879961^30972-255296Lelio R Paula08/2013
88002^183671-11253755291Enzo Doria06/2014
8801(2^183687+7)/49793974555287Lelio R Paula02/2012
88023^115873+5655286Lelio R Paula10/2012
880313^49629-8455284Lelio R Paula01/2013
88042^183632-555279Henri Lifchitz08/2005
880513981^8988+8988^1398155277Hans Havermann07/2016
8806(5*2^183585+1)/1355265Lelio R Paula07/2012
88072^183576+17155262Lelio R Paula03/2011
880813^49604+8255257Lelio R Paula01/2013
8809(11*10^55254+1)/355255Erik Branger03/2014
88103^115802-2655252Lelio R Paula10/2012
88112^183534-364555250Lelio R Paula01/2011
8812(15*2^183533-1)/11355249Lelio R Paula01/2014
88135^79032-1376655241Enzo Doria02/2013
88148*3^115759-755232Lelio R Paula03/2014
88156^70974-13755229Lelio R Paula10/2012
88162^183446-11307355223Enzo Doria07/2014
88172^183441+57729457555222Lelio R Paula03/2013
88185^79000-655219Lelio R Paula10/2012
88192^183413-90155213Yves Minet01/2012
882019^43168-5055202Lelio R Paula02/2013
88212^183340+1968355191Lelio R Paula02/2012
88226^70923+3555189Lelio R Paula10/2012
88232^183317-403555184Lelio R Paula01/2011
88242^183284-1555174Lelio R Paula03/2011
88252^183255+14955166Lelio R Paula02/2011
88264*10^55165+8755166Robert Price05/2016
8828(3^115574+4)/6303755139Lelio R Paula03/2012
88272^183165-11233355139Enzo Doria06/2014
8829(109^27061-1)/10855133Richard Fischer09/2017
88302^183142+85555132Lelio R Paula01/2011
8831(49*10^55129+383)/955130Robert Price04/2017
88322^183019+25525555095Lelio R Paula01/2011
8833(10^55084-19)/955084Robert Price10/2017
88343*10^55077+755078Erik Branger11/2013
8835(62*10^55075-71)/955076Robert Price09/2015
883627499!2-3255070Robert Price10/2015
883715307^3958+3958^1530755067Hans Havermann08/2016
883870^29836-6955051Norbert Schneider10/2012
883918^43854-8355049Lelio R Paula02/2013
88407^65126+5855038Lelio R Paula10/2012
88412^182827-161555037Lelio R Paula11/2009
88427*10^55030-955031Dmitry Domanov11/2010
88432^182768-405555019Yves Minet02/2018
88446^70702+2355017Lelio R Paula10/2012
8845(23*2^182753+1)/15155014Lelio R Paula07/2012
88462^182743-161555012Lelio R Paula11/2009
8847(24737*2^182736+1)/39955011Lelio R Paula05/2014
88483^115280-956855003Enzo Doria02/2013
88492^182656-1284954985Enzo Doria10/2012
885012791^13388-13388^1279154984Norbert Schneider03/2018
88519*19^42995+1654981Curtis Bright05/2015
88522^182627+2842554977Lelio R Paula11/2009
88532^182597-11305354968Enzo Doria07/2014
8854(3^115213+2)/3090672554964Lelio R Paula03/2012
88552^182581-197554963Yves Minet09/2012
8856(2*10^54960-179)/354960Robert Price11/2017
885727449!!-1654959Robert Price06/2015
8858(22*10^54958-73)/354959Robert Price09/2017
88604^91283-3^9128354958Jean-Louis Charton01/2004
88592^182565+10754958Lelio R Paula11/2009
88612^182560+205354957Lelio R Paula12/2010
88622^182451-18245154924Henri Lifchitz10/2004
88632^182444+8154922Henri Lifchitz10/2005
88642^182433+7410554918Enzo Doria04/2016
886520^42206-524354912Enzo Doria03/2013
88662^182394+8554907Lelio R Paula02/2011
88672^182374-11228754901Enzo Doria06/2014
8868(47^32833-33^32833)/1454899Serge Batalov12/2016
88692^182363-11316754897Enzo Doria07/2014
88702^182359-11222154896Enzo Doria06/2014
8871(F(1905)^139-F(1904)^139)/F(1903)54893Wayne Halsdorf05/2010
8872(17*2^182274+1)/146754869Lelio R Paula01/2012
887318^43698-554853Lelio R Paula02/2013
88742^182209-189354851Yves Minet09/2012
88752^182194-344354846Yves Minet12/2016
887615023^4468+4468^1502354836Hans Havermann08/2016
88772^182135+9014354829Yves Minet10/2010
88782^182119+7433354824Enzo Doria04/2016
887914289^6860+6860^1428954818Hans Havermann08/2016
88803^114892-114892^354818Norbert Schneider03/2017
88812^182070-4735554809Lelio R Paula01/2011
88823^114869+7654807Lelio R Paula10/2012
88838^60681-60681^854801Norbert Schneider12/2016
88841897^16710+16710^189754777Serge Batalov05/2014
8885Phi(61868,59)54776Enzo Doria04/2012
8886113^26679+254775Lelio R Paula05/2013
88873^114789-7454769Lelio R Paula10/2012
888815^46567+9854768Lelio R Paula02/2013
8889(2*10^54767-71)/354767Robert Price01/2017
8890(298*10^54765-7)/354767Robert Price06/2017
8891(21*2^181931-1)/16999754763Lelio R Paula01/2014
88932^181913+2954762Henri Lifchitz06/2005
8892(31*10^54761-121)/954762Robert Price06/2016
88942^181887+18954754Lelio R Paula02/2011
88952^181874+181874^2-154750Robert Price04/2014
8896(2^181865+9)/733954743Lelio R Paula02/2012
88975^78314-9254740Lelio R Paula10/2012
8898(163*10^54727-1)/954729Serge Batalov12/2014
889915^46531+7454725Lelio R Paula02/2013
8900277^22400-34854712Enzo Doria07/2012
89016^70302+10154706Lelio R Paula10/2012
89023^114622-1040854689Enzo Doria02/2013
8904(23*2^181674+1)/48954688Lelio R Paula01/2012
89032^181669-155154688Yves Minet08/2012
8905(57352^11491-1)/5735154676Serge Batalov04/2015
8906(31*2^181629-1)/1073472154671Lelio R Paula01/2014
8907(F(1048)^251-F(1047)^251)/F(1046)54668Wayne Halsdorf05/2010
890813^49073+4654665Lelio R Paula01/2013
8909(57042^11491-1)/5704154649Serge Batalov04/2015
891120^42000+7354644Lelio R Paula02/2013
8910(67607*2^181517+1)/165554644Lelio R Paula05/2014
891233*10^54634+754636Robert Price07/2016
891320^41988+6154628Lelio R Paula01/2013
891420^41988-812354628Enzo Doria03/2013
89152^181420+2118154613Yves Minet03/2011
8916(19*10^54608+161)/954609Robert Price07/2016
891719^42696-2454598Lelio R Paula02/2013
8918(44*10^54596-503)/954597Robert Price10/2017
8919(74*10^54583+61)/954584Robert Price10/2015
89202^181316-9439554582Lelio R Paula09/2011
892114751^5006+5006^1475154572Hans Havermann08/2016
892214^47609+3954567Lelio R Paula02/2013
892312696^13295-13295^1269654559Norbert Schneider01/2018
8924(2^124979+lucasV(2,-2,124979)+1)/354552Paul Vanderveen12/2017
89263^114327-7454548Lelio R Paula10/2012
8925(44*10^54547-161)/954548Robert Price11/2017
8927gcd(V(995625),5*F(199125)*(F(199125)-1)+1)54546Serge Batalov04/2015
8928(17*10^54537-47)/354538Robert Price05/2017
89292^181155-1155*18115554534Henri Lifchitz02/2005
8930Phi(61672,83)54533Enzo Doria05/2012
8931(2*10^54527-197)/354527Robert Price11/2017
89329*2^181128+754526Lelio R Paula03/2014
893389*10^54518-754520Robert Price03/2017
89342^181090-11324754514Enzo Doria07/2014
893514031^7670+7670^1403154508Hans Havermann08/2016
893614210^6849+6849^1421054505Hans Havermann08/2016
89372^181043-19954500Lelio R Paula02/2011
893812^50499+554498Lelio R Paula01/2013
893912^50491+554489Lelio R Paula01/2013
89406^70016-14554484Lelio R Paula10/2012
894111^52313-960054479Enzo Doria02/2013
89422^64459+3^64459+5^64459+7^6445954475Henri Lifchitz08/2001
89432^180946-11104154471Enzo Doria05/2014
8944(64*10^54467+287)/954468Robert Price04/2016
8945(32*10^54458+319)/954459Robert Price10/2017
89465^77907-2*3^7790754455Mike Oakes11/2009
894720^41853-562354453Enzo Doria03/2013
894814^47506-7554448Lelio R Paula02/2013
8949(25*10^54443-67)/354444Robert Price11/2017
89502^180839-11343754438Enzo Doria08/2014
89513^114085+2854433Lelio R Paula10/2012
8952Phi(141230,10)54432Ray Chandler08/2009
89536^69946-5554429Lelio R Paula10/2012
8954p(11796)#/2-102454427Robert Price09/2017
89555*2^180796+354426Lelio R Paula03/2014
8956(23*2^180782-1)/9154421Lelio R Paula01/2014
89579*6^69928-754416Lelio R Paula09/2014
895892^27701-91^2770154399Robert Price08/2015
8959(2^180687-3)*6-754393Gilbert Mozzo04/2016
8960(5*10^54388-11)/354389Erik Branger12/2013
896220^41799-304354382Enzo Doria03/2013
896113860^8387+8387^1386054382Hans Havermann08/2016
8963(F(19)^15017-F(18)^15017)/F(17)54378Wayne Halsdorf05/2010
89647^64329-1854365Lelio R Paula10/2012
89652^180551-96754352Yves Minet01/2012
896615^46209-7454347Lelio R Paula02/2013
896710^54345+2973954346Patrick De Geest08/2013
896810^54345-14138154345Patrick De Geest09/2013
8969lucasU(2098,1,16360)-lucasU(2098,1,16359)54342Mike Oakes05/2009
8970177^24171-254336Lelio R Paula10/2017
89712^180496+1554335Lelio R Paula02/2011
89721845^16636+16636^184554334Serge Batalov05/2014
897311^52169-7054329Lelio R Paula01/2013
89742^180446-403154320Yves Minet02/2018
897513693^9262+9262^1369354317Hans Havermann06/2016
89762^180429-11310154315Enzo Doria07/2014
89772^180423-11205154313Enzo Doria05/2014
897816112^2349+2349^1611254312Hans Havermann06/2016
8979(79^28621-1)/7854311Paul Bourdelais08/2017
8980(13^48751+4^48751)/1754305Robert Price05/2013
89812^180370+1291554297Lelio R Paula09/2012
8982(10^54290+41)/354290Robert Price01/2017
898315108^3917+3917^1510854283Hans Havermann06/2016
89842^180317-301954281Yves Minet10/2014
89852^180314+85554280Lelio R Paula10/2009
898619^42425+9454252Lelio R Paula02/2013
89872^180180-100544954240Paul Bourdelais11/2012
89892^180173-277354238Yves Minet07/2014
898813367^11418+11418^1336754238Hans Havermann06/2016
8990427^20614+20614^42754224Norbert Schneider06/2016
89912^180124-8795954223Gary Barnes08/2009
89922^180111-11310154219Enzo Doria07/2014
89932^180101-11487154216Enzo Doria05/2015
8994(11*2^180099+1)/5161754212Lelio R Paula07/2012
89952^180070+46554207Lelio R Paula09/2012
899613683^9154+9154^1368354207Hans Havermann06/2016
8997810522513*2^180009-9531*2^9531-154198Jiong Sun12/2003
89982^180014+61354190Jason Earls04/2008
89992^180007+10154188Lelio R Paula02/2011
90002^180001+4187754186Jim Fougeron08/2002


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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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