PRP Records

Probable Primes Top 10000

(173006 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 ?
62519*10^67468+767469Dmitry Domanov11/2010
6252(31*2^224115-1)/4772367463Lelio R Paula01/2014
6253128^32001+32001^12867433Serge Batalov05/2014
6254(89*10^67431-17)/967432Robert Price11/2015
62552^223912-11105967405Enzo Doria05/2014
62562^223913+7369767405Enzo Doria04/2016
6257(10^67404+179)/967404Serge Batalov12/2014
625818738^3955+3955^1873867404Hans Havermann09/2016
62599*7^79728-267379Lelio R Paula09/2014
6260(28*10^67378-43)/367379Robert Price04/2016
6261(3^141234-7)/43024128267378Lelio R Paula04/2012
6262211^28988-267377Lelio R Paula09/2013
62632^223793-1806967369Enzo Doria05/2013
62642^223777-252167364Yves Minet07/2014
6265(15185*2^223775-1)/1518367363Lelio R Paula04/2015
6266(2^223759-lucasV(1,2,223759)+1)/267358Mike Oakes11/2016
6267V(340138)67336Serge Batalov03/2015
626843125^14528-10667334Enzo Doria07/2012
626917458^7153+7153^1745867292Hans Havermann08/2016
627016366^12925+12925^1636667288Hans Havermann08/2016
627137^42906-267286Lelio R Paula08/2013
627218^53592-1367273Lelio R Paula08/2013
6273V(396221)67256Serge Batalov03/2015
6274(34*10^67245-7)/9/3^4/193/138153767236Makoto Morimoto04/2016
6275(14*10^67235-101)/367236Robert Price04/2017
627653^38993-52^3899367235Robert Price01/2013
6277(2^223349-7)/648567231Lelio R Paula04/2012
62782^223333+31567230Lelio R Paula04/2012
62792^223278-11104167214Enzo Doria05/2014
6280(2347*2^223281+1)/(3*5*197*1213*1783)67208Jens K. Andersen09/2007
62812^223256-4567207Lelio R Paula02/2012
62822^223253-11211167206Enzo Doria06/2014
628318407^4474+4474^1840767199Hans Havermann08/2016
628447^40182+40182^4767189Norbert Schneider11/2014
628513^60309+9467181Lelio R Paula07/2013
628611^64503-8467173Lelio R Paula07/2013
62873^140781+23667170Lelio R Paula06/2013
62882^223107-86505767162Paul Bourdelais03/2013
62892^223100-5967160Lelio R Paula02/2012
62902^223087+7196367156Enzo Doria04/2016
629118^53481-377967134Enzo Doria03/2013
62924^111473-6257367114Mike Oakes02/2011
62932^222943+2967113Henri Lifchitz08/2005
6294(2^222939-9)/10367110Lelio R Paula04/2012
62952^222862-45916167089Enzo Doria05/2015
62962^222828+819367078Lelio R Paula04/2012
62973^140570+266067069Lelio R Paula06/2013
62982^222744+85567053Lelio R Paula04/2012
629913^60189+8467048Lelio R Paula07/2013
63002^222701+57729457567040Lelio R Paula02/2016
6301(13*10^67038-31)/967039Serge Batalov11/2008
6302(58695*2^222620-1)/6167019Lelio R Paula04/2015
63032^222614-11104167014Enzo Doria05/2014
63042^222520-190766986Yves Minet03/2013
6305(4^111231+23)/366968Robert Price02/2017
63062^222408-11127566952Enzo Doria05/2014
630710^66949-9^6694966949Jean-Louis Charton12/2005
63082^222378-100566943Lelio R Paula04/2012
6309(9*2^222366+1)/7366938Lelio R Paula08/2012
63107^79202-6^(79202+1)66934Robert Price06/2016
63112^222325-11225566927Enzo Doria06/2014
631220^51428+3366910Lelio R Paula08/2013
63132^222224-1850966897Enzo Doria05/2013
63142^222192-86968810566887Lelio R Paula02/2016
631511^64219-6466878Lelio R Paula07/2013
63162^222151-1729566875Lelio R Paula04/2012
6317gcd(V(799885),5*F(159977)*(F(159977)+1)+1)66867Serge Batalov04/2015
63182^222085-11103166855Enzo Doria05/2014
63198*10^66848-1366849Robert Price05/2017
6320(3^140087+4)/1366838Lelio R Paula04/2012
6321(3^140102+4)/884360943766836Lelio R Paula04/2012
632219^52265+5266835Lelio R Paula08/2013
63232*10^66826-2766827Robert Price02/2017
63244*6^85867+566819Lelio R Paula09/2014
632515^56800+866802Lelio R Paula08/2013
6326(2^221891-2^110946+1)/56679611/2006
632710^66793+6944166794Patrick De Geest05/2013
632810^66793-6366793Robert Price05/2011
632935^43256-170466791Enzo Doria03/2013
63303^139976+2^(139976-1)66786Robert Price05/2016
63317^79023-5466783Lelio R Paula06/2013
6332104^33109-10366782Norbert Schneider11/2016
6333(34*10^66778-7)/9/37/35890166772Makoto Morimoto04/2016
6334(-lucasV(1,2,443622)+2)/(7*281*487)66766Mike Oakes04/2017
63352^221768+18366759Lelio R Paula02/2012
6336gcd(V(1197915),5*F(239583)*(F(239583)+1)+1)66759Serge Batalov04/2015
6337(154*10^66755-1)/966757Serge Batalov12/2014
633811^64097+4866751Lelio R Paula07/2013
6339(lucasV(1,2,443547)-2)/(7*13*79*1327*221773)66749Mike Oakes04/2017
6340(3*2^221696-1)/1366737Lelio R Paula01/2014
63418*6^85758-766734Lelio R Paula09/2014
6342135^31325+266733Lelio R Paula05/2013
6343(49*10^66729+41)/966730Robert Price07/2015
6344(349*10^66720-7)/966722Robert Price03/2017
6345(-lucasV(1,2,443285)+2)/(3^2*307)66718Mike Oakes04/2017
6346(25*10^66714+71)/366715Robert Price01/2017
634711^64061-78066713Enzo Doria11/2012
63487^78929+466703Lelio R Paula06/2013
634911^64048-93066700Enzo Doria11/2012
63502*7^78921+566697Lelio R Paula09/2014
6351(25*2^221526+1)/40966685Lelio R Paula08/2012
6352(2^221509-1)/29239188166673Jens K. Andersen02/2009
63532^221479+7295366672Enzo Doria04/2016
635410^66666+27540366667Patrick De Geest03/2010
635510^66666-11552166666Patrick De Geest03/2010
6356(18*10^66657-81)/9966657Ray Chandler01/2011
63574*10^66653+2166654Robert Price08/2016
6358(10^66650+149)/366650Serge Batalov12/2014
63599^69842+3*8^69842-2*4^69842-3*2^6984266647Mike Oakes12/2010
63602^221391-214566646Lelio R Paula04/2012
6361(5*10^66613-119)/366614Robert Price04/2016
63622^221273-11323366610Enzo Doria07/2014
63633^139571-4666593Lelio R Paula06/2013
63642^221181-86968810566583Lelio R Paula02/2016
6365(61*10^66575-7)/966576Ray Chandler02/2012
63662^221126+13366566Lelio R Paula02/2012
636812^61680+9166564Lelio R Paula07/2013
6367(lucasV(1,2,442258)+2)/10366564Mike Oakes04/2017
6369(13*10^66551-73)/366552Robert Price12/2016
637011^63901-159066547Enzo Doria12/2012
637111^63901-150066547Enzo Doria12/2012
63726^85517+2366546Lelio R Paula07/2013
637317^54069-4066530Lelio R Paula08/2013
6374(2^110503+4725)^2+(2^110503+4725)+4166530Makoto Morimoto05/2016
6375(2^110503+8099)^2+(2^110503+8099)+4166530Makoto Morimoto05/2016
6376(2^221008-1017)/7853366526Lelio R Paula04/2012
63773^139432+2666526Lelio R Paula06/2013
6378((2^110503+5139)^2+(2^110503+5139)+41)/2086579766523Makoto Morimoto05/2016
6379((2^110503+6647)^2+(2^110503+6647)+41)/197/1732766523Makoto Morimoto05/2016
63806^85481+8548166518Henri Lifchitz08/2014
6381(9179*2^220913-1)/39966503Lelio R Paula04/2015
638213^59687+6666488Lelio R Paula07/2013
6383(49*10^66485-31)/966486Robert Price07/2015
6384(46*10^66469+17)/966470Robert Price06/2015
63852^220790+9766465Lelio R Paula02/2012
6386(23*2^220790+1)/80766463Lelio R Paula06/2012
638740009^14441-10266460Enzo Doria07/2012
63882^220736-14366449Lelio R Paula02/2012
6389(79*10^66447-97)/9966447Ray Chandler01/2011
63902^220675+6966430Lelio R Paula02/2012
63912^220633-11138166418Enzo Doria05/2014
6392(2^220625-509203)/400032166409Lelio R Paula05/2012
63932^220596-1581366407Enzo Doria04/2013
6394(5*10^66394-17)/366395Serge Batalov05/2009
63952^220549-185917366392Enzo Doria04/2016
63962^220478-16166371Lelio R Paula02/2012
63975^94938-1463666359Enzo Doria02/2013
6398(F(67)^4861-F(66)^4861)/F(65)66353Wayne Halsdorf03/2012
63992^220253-11487166303Enzo Doria05/2015
640012^61432+9566297Lelio R Paula07/2013
64012^220192-11156366285Enzo Doria05/2014
64022^220188-11144966284Enzo Doria05/2014
6403(4*10^66284+23)/966284Robert Price11/2014
640432501!2+266266Robert Price01/2015
64051530*10^66254+R(66254)66258Patrick De Geest05/2016
6406(47^39623-1)/4666252Robert Price06/2014
64072^220044-9730566240Lelio R Paula04/2012
640829^45285+266225Ray Chandler08/2011
640915^56289+3866202Lelio R Paula08/2013
64103^138749+9866201Lelio R Paula06/2013
6411(21*2^219912-1)/566201Lelio R Paula01/2014
64122^219904-1699566198Lelio R Paula10/2011
6413(3^138712-2)/529766179Lelio R Paula04/2012
6414Phi(198552,10)66177Ray Chandler07/2010
64154*6^85041+766176Lelio R Paula09/2014
64162^219812-314966171Yves Minet10/2009
64172^219795-61116766165Paul Bourdelais03/2013
641832455!2+51266162Robert Price02/2015
6419(27*2^219760-1)/22766154Lelio R Paula01/2014
6421(11^63521-4^63521)/766150Robert Price03/2013
64205*7^78274-666150Lelio R Paula09/2014
6422(-lucasV(1,2,439441)-2)/(3*11927*81359)66134Mike Oakes04/2017
64232^219679-11201566130Enzo Doria05/2014
64242^219653+15015*21965366123Henri Lifchitz04/2005
64252^219600+7656166107Enzo Doria05/2016
64262^219594+25525566105Lelio R Paula10/2011
64274*7^78210-366096Lelio R Paula09/2014
6428(15185*2^219557-1)/6366096Lelio R Paula04/2015
6429(19*2^219499-1)/1366076Lelio R Paula01/2014
64302^219496+6661566075Lelio R Paula10/2011
6431(F(79021)^5-F(79020)^5)/F(79019)66057Wayne Halsdorf03/2012
6432(2^219414+7)/44365766045Lelio R Paula04/2012
6433(115*10^66043-1)/366045Serge Batalov12/2014
643410^66033+1966034Robert Price01/2011
643510^66033-7830966033Patrick De Geest05/2013
6436(lucasV(1,2,438701)+2)/759941966025Mike Oakes04/2017
64372^219304+45424566018Henri Lifchitz03/2007
6438(27*2^219293+1)/914566012Lelio R Paula08/2012
64392^219273-11263566008Enzo Doria06/2014
64402^219250+2566001Lelio R Paula08/2011
6441132^31123+13165999Norbert Schneider03/2015
6442V(319871)65987Serge Batalov03/2015
64432^219189-19565983Lelio R Paula08/2011
6444(7*2^219143-1)/5565968Lelio R Paula01/2014
64452^219112-1700965960Enzo Doria05/2013
64462^219093-11120165954Enzo Doria05/2014
64472^219089-11209965953Enzo Doria06/2014
644846714!3+8165950Robert Price09/2014
6449(11*10^65944-131)/365945Robert Price02/2017
64502^219021-355365932Yves Minet03/2017
6451Pell-LucasQ(172243)/265931Eric W. Weisstein01/2007
64522^218990+7351965923Enzo Doria04/2016
645358^37378-5765914Norbert Schneider09/2014
6454(2^218945-7)/167565906Lelio R Paula04/2012
6455(-lucasV(1,2,437845)-2)/167991765896Mike Oakes04/2017
64562^218897-11188965895Enzo Doria05/2014
64572^218896+186945165895Enzo Doria05/2016
645863^36616+265885Lelio R Paula05/2013
6459(3*2^218822-1)/1165872Lelio R Paula01/2014
64602^218796-11329765865Enzo Doria07/2014
64612^218797+7372765865Enzo Doria04/2016
64623^138040-11065862Lelio R Paula06/2013
646311^63240-195065858Enzo Doria12/2012
64642^218764-11187365855Enzo Doria05/2014
6465(34*10^65839-7)/9/3765839Makoto Morimoto04/2016
64663^137988+2665838Lelio R Paula06/2013
64672^218680-71965830Yves Minet05/2012
646818^52424+1765807Lelio R Paula08/2013
6469(2*15683^15683+1)/73238442565789David Broadhurst09/2010
6470(23*2^218517+1)/1900365778Lelio R Paula07/2012
6471(5*10^65773+1)/365774Erik Branger12/2013
64722^218457-1732965763Enzo Doria05/2013
6473151703#+22338165759Nicolas PALAU10/2016
64742^218436+4075565756Lelio R Paula10/2011
6475(F(44)^7433-F(43)^7433)/F(42)65744Wayne Halsdorf03/2012
6476157^29934+29934^15765733Serge Batalov05/2014
6477211^28273-265715Lelio R Paula09/2013
6478(59*10^65712+31)/965713Robert Price09/2015
6479611^23586+23586^61165712Norbert Schneider08/2016
6480p(13991)#/2+3265712Robert Price12/2016
64812^218282-1848565710Enzo Doria05/2013
64822^218274-11125165708Enzo Doria05/2014
64832*F(314335)-165693Henri Lifchitz12/2009
64842^218200+42765685Henri Lifchitz01/2005
648546532!3+365667Robert Price10/2014
64862^218120-14765661Lelio R Paula08/2011
6487452^24729+24729^45265659Norbert Schneider09/2016
64882^218102-11489365656Enzo Doria05/2015
6489(15*2^218083-1)/1765650Lelio R Paula01/2014
6490(15*2^218081+1)/1894165646Lelio R Paula08/2012
649219^51326+3665634Lelio R Paula08/2013
6491(21*2^218045-1)/45158365634Lelio R Paula01/2014
64932^217989-3365622Lelio R Paula08/2011
6494(13*2^217961+1)/365614Lelio R Paula06/2012
64954*6^84315-565611Lelio R Paula09/2014
6496(315047^11933+1)/31504865607Faysal YAtim06/2008
64976^84303+5565601Lelio R Paula07/2013
6498(-lucasV(1,2,435857)+2)/(173*859*8017)65595Mike Oakes04/2017
6499(9787*2^217873-1)/3765589Lelio R Paula04/2015
65005*2^217858+365583Lelio R Paula04/2014


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Created by  Henri Lifchitz & Renaud Lifchitz : October, 26 2000, last modification: May, 25 2017 10:58 (Time in France)

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