PRP Records

Probable Primes Top 10000

(174961 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 ?
62512^225120+15167768Lelio R Paula02/2012
6252(44^41233+1)/4567763Robert Price11/2013
62538*10^67742+967743Dmitry Domanov11/2010
62542^224977+108967725Lelio R Paula04/2012
6255(2^224950+5)/1950967713Lelio R Paula04/2012
625611^65011-597067702Enzo Doria01/2013
625788*10^67691+767693Robert Price11/2016
625811^65000-714067691Enzo Doria01/2013
62592^224841+5967684Lelio R Paula02/2012
626033129!2+2^3312967684Robert Price09/2015
62612^224827+841567680Lelio R Paula02/2013
6262(9913*2^224821-1)/1982567678Lelio R Paula04/2015
62632^224815-4978967677Henri Lifchitz04/2005
6264(43*10^67664+11)/967665Robert Price06/2015
6265(292*10^67659-1)/367661Robert Price01/2017
6266(17*2^224766+1)/2900767659Lelio R Paula06/2012
62672^224744+57729457567655Lelio R Paula02/2016
6268((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
6269(2^224721+78557)/173967645Lelio R Paula05/2012
62702^224700+191567642Lelio R Paula04/2012
6271(29*2^224694-1)/19890567636Lelio R Paula01/2014
62722^224658-9367629Lelio R Paula02/2012
62732^224624-1307767619Enzo Doria10/2012
627418^53860-331967609Enzo Doria03/2013
6275(21181*2^224570+1)/567606Lelio R Paula06/2014
62762^224578-11104167605Enzo Doria05/2014
62772^224569-11323367603Enzo Doria07/2014
62782^224562-11317167600Enzo Doria07/2014
62792^224556-11312967599Enzo Doria07/2014
62806*7^79980-567592Lelio R Paula09/2014
6281(6883*2^224523-1)/1603167588Lelio R Paula04/2015
6282(52*10^67578-61)/967579Robert Price09/2015
628310^67579-40167579Robert Price06/2017
6284(17^54919-1)/1667574Paul Bourdelais03/2010
6285(2^224363-9)/195167537Lelio R Paula04/2012
628647719!3-5904967516Robert Price12/2015
6287(22^50287+1)/2367506Robert Price06/2013
628811^64811-582067494Enzo Doria01/2013
6289131^31870+31870^13167478Serge Batalov05/2014
62909*10^67468+767469Dmitry Domanov11/2010
6291(31*2^224115-1)/4772367463Lelio R Paula01/2014
6292128^32001+32001^12867433Serge Batalov05/2014
6293(89*10^67431-17)/967432Robert Price11/2015
62942^223912-11105967405Enzo Doria05/2014
62952^223913+7369767405Enzo Doria04/2016
6297(10^67404+179)/967404Serge Batalov12/2014
629618738^3955+3955^1873867404Hans Havermann09/2016
62989*7^79728-267379Lelio R Paula09/2014
6299(28*10^67378-43)/367379Robert Price04/2016
6300(3^141234-7)/43024128267378Lelio R Paula04/2012
6301211^28988-267377Lelio R Paula09/2013
63022^223793-1806967369Enzo Doria05/2013
63032^223777-252167364Yves Minet07/2014
6304(15185*2^223775-1)/1518367363Lelio R Paula04/2015
6305(2^223759-lucasV(1,2,223759)+1)/267358Mike Oakes11/2016
6306V(340138)67336Serge Batalov03/2015
630743125^14528-10667334Enzo Doria07/2012
630817458^7153+7153^1745867292Hans Havermann08/2016
630916366^12925+12925^1636667288Hans Havermann08/2016
631037^42906-267286Lelio R Paula08/2013
631118^53592-1367273Lelio R Paula08/2013
6312V(396221)67256Serge Batalov03/2015
6314(34*10^67245-7)/9/3^4/193/138153767236Makoto Morimoto04/2016
6313(14*10^67235-101)/367236Robert Price04/2017
631553^38993-52^3899367235Robert Price01/2013
6316(2^223349-7)/648567231Lelio R Paula04/2012
63172^223333+31567230Lelio R Paula04/2012
63182^223278-11104167214Enzo Doria05/2014
6319(2347*2^223281+1)/(3*5*197*1213*1783)67208Jens K. Andersen09/2007
63202^223256-4567207Lelio R Paula02/2012
63212^223253-11211167206Enzo Doria06/2014
632218407^4474+4474^1840767199Hans Havermann08/2016
632347^40182+40182^4767189Norbert Schneider11/2014
632413^60309+9467181Lelio R Paula07/2013
632511^64503-8467173Lelio R Paula07/2013
63263^140781+23667170Lelio R Paula06/2013
63272^223107-86505767162Paul Bourdelais03/2013
63282^223100-5967160Lelio R Paula02/2012
63292^223087+7196367156Enzo Doria04/2016
633018^53481-377967134Enzo Doria03/2013
63314^111473-6257367114Mike Oakes02/2011
63322^222943+2967113Henri Lifchitz08/2005
6333(2^222939-9)/10367110Lelio R Paula04/2012
63342^222862-45916167089Enzo Doria05/2015
63352^222828+819367078Lelio R Paula04/2012
63363^140570+266067069Lelio R Paula06/2013
63372^222744+85567053Lelio R Paula04/2012
633813^60189+8467048Lelio R Paula07/2013
63392^222701+57729457567040Lelio R Paula02/2016
6340(13*10^67038-31)/967039Serge Batalov11/2008
6341(58695*2^222620-1)/6167019Lelio R Paula04/2015
63422^222614-11104167014Enzo Doria05/2014
63432^222520-190766986Yves Minet03/2013
6344(4^111231+23)/366968Robert Price02/2017
63452^222408-11127566952Enzo Doria05/2014
634610^66949-9^6694966949Jean-Louis Charton12/2005
63472^222378-100566943Lelio R Paula04/2012
6348(9*2^222366+1)/7366938Lelio R Paula08/2012
63497^79202-6^(79202+1)66934Robert Price06/2016
63502^222325-11225566927Enzo Doria06/2014
635120^51428+3366910Lelio R Paula08/2013
63522^222224-1850966897Enzo Doria05/2013
63532^222192-86968810566887Lelio R Paula02/2016
635411^64219-6466878Lelio R Paula07/2013
63552^222151-1729566875Lelio R Paula04/2012
6356gcd(V(799885),5*F(159977)*(F(159977)+1)+1)66867Serge Batalov04/2015
63572^222085-11103166855Enzo Doria05/2014
63588*10^66848-1366849Robert Price05/2017
6359(3^140087+4)/1366838Lelio R Paula04/2012
6360(3^140102+4)/884360943766836Lelio R Paula04/2012
636119^52265+5266835Lelio R Paula08/2013
63622*10^66826-2766827Robert Price02/2017
63634*6^85867+566819Lelio R Paula09/2014
636415^56800+866802Lelio R Paula08/2013
6365(2^221891-2^110946+1)/56679611/2006
636610^66793+6944166794Patrick De Geest05/2013
636710^66793-6366793Robert Price05/2011
636835^43256-170466791Enzo Doria03/2013
63693^139976+2^(139976-1)66786Robert Price05/2016
63707^79023-5466783Lelio R Paula06/2013
6371104^33109-10366782Norbert Schneider11/2016
6372(34*10^66778-7)/9/37/35890166772Makoto Morimoto04/2016
6373(-lucasV(1,2,443622)+2)/(7*281*487)66766Mike Oakes04/2017
63752^221768+18366759Lelio R Paula02/2012
6374gcd(V(1197915),5*F(239583)*(F(239583)+1)+1)66759Serge Batalov04/2015
6376(154*10^66755-1)/966757Serge Batalov12/2014
637711^64097+4866751Lelio R Paula07/2013
6378(lucasV(1,2,443547)-2)/(7*13*79*1327*221773)66749Mike Oakes04/2017
6379(3*2^221696-1)/1366737Lelio R Paula01/2014
63808*6^85758-766734Lelio R Paula09/2014
6381135^31325+266733Lelio R Paula05/2013
6382(49*10^66729+41)/966730Robert Price07/2015
6383(349*10^66720-7)/966722Robert Price03/2017
6384(-lucasV(1,2,443285)+2)/(3^2*307)66718Mike Oakes04/2017
6385(25*10^66714+71)/366715Robert Price01/2017
638611^64061-78066713Enzo Doria11/2012
63877^78929+466703Lelio R Paula06/2013
638811^64048-93066700Enzo Doria11/2012
63892*7^78921+566697Lelio R Paula09/2014
6390(25*2^221526+1)/40966685Lelio R Paula08/2012
6391(2^221509-1)/29239188166673Jens K. Andersen02/2009
63922^221479+7295366672Enzo Doria04/2016
639310^66666+27540366667Patrick De Geest03/2010
639410^66666-11552166666Patrick De Geest03/2010
6395(18*10^66657-81)/9966657Ray Chandler01/2011
63964*10^66653+2166654Robert Price08/2016
6397(10^66650+149)/366650Serge Batalov12/2014
63989^69842+3*8^69842-2*4^69842-3*2^6984266647Mike Oakes12/2010
63992^221391-214566646Lelio R Paula04/2012
6400(5*10^66613-119)/366614Robert Price04/2016
64012^221273-11323366610Enzo Doria07/2014
64023^139571-4666593Lelio R Paula06/2013
64032^221181-86968810566583Lelio R Paula02/2016
6404(61*10^66575-7)/966576Ray Chandler02/2012
64052^221126+13366566Lelio R Paula02/2012
640712^61680+9166564Lelio R Paula07/2013
6406(lucasV(1,2,442258)+2)/10366564Mike Oakes04/2017
6408(13*10^66551-73)/366552Robert Price12/2016
640911^63901-159066547Enzo Doria12/2012
641011^63901-150066547Enzo Doria12/2012
64116^85517+2366546Lelio R Paula07/2013
641217^54069-4066530Lelio R Paula08/2013
6413(2^110503+4725)^2+(2^110503+4725)+4166530Makoto Morimoto05/2016
6414(2^110503+8099)^2+(2^110503+8099)+4166530Makoto Morimoto05/2016
6415(2^221008-1017)/7853366526Lelio R Paula04/2012
64163^139432+2666526Lelio R Paula06/2013
6417((2^110503+5139)^2+(2^110503+5139)+41)/2086579766523Makoto Morimoto05/2016
6418((2^110503+6647)^2+(2^110503+6647)+41)/197/1732766523Makoto Morimoto05/2016
64196^85481+8548166518Henri Lifchitz08/2014
6420(9179*2^220913-1)/39966503Lelio R Paula04/2015
642113^59687+6666488Lelio R Paula07/2013
6422(49*10^66485-31)/966486Robert Price07/2015
6423(46*10^66469+17)/966470Robert Price06/2015
64242^220790+9766465Lelio R Paula02/2012
6425(23*2^220790+1)/80766463Lelio R Paula06/2012
642640009^14441-10266460Enzo Doria07/2012
64272^220736-14366449Lelio R Paula02/2012
6428(79*10^66447-97)/9966447Ray Chandler01/2011
64292^220675+6966430Lelio R Paula02/2012
64302^220633-11138166418Enzo Doria05/2014
6431(2^220625-509203)/400032166409Lelio R Paula05/2012
64322^220596-1581366407Enzo Doria04/2013
6433(5*10^66394-17)/366395Serge Batalov05/2009
64342^220549-185917366392Enzo Doria04/2016
64352^220478-16166371Lelio R Paula02/2012
64365^94938-1463666359Enzo Doria02/2013
6437(F(67)^4861-F(66)^4861)/F(65)66353Wayne Halsdorf03/2012
64382^220253-11487166303Enzo Doria05/2015
643912^61432+9566297Lelio R Paula07/2013
64402^220192-11156366285Enzo Doria05/2014
64412^220188-11144966284Enzo Doria05/2014
6442(4*10^66284+23)/966284Robert Price11/2014
644332501!2+266266Robert Price01/2015
64441530*10^66254+R(66254)66258Patrick De Geest05/2016
6445(47^39623-1)/4666252Robert Price06/2014
64462^220044-9730566240Lelio R Paula04/2012
644729^45285+266225Ray Chandler08/2011
644815^56289+3866202Lelio R Paula08/2013
64493^138749+9866201Lelio R Paula06/2013
6450(21*2^219912-1)/566201Lelio R Paula01/2014
64512^219904-1699566198Lelio R Paula10/2011
6452(3^138712-2)/529766179Lelio R Paula04/2012
6453Phi(198552,10)66177Ray Chandler07/2010
64544*6^85041+766176Lelio R Paula09/2014
64552^219812-314966171Yves Minet10/2009
64562^219795-61116766165Paul Bourdelais03/2013
645732455!2+51266162Robert Price02/2015
6458(27*2^219760-1)/22766154Lelio R Paula01/2014
6460(11^63521-4^63521)/766150Robert Price03/2013
64595*7^78274-666150Lelio R Paula09/2014
6461(-lucasV(1,2,439441)-2)/(3*11927*81359)66134Mike Oakes04/2017
64622^219679-11201566130Enzo Doria05/2014
64632^219653+15015*21965366123Henri Lifchitz04/2005
64642^219600+7656166107Enzo Doria05/2016
64652^219594+25525566105Lelio R Paula10/2011
64664*7^78210-366096Lelio R Paula09/2014
6467(15185*2^219557-1)/6366096Lelio R Paula04/2015
6468(19*2^219499-1)/1366076Lelio R Paula01/2014
64692^219496+6661566075Lelio R Paula10/2011
6470(F(79021)^5-F(79020)^5)/F(79019)66057Wayne Halsdorf03/2012
6471(2^219414+7)/44365766045Lelio R Paula04/2012
6472(115*10^66043-1)/366045Serge Batalov12/2014
647310^66033+1966034Robert Price01/2011
647410^66033-7830966033Patrick De Geest05/2013
6475(lucasV(1,2,438701)+2)/759941966025Mike Oakes04/2017
64762^219304+45424566018Henri Lifchitz03/2007
6477(27*2^219293+1)/914566012Lelio R Paula08/2012
64782^219273-11263566008Enzo Doria06/2014
64792^219250+2566001Lelio R Paula08/2011
6480132^31123+13165999Norbert Schneider03/2015
6481V(319871)65987Serge Batalov03/2015
64822^219189-19565983Lelio R Paula08/2011
6483(7*2^219143-1)/5565968Lelio R Paula01/2014
64842^219112-1700965960Enzo Doria05/2013
64852^219093-11120165954Enzo Doria05/2014
64862^219089-11209965953Enzo Doria06/2014
648746714!3+8165950Robert Price09/2014
6488(11*10^65944-131)/365945Robert Price02/2017
64892^219021-355365932Yves Minet03/2017
6490Pell-LucasQ(172243)/265931Eric W. Weisstein01/2007
64912^218990+7351965923Enzo Doria04/2016
649258^37378-5765914Norbert Schneider09/2014
6493(2^218945-7)/167565906Lelio R Paula04/2012
6494(-lucasV(1,2,437845)-2)/167991765896Mike Oakes04/2017
64962^218897-11188965895Enzo Doria05/2014
64952^218896+186945165895Enzo Doria05/2016
649763^36616+265885Lelio R Paula05/2013
6498(3*2^218822-1)/1165872Lelio R Paula01/2014
64992^218796-11329765865Enzo Doria07/2014
65002^218797+7372765865Enzo Doria04/2016


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Created by  Henri Lifchitz & Renaud Lifchitz : October, 26 2000, last modification: June, 22 2017 08:34 (Time in France)

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