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 ?
65012^227303-11061768426Enzo Doria05/2014
65027^80963+6668422Lelio R Paula07/2013
65032^227290+7384968422Enzo Doria04/2016
6504(14^59693-1)/1368415Paul Bourdelais06/2008
65052^227256-278624968411Enzo Doria03/2016
65078*10^68400-768401Dmitry Domanov11/2010
6506(15*2^227228-1)/58368401Lelio R Paula01/2014
65082^227210+186916968398Enzo Doria05/2016
65092^227159-183863568382Enzo Doria05/2015
651044*10^68368+368370Robert Price08/2017
65112^227115-780768369Lelio R Paula10/2009
65122^227078-4735568358Lelio R Paula04/2012
6513(2^227063-1017)/34968351Lelio R Paula04/2012
65142^227057+14809168351Lelio R Paula04/2012
65152^227046+18768348Lelio R Paula02/2012
65169*10^68331+5968332Robert Price10/2017
651711^65608-72068324Enzo Doria11/2012
6518(32*10^68320+319)/968321Robert Price10/2017
651933408!2-2^33408-168315Joe McLean05/2017
65202^226894-12368302Lelio R Paula02/2012
652110^68297+14155968298Patrick De Geest05/2013
652210^68297-9368297Robert Price05/2011
6523680^24107-679^2410768284Jean-Louis Charton07/2010
652412^63267+5968277Lelio R Paula07/2013
65252^226785-115968270Yves Minet11/2012
65267^80769+9068258Lelio R Paula07/2013
6527(88*10^68256-1)/368258Robert Price10/2017
65282^226741+6658768256Yves Minet10/2010
65292^226720-11240368250Enzo Doria06/2014
6530(78557*2^226694+1)/368247Lelio R Paula06/2014
6531(83*10^68231+7)/968232Robert Price10/2015
653265^37636+1668231Lelio R Paula01/2016
65335^97615-4^(97615+1)68230Robert Price04/2016
653412^63200-4368205Lelio R Paula07/2013
6535-330*Bern(21940)/22379062073368201Serge Batalov04/2015
65363^142925+868068193Lelio R Paula06/2013
65373*2^226512-768188Lelio R Paula04/2014
653814^59484+5768177Lelio R Paula08/2013
653911^65438-219068147Enzo Doria12/2012
654091^34784-268144Lelio R Paula09/2013
6541(2^226336-3)*6-768135Gilbert Mozzo06/2016
6542(22*10^68133-37)/368134Robert Price05/2017
65435^97476+3668133Lelio R Paula06/2013
65443*5^97474-268132Lelio R Paula09/2014
654512^63130+4968129Lelio R Paula07/2013
65462^226281+538568118Lelio R Paula04/2012
65472^226257-304968111Yves Minet10/2014
6548(28*10^68107-43)/368108Robert Price04/2016
65492^226243-258768106Yves Minet07/2014
655020^52346-1168104Lelio R Paula09/2013
65512^226205-9968095Lelio R Paula02/2012
65522^226187-4968090Lelio R Paula02/2012
65533^142708+7668090Lelio R Paula06/2013
65547*10^68088-8968089Robert Price01/2017
65552^226154+7183968080Enzo Doria04/2016
6556(10^68078+59)/368078Serge Batalov12/2014
655814^59387+6968066Lelio R Paula08/2013
65572^226108-11342968066Enzo Doria07/2014
6559(62*10^68059-197)/968060Robert Price10/2017
6560(24^49307-1)/2368053Robert Price04/2012
656115^57859-2868048Lelio R Paula08/2013
6562(509203*2^226003-1)/1368039Lelio R Paula04/2015
65632^226015-11136168038Enzo Doria05/2014
6564(10^(2*34016+1)+72*10^34016-1)/968033Robert Price09/2017
65654*10^68020+9168021Robert Price11/2017
6566156*(10^(4*17000)-1)/101-168001Robert Price05/2014
65672^225878-101767997Lelio R Paula04/2012
65683*8^75289+5^75289-3*4^75289+3*2^7528967994Mike Oakes11/2010
65693*2^225865+567993Lelio R Paula04/2014
657011^65284-582067987Enzo Doria01/2013
657119^53166+7067987Lelio R Paula08/2013
65722^225837+7540767984Enzo Doria04/2016
65733^142464-11265467973Enzo Doria06/2014
65742^225777+9567966Lelio R Paula02/2012
6575(2^225641-1017)/13881567920Lelio R Paula04/2012
65762^225609-1844567916Enzo Doria05/2013
65772^225542-17767895Lelio R Paula02/2012
65782^225536-2967894Henri Lifchitz05/2005
657911^65190-339067889Enzo Doria12/2012
65803^142249-2^(142249-1)67871Robert Price01/2016
658111^65168-483067866Enzo Doria01/2013
658210^67863+5862767864Patrick De Geest01/2016
658310^67863-1167863Robert Price05/2011
6584(1!)^2+(2!)^2+(3!)^2+...+(9566!)^267856T. D. Noe02/2006
6585(19*2^225357-1)/1167840Lelio R Paula01/2014
65869*6^87164-767828Lelio R Paula09/2014
6587131^32034+13067825Norbert Schneider03/2015
6588(29*2^225314+1)/1088167824Lelio R Paula08/2012
6589(134*10^67816+7)/367818Robert Price02/2017
65902^225261+85567811Lelio R Paula04/2012
6591(29*2^225252-1)/293367806Lelio R Paula01/2014
6592(4*10^67796+23)/967796Robert Price11/2014
6593(23*2^225177+1)/3167785Lelio R Paula08/2012
6594(4*10^67784+149)/967784Robert Price03/2017
65952^225120+15167768Lelio R Paula02/2012
6596(44^41233+1)/4567763Robert Price11/2013
65978*10^67742+967743Dmitry Domanov11/2010
65982^224977+108967725Lelio R Paula04/2012
6599(2^224950+5)/1950967713Lelio R Paula04/2012
660011^65011-597067702Enzo Doria01/2013
660188*10^67691+767693Robert Price11/2016
660211^65000-714067691Enzo Doria01/2013
66032^224841+5967684Lelio R Paula02/2012
660433129!2+2^3312967684Robert Price09/2015
66052^224827+841567680Lelio R Paula02/2013
6606(9913*2^224821-1)/1982567678Lelio R Paula04/2015
66072^224815-4978967677Henri Lifchitz04/2005
6608(43*10^67664+11)/967665Robert Price06/2015
6609(292*10^67659-1)/367661Robert Price01/2017
6610(17*2^224766+1)/2900767659Lelio R Paula06/2012
66112^224744+57729457567655Lelio R Paula02/2016
6612((1+sqrt(7)+sqrt(6))^45863-1)*((1+sqrt(7)-sqrt(6))^45863-1)*((1-sqrt(7)+sqrt(6))^45863-1)*((1-sqrt(767653Mike Oakes05/2009
6613(2^224721+78557)/173967645Lelio R Paula05/2012
66142^224700+191567642Lelio R Paula04/2012
6615(29*2^224694-1)/19890567636Lelio R Paula01/2014
66162^224658-9367629Lelio R Paula02/2012
66172^224624-1307767619Enzo Doria10/2012
661818^53860-331967609Enzo Doria03/2013
6619(21181*2^224570+1)/567606Lelio R Paula06/2014
66202^224578-11104167605Enzo Doria05/2014
66212^224569-11323367603Enzo Doria07/2014
66222^224562-11317167600Enzo Doria07/2014
66232^224556-11312967599Enzo Doria07/2014
66246*7^79980-567592Lelio R Paula09/2014
6625(6883*2^224523-1)/1603167588Lelio R Paula04/2015
662610^67579+16477967580Patrick De Geest07/2017
6628(52*10^67578-61)/967579Robert Price09/2015
662710^67579-40167579Robert Price06/2017
6629(17^54919-1)/1667574Paul Bourdelais03/2010
6630(2^224363-9)/195167537Lelio R Paula04/2012
6631(709*10^67517-7)/967519Robert Price09/2017
663247719!3-5904967516Robert Price12/2015
6633(22^50287+1)/2367506Robert Price06/2013
66343*10^67499+6767500Robert Price11/2017
663511^64811-582067494Enzo Doria01/2013
6636131^31870+31870^13167478Serge Batalov05/2014
66379*10^67468+767469Dmitry Domanov11/2010
6638(31*2^224115-1)/4772367463Lelio R Paula01/2014
6639128^32001+32001^12867433Serge Batalov05/2014
6640(89*10^67431-17)/967432Robert Price11/2015
66412^223912-11105967405Enzo Doria05/2014
66432^223913+7369767405Enzo Doria04/2016
6642(2*10^67405-23)/367405Robert Price09/2017
6645(10^67404+179)/967404Serge Batalov12/2014
664418738^3955+3955^1873867404Hans Havermann09/2016
66469*7^79728-267379Lelio R Paula09/2014
6647(28*10^67378-43)/367379Robert Price04/2016
6648(3^141234-7)/43024128267378Lelio R Paula04/2012
6649211^28988-267377Lelio R Paula09/2013
66504*10^67375+9167376Robert Price11/2017
66512^223793-1806967369Enzo Doria05/2013
66522^223777-252167364Yves Minet07/2014
6653(15185*2^223775-1)/1518367363Lelio R Paula04/2015
6654(2^223759-lucasV(1,2,223759)+1)/267358Mike Oakes11/2016
6655V(340138)67336Serge Batalov03/2015
665643125^14528-10667334Enzo Doria07/2012
66578*10^67302-5167303Robert Price10/2017
665817458^7153+7153^1745867292Hans Havermann08/2016
665916366^12925+12925^1636667288Hans Havermann08/2016
666037^42906-267286Lelio R Paula08/2013
666118^53592-1367273Lelio R Paula08/2013
6662V(396221)67256Serge Batalov03/2015
6663(34*10^67245-7)/9/3^4/193/138153767236Makoto Morimoto04/2016
6664(14*10^67235-101)/367236Robert Price04/2017
666553^38993-52^3899367235Robert Price01/2013
6666(2^223349-7)/648567231Lelio R Paula04/2012
66672^223333+31567230Lelio R Paula04/2012
66682^223278-11104167214Enzo Doria05/2014
6669(2347*2^223281+1)/(3*5*197*1213*1783)67208Jens K. Andersen09/2007
66702^223256-4567207Lelio R Paula02/2012
66712^223253-11211167206Enzo Doria06/2014
667218407^4474+4474^1840767199Hans Havermann08/2016
667347^40182+40182^4767189Norbert Schneider11/2014
667413^60309+9467181Lelio R Paula07/2013
667511^64503-8467173Lelio R Paula07/2013
66763^140781+23667170Lelio R Paula06/2013
66772^223107-86505767162Paul Bourdelais03/2013
66782^223100-5967160Lelio R Paula02/2012
66792^223087+7196367156Enzo Doria04/2016
668118^53481-377967134Enzo Doria03/2013
6680(326^26713-1)/32567134Eric Chen09/2017
66824^111473-6257367114Mike Oakes02/2011
66832^222943+2967113Henri Lifchitz08/2005
6684(2^222939-9)/10367110Lelio R Paula04/2012
66852^222862-45916167089Enzo Doria05/2015
66862^222828+819367078Lelio R Paula04/2012
66873^140570+266067069Lelio R Paula06/2013
66882^222744+85567053Lelio R Paula04/2012
668913^60189+8467048Lelio R Paula07/2013
66902*10^67043-5167044Robert Price11/2017
66912^222701+57729457567040Lelio R Paula02/2016
6692(13*10^67038-31)/967039Serge Batalov11/2008
6693(151*10^67027-7)/967029Robert Price07/2017
6694(58695*2^222620-1)/6167019Lelio R Paula04/2015
66952^222614-11104167014Enzo Doria05/2014
66962^222520-190766986Yves Minet03/2013
6697(4^111231+23)/366968Robert Price02/2017
66982^222408-11127566952Enzo Doria05/2014
669910^66949-9^6694966949Jean-Louis Charton12/2005
67002^222378-100566943Lelio R Paula04/2012
6701(9*2^222366+1)/7366938Lelio R Paula08/2012
67027^79202-6^(79202+1)66934Robert Price06/2016
67032^222325-11225566927Enzo Doria06/2014
670420^51428+3366910Lelio R Paula08/2013
67062^222224-1850966897Enzo Doria05/2013
6705(38*10^66896+187)/966897Robert Price11/2017
67072^222192-86968810566887Lelio R Paula02/2016
6708(19*10^66878-43)/366879Robert Price10/2017
670911^64219-6466878Lelio R Paula07/2013
67102^222151-1729566875Lelio R Paula04/2012
6711gcd(V(799885),5*F(159977)*(F(159977)+1)+1)66867Serge Batalov04/2015
67122^222085-11103166855Enzo Doria05/2014
67138*10^66848-1366849Robert Price05/2017
6714(3^140087+4)/1366838Lelio R Paula04/2012
6715(3^140102+4)/884360943766836Lelio R Paula04/2012
671619^52265+5266835Lelio R Paula08/2013
67172*10^66826-2766827Robert Price02/2017
67184*6^85867+566819Lelio R Paula09/2014
671915^56800+866802Lelio R Paula08/2013
6720(2^221891-2^110946+1)/56679611/2006
672110^66793+6944166794Patrick De Geest05/2013
672210^66793-6366793Robert Price05/2011
672335^43256-170466791Enzo Doria03/2013
67243^139976+2^(139976-1)66786Robert Price05/2016
67257^79023-5466783Lelio R Paula06/2013
6726104^33109-10366782Norbert Schneider11/2016
6727(34*10^66778-7)/9/37/35890166772Makoto Morimoto04/2016
6728(-lucasV(1,2,443622)+2)/(7*281*487)66766Mike Oakes04/2017
67292^221768+18366759Lelio R Paula02/2012
6730gcd(V(1197915),5*F(239583)*(F(239583)+1)+1)66759Serge Batalov04/2015
6731(154*10^66755-1)/966757Serge Batalov12/2014
673211^64097+4866751Lelio R Paula07/2013
6733(lucasV(1,2,443547)-2)/(7*13*79*1327*221773)66749Mike Oakes04/2017
6734(19*10^66748+413)/966749Robert Price10/2017
6735(3*2^221696-1)/1366737Lelio R Paula01/2014
67368*6^85758-766734Lelio R Paula09/2014
6737135^31325+266733Lelio R Paula05/2013
6738(49*10^66729+41)/966730Robert Price07/2015
6739(349*10^66720-7)/966722Robert Price03/2017
6740(-lucasV(1,2,443285)+2)/(3^2*307)66718Mike Oakes04/2017
6741(25*10^66714+71)/366715Robert Price01/2017
674211^64061-78066713Enzo Doria11/2012
67437^78929+466703Lelio R Paula06/2013
674411^64048-93066700Enzo Doria11/2012
67452*7^78921+566697Lelio R Paula09/2014
6746(25*2^221526+1)/40966685Lelio R Paula08/2012
6747(2^221509-1)/29239188166673Jens K. Andersen02/2009
67482^221479+7295366672Enzo Doria04/2016
674910^66666+27540366667Patrick De Geest03/2010
675010^66666-11552166666Patrick De Geest03/2010


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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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