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 ?
6501(8*10^69674-53)/969674Robert Price11/2014
6502(44*10^69663-413)/969664Robert Price10/2017
6503(77*10^69656-23)/969657Robert Price10/2015
65046^89509+13169652Lelio R Paula09/2013
6505(78557*2^231349+1)/3569647Lelio R Paula06/2014
6506(11*10^69645+19)/369646Robert Price03/2016
650711^66875-2869644Lelio R Paula09/2013
65082^231347+7148369643Enzo Doria04/2016
6509(14^60763+3^60763)/1769641Robert Price04/2013
6510(4*10^69626+173)/369627Robert Price01/2017
65112^231289+25569625Lelio R Paula04/2012
65122^231234-11291369609Enzo Doria06/2014
6513(265*10^69602-7)/369604Robert Price07/2016
65142^231182-11284169593Enzo Doria06/2014
6515(15*2^231129+1)/2369577Lelio R Paula08/2012
65163^145806-2869568Lelio R Paula09/2013
6517(265*10^69554-7)/369556Robert Price07/2016
65182^231052-11315969554Enzo Doria07/2014
651911^66784-869549Lelio R Paula09/2013
6520Phi(104409,10)/229699969546Maksym Voznyy07/2015
65212^231016-11052369543Enzo Doria05/2014
65222^231014+57729457569543Lelio R Paula02/2016
652314^60658+6769522Lelio R Paula09/2013
65245^99418+3669491Lelio R Paula06/2013
65257^82203-3069470Lelio R Paula09/2013
6526(63^38609-1)/6269469Paul Bourdelais08/2017
65275^99359-2^9936069449Mike Oakes12/2010
6528(29*2^230684+1)/139569442Lelio R Paula08/2012
6529(19*10^69424+77)/369425Robert Price08/2016
653019^54287-9669420Lelio R Paula09/2013
65312^230541+5890569400Lelio R Paula04/2012
65322^230506+1270569390Lelio R Paula02/2013
65338*6^89156-569378Lelio R Paula09/2014
65342^230438-11134769369Enzo Doria05/2014
65352^230428-9969366Lelio R Paula02/2012
6536(62^38699+1)/6369362Paul Bourdelais08/2017
65373*10^69354+1769355Robert Price03/2017
6538(493*10^69340-7)/969342Robert Price07/2016
6539(41*10^69321+373)/969322Robert Price04/2017
65406^89072+5369312Lelio R Paula09/2013
6541155^31639+269300Lelio R Paula05/2013
65423*7^81965-469269Lelio R Paula09/2014
6543(16*10^69265+41)/369266Robert Price10/2017
6544(86*10^69260-77)/969261Robert Price05/2016
65459*5^99087+469260Lelio R Paula09/2014
65463^145145+266069252Lelio R Paula09/2013
654711^66492-114069245Enzo Doria11/2012
65485*3^145129-469245Lelio R Paula04/2014
65497*3^145126+869244Lelio R Paula04/2014
655011^66480-237069232Enzo Doria12/2012
65512^229962-6569226Lelio R Paula02/2012
65522^229958-11073369225Enzo Doria05/2014
6553V(332407)69225Serge Batalov03/2015
65546^88959+769224Lelio R Paula09/2013
655515^58855-9469219Lelio R Paula09/2013
6556(2^229838+47)/1208169185Lelio R Paula04/2012
65573^144952+9869160Lelio R Paula09/2013
65585^98941-7269157Lelio R Paula06/2013
6559(17*2^229604-1)/22969117Lelio R Paula01/2014
65602^229585-106369112Yves Minet11/2012
6561(13*2^229567-1)/1969107Lelio R Paula01/2014
6562(13*2^229393-1)/569055Lelio R Paula01/2014
6563(53*10^69050-17)/969051Robert Price09/2015
6564(43*10^69048+47)/969049Robert Price12/2017
65652^229305-186853369028Enzo Doria04/2016
65662^229297+138569026Lelio R Paula04/2012
656718^54986-244169023Enzo Doria03/2013
6568(34*10^69021-7)/9/3/6769020Makoto Morimoto04/2016
65695^98736-1463669014Enzo Doria02/2013
6570(13^61949-5^61949)/869007Robert Price03/2013
6571(2^229227+5)/61169002Lelio R Paula04/2012
65722^229216-11327969001Enzo Doria07/2014
657310^68994+5191368995Patrick De Geest03/2016
657510^68994-10^5814-168994Serge Batalov01/2011
657410^68994-8294768994Patrick De Geest03/2016
6576(17*2^229136-1)/238168975Lelio R Paula01/2014
65772^229113+10768970Lelio R Paula02/2012
657811^66202-441068943Enzo Doria01/2013
657912^63883+568942Lelio R Paula07/2013
6580(9913*2^229002-1)/39990368935Lelio R Paula04/2015
65812^228962-11158168925Enzo Doria05/2014
65822^228944+8168920Henri Lifchitz01/2007
658311^66174-5468914Lelio R Paula09/2013
65842^228913-11126568910Enzo Doria05/2014
65852^228902+7351968907Enzo Doria04/2016
6586(47*2^228884+1)/6368901Lelio R Paula04/2015
65872^228821+7642768882Enzo Doria05/2016
65883^144340+5068868Lelio R Paula09/2013
65892^228758-11296768864Enzo Doria06/2014
65902^228743-11137968859Enzo Doria05/2014
65912^228741-11091168858Enzo Doria05/2014
6593lucasU(1926,1,20964)-lucasU(1926,1,20963)68857Mike Oakes05/2009
65923*5^98511-868857Lelio R Paula09/2014
65942^228717+46768851Lelio R Paula02/2011
6595Phi(153218,10)/2211855049/23592660859/49771411729168849Maksym Voznyy10/2011
6596(509203*2^228665-1)/3568840Lelio R Paula04/2015
65978^76213-7^7621368828Ananda Tallur & Jean-Louis Charton11/2003
659811^66074-105068809Enzo Doria11/2012
6599(68*10^68798-11)/368800Robert Price10/2017
66002^228484+18168781Lelio R Paula02/2012
66012^228479-5869568780Lelio R Paula04/2012
66022^228465-1585368775Enzo Doria04/2013
660311^66040-540068774Enzo Doria01/2013
6604(13*2^228441-1)/57568766Lelio R Paula01/2014
6605(17*2^228393+1)/29568752Lelio R Paula08/2012
66062*10^68744+4168745Robert Price01/2017
660711^66011-15068744Enzo Doria08/2012
6608(13*2^228304-1)/8168726Lelio R Paula01/2014
66092^228295-11107968724Enzo Doria05/2014
6611(3^144039+7)/2268723Lelio R Paula04/2012
6610(8*10^68722+49)/368723Robert Price03/2016
6612(35*10^68718+1)/968719Serge Batalov11/2010
66132^228271-22827168717Henri Lifchitz11/2004
66142^228257+8287568713Lelio R Paula02/2013
66153^144013+4068712Lelio R Paula09/2013
661613^61671-8668699Lelio R Paula09/2013
6617(46*10^68698+683)/968699Robert Price12/2017
661817^55828-7268694Lelio R Paula09/2013
66196^88259+6168679Lelio R Paula09/2013
662018^54699-568663Lelio R Paula09/2013
662133^45216+268662Lelio R Paula05/2013
6623(2^228073-5)/368657Lelio R Paula04/2012
6622(2^(6*38012+1)-5)/368657Kevin Acres11/2013
66242^228055-11160768652Enzo Doria05/2014
66252^228054-11476168652Enzo Doria05/2015
66262^228041+118568648Lelio R Paula04/2012
66272^228040-103768647Yves Minet11/2012
66282*F(328450)-168642Henri Lifchitz12/2009
66295^98201-3468640Lelio R Paula06/2013
66309^71910+3*8^71910-2*4^71910-3*2^7191068620Mike Oakes12/2010
66317*2^227780-368570Lelio R Paula04/2014
66322^227733-12168555Lelio R Paula02/2012
66332^227702-1696768546Enzo Doria05/2013
66342^227689-11165568542Enzo Doria05/2014
6635gcd(V(823915),5*F(164783)*(F(164783)-1)+1)68536Serge Batalov04/2015
66365^98051+268535Ray Chandler07/2011
66375*10^68524+5168525Robert Price01/2017
6638(11*10^68520-149)/368521Robert Price01/2017
663919^53573-7868507Lelio R Paula09/2013
6640(68*10^68504+13)/968505Ray Chandler10/2010
66419*5^98003+468503Lelio R Paula09/2014
66422^227528+5168493Lelio R Paula02/2012
66433^143497+868466Lelio R Paula04/2012
66442^227430-9568464Lelio R Paula02/2012
6645(8*10^68455+13)/368456Robert Price11/2017
66463*5^97934-268454Lelio R Paula09/2014
664720^52613+7768452Lelio R Paula09/2013
66482^227371+3276968446Lelio R Paula04/2012
6649(3^143465+4)/2127042006768440Lelio R Paula04/2012
6650CopelandErdos(68433)68433Eric W. Weisstein08/2013
66512^227323+7543168432Enzo Doria04/2016
66522^227314-196568429Lelio R Paula04/2012
66532^227303-11061768426Enzo Doria05/2014
66547^80963+6668422Lelio R Paula07/2013
66552^227290+7384968422Enzo Doria04/2016
6656(14^59693-1)/1368415Paul Bourdelais06/2008
66572^227256-278624968411Enzo Doria03/2016
66598*10^68400-768401Dmitry Domanov11/2010
6658(15*2^227228-1)/58368401Lelio R Paula01/2014
66602^227210+186916968398Enzo Doria05/2016
66612^227159-183863568382Enzo Doria05/2015
666244*10^68368+368370Robert Price08/2017
66632^227115-780768369Lelio R Paula10/2009
66642^227078-4735568358Lelio R Paula04/2012
6665(2^227063-1017)/34968351Lelio R Paula04/2012
66662^227057+14809168351Lelio R Paula04/2012
66672^227046+18768348Lelio R Paula02/2012
66689*10^68331+5968332Robert Price10/2017
666911^65608-72068324Enzo Doria11/2012
6670(32*10^68320+319)/968321Robert Price10/2017
667133408!2-2^33408-168315Joe McLean05/2017
66722^226894-12368302Lelio R Paula02/2012
667310^68297+14155968298Patrick De Geest05/2013
667410^68297-9368297Robert Price05/2011
6675680^24107-679^2410768284Jean-Louis Charton07/2010
667612^63267+5968277Lelio R Paula07/2013
66772^226785-115968270Yves Minet11/2012
66787^80769+9068258Lelio R Paula07/2013
6679(88*10^68256-1)/368258Robert Price10/2017
66802^226741+6658768256Yves Minet10/2010
66812^226720-11240368250Enzo Doria06/2014
6682(78557*2^226694+1)/368247Lelio R Paula06/2014
6683(83*10^68231+7)/968232Robert Price10/2015
668465^37636+1668231Lelio R Paula01/2016
66855^97615-4^(97615+1)68230Robert Price04/2016
668612^63200-4368205Lelio R Paula07/2013
6687-330*Bern(21940)/22379062073368201Serge Batalov04/2015
66883^142925+868068193Lelio R Paula06/2013
66893*2^226512-768188Lelio R Paula04/2014
669014^59484+5768177Lelio R Paula08/2013
669111^65438-219068147Enzo Doria12/2012
669291^34784-268144Lelio R Paula09/2013
6693(2^226336-3)*6-768135Gilbert Mozzo06/2016
6694(22*10^68133-37)/368134Robert Price05/2017
66955^97476+3668133Lelio R Paula06/2013
66963*5^97474-268132Lelio R Paula09/2014
669712^63130+4968129Lelio R Paula07/2013
66982^226281+538568118Lelio R Paula04/2012
66992^226257-304968111Yves Minet10/2014
6700(28*10^68107-43)/368108Robert Price04/2016
67012^226243-258768106Yves Minet07/2014
670220^52346-1168104Lelio R Paula09/2013
67032^226205-9968095Lelio R Paula02/2012
67042^226187-4968090Lelio R Paula02/2012
67053^142708+7668090Lelio R Paula06/2013
67067*10^68088-8968089Robert Price01/2017
67072^226154+7183968080Enzo Doria04/2016
6708(10^68078+59)/368078Serge Batalov12/2014
671014^59387+6968066Lelio R Paula08/2013
67092^226108-11342968066Enzo Doria07/2014
6711(62*10^68059-197)/968060Robert Price10/2017
6712(24^49307-1)/2368053Robert Price04/2012
671315^57859-2868048Lelio R Paula08/2013
6714(509203*2^226003-1)/1368039Lelio R Paula04/2015
67152^226015-11136168038Enzo Doria05/2014
6716(10^(2*34016+1)+72*10^34016-1)/968033Robert Price09/2017
67174*10^68020+9168021Robert Price11/2017
6718156*(10^(4*17000)-1)/101-168001Robert Price05/2014
67192^225878-101767997Lelio R Paula04/2012
67203*8^75289+5^75289-3*4^75289+3*2^7528967994Mike Oakes11/2010
67213*2^225865+567993Lelio R Paula04/2014
672311^65284-582067987Enzo Doria01/2013
672219^53166+7067987Lelio R Paula08/2013
67242^225837+7540767984Enzo Doria04/2016
67253^142464-11265467973Enzo Doria06/2014
67262^225777+9567966Lelio R Paula02/2012
6727(2^225641-1017)/13881567920Lelio R Paula04/2012
67282^225609-1844567916Enzo Doria05/2013
67292^225542-17767895Lelio R Paula02/2012
67302^225536-2967894Henri Lifchitz05/2005
673111^65190-339067889Enzo Doria12/2012
67323^142249-2^(142249-1)67871Robert Price01/2016
673311^65168-483067866Enzo Doria01/2013
673410^67863+5862767864Patrick De Geest01/2016
673510^67863-1167863Robert Price05/2011
6736(1!)^2+(2!)^2+(3!)^2+...+(9566!)^267856T. D. Noe02/2006
6737(19*2^225357-1)/1167840Lelio R Paula01/2014
67389*6^87164-767828Lelio R Paula09/2014
6739131^32034+13067825Norbert Schneider03/2015
6740(29*2^225314+1)/1088167824Lelio R Paula08/2012
6741(134*10^67816+7)/367818Robert Price02/2017
67422^225261+85567811Lelio R Paula04/2012
6743(29*2^225252-1)/293367806Lelio R Paula01/2014
6744(4*10^67796+23)/967796Robert Price11/2014
6745(23*2^225177+1)/3167785Lelio R Paula08/2012
6746(4*10^67784+149)/967784Robert Price03/2017
67472^225120+15167768Lelio R Paula02/2012
6748(44^41233+1)/4567763Robert Price11/2013
67498*10^67742+967743Dmitry Domanov11/2010
67502^224977+108967725Lelio R Paula04/2012


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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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