PRP Records

Probable Primes Top 10000

(180278 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 ?
6251-330*Bern(21940)/22379062073368201Serge Batalov04/2015
62523^142925+868068193Lelio R Paula06/2013
62533*2^226512-768188Lelio R Paula04/2014
625414^59484+5768177Lelio R Paula08/2013
625511^65438-219068147Enzo Doria12/2012
625691^34784-268144Lelio R Paula09/2013
6257(2^226336-3)*6-768135Gilbert Mozzo06/2016
6258(22*10^68133-37)/368134Robert Price05/2017
62595^97476+3668133Lelio R Paula06/2013
62603*5^97474-268132Lelio R Paula09/2014
626112^63130+4968129Lelio R Paula07/2013
62622^226281+538568118Lelio R Paula04/2012
62632^226257-304968111Yves Minet10/2014
6264(28*10^68107-43)/368108Robert Price04/2016
62652^226243-258768106Yves Minet07/2014
626620^52346-1168104Lelio R Paula09/2013
62672^226205-9968095Lelio R Paula02/2012
62682^226187-4968090Lelio R Paula02/2012
62693^142708+7668090Lelio R Paula06/2013
62707*10^68088-8968089Robert Price01/2017
62712^226154+7183968080Enzo Doria04/2016
6272(10^68078+59)/368078Serge Batalov12/2014
627414^59387+6968066Lelio R Paula08/2013
62732^226108-11342968066Enzo Doria07/2014
6275(24^49307-1)/2368053Robert Price04/2012
627615^57859-2868048Lelio R Paula08/2013
6277(509203*2^226003-1)/1368039Lelio R Paula04/2015
62782^226015-11136168038Enzo Doria05/2014
6279156*(10^(4*17000)-1)/101-168001Robert Price05/2014
62802^225878-101767997Lelio R Paula04/2012
62813*8^75289+5^75289-3*4^75289+3*2^7528967994Mike Oakes11/2010
62823*2^225865+567993Lelio R Paula04/2014
628311^65284-582067987Enzo Doria01/2013
628419^53166+7067987Lelio R Paula08/2013
62852^225837+7540767984Enzo Doria04/2016
62863^142464-11265467973Enzo Doria06/2014
62872^225777+9567966Lelio R Paula02/2012
6288(2^225641-1017)/13881567920Lelio R Paula04/2012
62892^225609-1844567916Enzo Doria05/2013
62902^225542-17767895Lelio R Paula02/2012
62912^225536-2967894Henri Lifchitz05/2005
629211^65190-339067889Enzo Doria12/2012
62933^142249-2^(142249-1)67871Robert Price01/2016
629411^65168-483067866Enzo Doria01/2013
629510^67863+5862767864Patrick De Geest01/2016
629610^67863-1167863Robert Price05/2011
6297(1!)^2+(2!)^2+(3!)^2+...+(9566!)^267856T. D. Noe02/2006
6298(19*2^225357-1)/1167840Lelio R Paula01/2014
62999*6^87164-767828Lelio R Paula09/2014
6300131^32034+13067825Norbert Schneider03/2015
6301(29*2^225314+1)/1088167824Lelio R Paula08/2012
6302(134*10^67816+7)/367818Robert Price02/2017
63032^225261+85567811Lelio R Paula04/2012
6304(29*2^225252-1)/293367806Lelio R Paula01/2014
6305(4*10^67796+23)/967796Robert Price11/2014
6306(23*2^225177+1)/3167785Lelio R Paula08/2012
6307(4*10^67784+149)/967784Robert Price03/2017
63082^225120+15167768Lelio R Paula02/2012
6309(44^41233+1)/4567763Robert Price11/2013
63108*10^67742+967743Dmitry Domanov11/2010
63112^224977+108967725Lelio R Paula04/2012
6312(2^224950+5)/1950967713Lelio R Paula04/2012
631311^65011-597067702Enzo Doria01/2013
631488*10^67691+767693Robert Price11/2016
631511^65000-714067691Enzo Doria01/2013
63162^224841+5967684Lelio R Paula02/2012
631733129!2+2^3312967684Robert Price09/2015
63182^224827+841567680Lelio R Paula02/2013
6319(9913*2^224821-1)/1982567678Lelio R Paula04/2015
63202^224815-4978967677Henri Lifchitz04/2005
6321(43*10^67664+11)/967665Robert Price06/2015
6322(292*10^67659-1)/367661Robert Price01/2017
6323(17*2^224766+1)/2900767659Lelio R Paula06/2012
63242^224744+57729457567655Lelio R Paula02/2016
6325((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
6326(2^224721+78557)/173967645Lelio R Paula05/2012
63272^224700+191567642Lelio R Paula04/2012
6328(29*2^224694-1)/19890567636Lelio R Paula01/2014
63292^224658-9367629Lelio R Paula02/2012
63302^224624-1307767619Enzo Doria10/2012
633118^53860-331967609Enzo Doria03/2013
6332(21181*2^224570+1)/567606Lelio R Paula06/2014
63332^224578-11104167605Enzo Doria05/2014
63342^224569-11323367603Enzo Doria07/2014
63352^224562-11317167600Enzo Doria07/2014
63362^224556-11312967599Enzo Doria07/2014
63376*7^79980-567592Lelio R Paula09/2014
6338(6883*2^224523-1)/1603167588Lelio R Paula04/2015
633910^67579+16477967580Patrick De Geest07/2017
6341(52*10^67578-61)/967579Robert Price09/2015
634010^67579-40167579Robert Price06/2017
6342(17^54919-1)/1667574Paul Bourdelais03/2010
6343(2^224363-9)/195167537Lelio R Paula04/2012
634447719!3-5904967516Robert Price12/2015
6345(22^50287+1)/2367506Robert Price06/2013
634611^64811-582067494Enzo Doria01/2013
6347131^31870+31870^13167478Serge Batalov05/2014
63489*10^67468+767469Dmitry Domanov11/2010
6349(31*2^224115-1)/4772367463Lelio R Paula01/2014
6350128^32001+32001^12867433Serge Batalov05/2014
6351(89*10^67431-17)/967432Robert Price11/2015
63522^223912-11105967405Enzo Doria05/2014
63532^223913+7369767405Enzo Doria04/2016
6354(10^67404+179)/967404Serge Batalov12/2014
635518738^3955+3955^1873867404Hans Havermann09/2016
63569*7^79728-267379Lelio R Paula09/2014
6357(28*10^67378-43)/367379Robert Price04/2016
6358(3^141234-7)/43024128267378Lelio R Paula04/2012
6359211^28988-267377Lelio R Paula09/2013
63602^223793-1806967369Enzo Doria05/2013
63612^223777-252167364Yves Minet07/2014
6362(15185*2^223775-1)/1518367363Lelio R Paula04/2015
6363(2^223759-lucasV(1,2,223759)+1)/267358Mike Oakes11/2016
6364V(340138)67336Serge Batalov03/2015
636543125^14528-10667334Enzo Doria07/2012
636617458^7153+7153^1745867292Hans Havermann08/2016
636716366^12925+12925^1636667288Hans Havermann08/2016
636837^42906-267286Lelio R Paula08/2013
636918^53592-1367273Lelio R Paula08/2013
6370V(396221)67256Serge Batalov03/2015
6372(34*10^67245-7)/9/3^4/193/138153767236Makoto Morimoto04/2016
6371(14*10^67235-101)/367236Robert Price04/2017
637353^38993-52^3899367235Robert Price01/2013
6374(2^223349-7)/648567231Lelio R Paula04/2012
63752^223333+31567230Lelio R Paula04/2012
63762^223278-11104167214Enzo Doria05/2014
6377(2347*2^223281+1)/(3*5*197*1213*1783)67208Jens K. Andersen09/2007
63782^223256-4567207Lelio R Paula02/2012
63792^223253-11211167206Enzo Doria06/2014
638018407^4474+4474^1840767199Hans Havermann08/2016
638147^40182+40182^4767189Norbert Schneider11/2014
638213^60309+9467181Lelio R Paula07/2013
638311^64503-8467173Lelio R Paula07/2013
63843^140781+23667170Lelio R Paula06/2013
63852^223107-86505767162Paul Bourdelais03/2013
63862^223100-5967160Lelio R Paula02/2012
63872^223087+7196367156Enzo Doria04/2016
638818^53481-377967134Enzo Doria03/2013
63894^111473-6257367114Mike Oakes02/2011
63902^222943+2967113Henri Lifchitz08/2005
6391(2^222939-9)/10367110Lelio R Paula04/2012
63922^222862-45916167089Enzo Doria05/2015
63932^222828+819367078Lelio R Paula04/2012
63943^140570+266067069Lelio R Paula06/2013
63952^222744+85567053Lelio R Paula04/2012
639613^60189+8467048Lelio R Paula07/2013
63972^222701+57729457567040Lelio R Paula02/2016
6398(13*10^67038-31)/967039Serge Batalov11/2008
6399(151*10^67027-7)/967029Robert Price07/2017
6400(58695*2^222620-1)/6167019Lelio R Paula04/2015
64012^222614-11104167014Enzo Doria05/2014
64022^222520-190766986Yves Minet03/2013
6403(4^111231+23)/366968Robert Price02/2017
64042^222408-11127566952Enzo Doria05/2014
640510^66949-9^6694966949Jean-Louis Charton12/2005
64062^222378-100566943Lelio R Paula04/2012
6407(9*2^222366+1)/7366938Lelio R Paula08/2012
64087^79202-6^(79202+1)66934Robert Price06/2016
64092^222325-11225566927Enzo Doria06/2014
641020^51428+3366910Lelio R Paula08/2013
64112^222224-1850966897Enzo Doria05/2013
64122^222192-86968810566887Lelio R Paula02/2016
641311^64219-6466878Lelio R Paula07/2013
64142^222151-1729566875Lelio R Paula04/2012
6415gcd(V(799885),5*F(159977)*(F(159977)+1)+1)66867Serge Batalov04/2015
64162^222085-11103166855Enzo Doria05/2014
64178*10^66848-1366849Robert Price05/2017
6418(3^140087+4)/1366838Lelio R Paula04/2012
6419(3^140102+4)/884360943766836Lelio R Paula04/2012
642019^52265+5266835Lelio R Paula08/2013
64212*10^66826-2766827Robert Price02/2017
64224*6^85867+566819Lelio R Paula09/2014
642315^56800+866802Lelio R Paula08/2013
6424(2^221891-2^110946+1)/56679611/2006
642510^66793+6944166794Patrick De Geest05/2013
642610^66793-6366793Robert Price05/2011
642735^43256-170466791Enzo Doria03/2013
64283^139976+2^(139976-1)66786Robert Price05/2016
64297^79023-5466783Lelio R Paula06/2013
6430104^33109-10366782Norbert Schneider11/2016
6431(34*10^66778-7)/9/37/35890166772Makoto Morimoto04/2016
6432(-lucasV(1,2,443622)+2)/(7*281*487)66766Mike Oakes04/2017
64342^221768+18366759Lelio R Paula02/2012
6433gcd(V(1197915),5*F(239583)*(F(239583)+1)+1)66759Serge Batalov04/2015
6435(154*10^66755-1)/966757Serge Batalov12/2014
643611^64097+4866751Lelio R Paula07/2013
6437(lucasV(1,2,443547)-2)/(7*13*79*1327*221773)66749Mike Oakes04/2017
6438(3*2^221696-1)/1366737Lelio R Paula01/2014
64398*6^85758-766734Lelio R Paula09/2014
6440135^31325+266733Lelio R Paula05/2013
6441(49*10^66729+41)/966730Robert Price07/2015
6442(349*10^66720-7)/966722Robert Price03/2017
6443(-lucasV(1,2,443285)+2)/(3^2*307)66718Mike Oakes04/2017
6444(25*10^66714+71)/366715Robert Price01/2017
644511^64061-78066713Enzo Doria11/2012
64467^78929+466703Lelio R Paula06/2013
644711^64048-93066700Enzo Doria11/2012
64482*7^78921+566697Lelio R Paula09/2014
6449(25*2^221526+1)/40966685Lelio R Paula08/2012
6450(2^221509-1)/29239188166673Jens K. Andersen02/2009
64512^221479+7295366672Enzo Doria04/2016
645210^66666+27540366667Patrick De Geest03/2010
645310^66666-11552166666Patrick De Geest03/2010
6454(18*10^66657-81)/9966657Ray Chandler01/2011
64554*10^66653+2166654Robert Price08/2016
6456(10^66650+149)/366650Serge Batalov12/2014
64579^69842+3*8^69842-2*4^69842-3*2^6984266647Mike Oakes12/2010
64582^221391-214566646Lelio R Paula04/2012
6459(5*10^66613-119)/366614Robert Price04/2016
64602^221273-11323366610Enzo Doria07/2014
64613^139571-4666593Lelio R Paula06/2013
64622^221181-86968810566583Lelio R Paula02/2016
6463(61*10^66575-7)/966576Ray Chandler02/2012
64642^221126+13366566Lelio R Paula02/2012
646512^61680+9166564Lelio R Paula07/2013
6466(lucasV(1,2,442258)+2)/10366564Mike Oakes04/2017
6467(13*10^66551-73)/366552Robert Price12/2016
646811^63901-159066547Enzo Doria12/2012
646911^63901-150066547Enzo Doria12/2012
64706^85517+2366546Lelio R Paula07/2013
647117^54069-4066530Lelio R Paula08/2013
6472(2^110503+4725)^2+(2^110503+4725)+4166530Makoto Morimoto05/2016
6473(2^110503+8099)^2+(2^110503+8099)+4166530Makoto Morimoto05/2016
6475(2^221008-1017)/7853366526Lelio R Paula04/2012
64743^139432+2666526Lelio R Paula06/2013
6476((2^110503+5139)^2+(2^110503+5139)+41)/2086579766523Makoto Morimoto05/2016
6477((2^110503+6647)^2+(2^110503+6647)+41)/197/1732766523Makoto Morimoto05/2016
64786^85481+8548166518Henri Lifchitz08/2014
6479(9179*2^220913-1)/39966503Lelio R Paula04/2015
648013^59687+6666488Lelio R Paula07/2013
6481(49*10^66485-31)/966486Robert Price07/2015
6482(46*10^66469+17)/966470Robert Price06/2015
64832^220790+9766465Lelio R Paula02/2012
6484(23*2^220790+1)/80766463Lelio R Paula06/2012
648540009^14441-10266460Enzo Doria07/2012
64862^220736-14366449Lelio R Paula02/2012
6487(79*10^66447-97)/9966447Ray Chandler01/2011
64882^220675+6966430Lelio R Paula02/2012
64892^220633-11138166418Enzo Doria05/2014
6490(2^220625-509203)/400032166409Lelio R Paula05/2012
64912^220596-1581366407Enzo Doria04/2013
6492(5*10^66394-17)/366395Serge Batalov05/2009
64932^220549-185917366392Enzo Doria04/2016
64942^220478-16166371Lelio R Paula02/2012
64955^94938-1463666359Enzo Doria02/2013
6496(F(67)^4861-F(66)^4861)/F(65)66353Wayne Halsdorf03/2012
64972^220253-11487166303Enzo Doria05/2015
649812^61432+9566297Lelio R Paula07/2013
64992^220192-11156366285Enzo Doria05/2014
65002^220188-11144966284Enzo Doria05/2014


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Created by  Henri Lifchitz & Renaud Lifchitz : October, 26 2000, last modification: August, 20 2017 08:36 (Time in France)

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