PRP Records

Probable Primes Top 10000

(172751 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 ?
625111^64219-6466878Lelio R Paula07/2013
62522^222151-1729566875Lelio R Paula04/2012
6253gcd(V(799885),5*F(159977)*(F(159977)+1)+1)66867Serge Batalov04/2015
62542^222085-11103166855Enzo Doria05/2014
6255(3^140087+4)/1366838Lelio R Paula04/2012
6256(3^140102+4)/884360943766836Lelio R Paula04/2012
625719^52265+5266835Lelio R Paula08/2013
62582*10^66826-2766827Robert Price02/2017
62594*6^85867+566819Lelio R Paula09/2014
626015^56800+866802Lelio R Paula08/2013
6261(2^221891-2^110946+1)/56679611/2006
626210^66793+6944166794Patrick De Geest05/2013
626310^66793-6366793Robert Price05/2011
626435^43256-170466791Enzo Doria03/2013
62653^139976+2^(139976-1)66786Robert Price05/2016
62667^79023-5466783Lelio R Paula06/2013
6267104^33109-10366782Norbert Schneider11/2016
6268(34*10^66778-7)/9/37/35890166772Makoto Morimoto04/2016
6269(-lucasV(1,2,443622)+2)/(7*281*487)66766Mike Oakes04/2017
62712^221768+18366759Lelio R Paula02/2012
6270gcd(V(1197915),5*F(239583)*(F(239583)+1)+1)66759Serge Batalov04/2015
6272(154*10^66755-1)/966757Serge Batalov12/2014
627311^64097+4866751Lelio R Paula07/2013
6274(lucasV(1,2,443547)-2)/(7*13*79*1327*221773)66749Mike Oakes04/2017
6275(3*2^221696-1)/1366737Lelio R Paula01/2014
62768*6^85758-766734Lelio R Paula09/2014
6277135^31325+266733Lelio R Paula05/2013
6278(49*10^66729+41)/966730Robert Price07/2015
6279(349*10^66720-7)/966722Robert Price03/2017
6280(-lucasV(1,2,443285)+2)/(3^2*307)66718Mike Oakes04/2017
6281(25*10^66714+71)/366715Robert Price01/2017
628211^64061-78066713Enzo Doria11/2012
62837^78929+466703Lelio R Paula06/2013
628411^64048-93066700Enzo Doria11/2012
62852*7^78921+566697Lelio R Paula09/2014
6286(25*2^221526+1)/40966685Lelio R Paula08/2012
6287(2^221509-1)/29239188166673Jens K. Andersen02/2009
62882^221479+7295366672Enzo Doria04/2016
628910^66666+27540366667Patrick De Geest03/2010
629010^66666-11552166666Patrick De Geest03/2010
6291(18*10^66657-81)/9966657Ray Chandler01/2011
62924*10^66653+2166654Robert Price08/2016
6293(10^66650+149)/366650Serge Batalov12/2014
62949^69842+3*8^69842-2*4^69842-3*2^6984266647Mike Oakes12/2010
62952^221391-214566646Lelio R Paula04/2012
6296(5*10^66613-119)/366614Robert Price04/2016
62972^221273-11323366610Enzo Doria07/2014
62983^139571-4666593Lelio R Paula06/2013
62992^221181-86968810566583Lelio R Paula02/2016
6300(61*10^66575-7)/966576Ray Chandler02/2012
63012^221126+13366566Lelio R Paula02/2012
630212^61680+9166564Lelio R Paula07/2013
6303(lucasV(1,2,442258)+2)/10366564Mike Oakes04/2017
6304(13*10^66551-73)/366552Robert Price12/2016
630511^63901-159066547Enzo Doria12/2012
630611^63901-150066547Enzo Doria12/2012
63076^85517+2366546Lelio R Paula07/2013
630817^54069-4066530Lelio R Paula08/2013
6309(2^110503+4725)^2+(2^110503+4725)+4166530Makoto Morimoto05/2016
6310(2^110503+8099)^2+(2^110503+8099)+4166530Makoto Morimoto05/2016
6311(2^221008-1017)/7853366526Lelio R Paula04/2012
63123^139432+2666526Lelio R Paula06/2013
6313((2^110503+5139)^2+(2^110503+5139)+41)/2086579766523Makoto Morimoto05/2016
6314((2^110503+6647)^2+(2^110503+6647)+41)/197/1732766523Makoto Morimoto05/2016
63156^85481+8548166518Henri Lifchitz08/2014
6316(9179*2^220913-1)/39966503Lelio R Paula04/2015
631713^59687+6666488Lelio R Paula07/2013
6318(49*10^66485-31)/966486Robert Price07/2015
6319(46*10^66469+17)/966470Robert Price06/2015
63202^220790+9766465Lelio R Paula02/2012
6321(23*2^220790+1)/80766463Lelio R Paula06/2012
632240009^14441-10266460Enzo Doria07/2012
63232^220736-14366449Lelio R Paula02/2012
6324(79*10^66447-97)/9966447Ray Chandler01/2011
63252^220675+6966430Lelio R Paula02/2012
63262^220633-11138166418Enzo Doria05/2014
6327(2^220625-509203)/400032166409Lelio R Paula05/2012
63282^220596-1581366407Enzo Doria04/2013
6329(5*10^66394-17)/366395Serge Batalov05/2009
63302^220549-185917366392Enzo Doria04/2016
63312^220478-16166371Lelio R Paula02/2012
63325^94938-1463666359Enzo Doria02/2013
6333(F(67)^4861-F(66)^4861)/F(65)66353Wayne Halsdorf03/2012
63342^220253-11487166303Enzo Doria05/2015
633512^61432+9566297Lelio R Paula07/2013
63362^220192-11156366285Enzo Doria05/2014
63372^220188-11144966284Enzo Doria05/2014
6338(4*10^66284+23)/966284Robert Price11/2014
633932501!2+266266Robert Price01/2015
63401530*10^66254+R(66254)66258Patrick De Geest05/2016
6341(47^39623-1)/4666252Robert Price06/2014
63422^220044-9730566240Lelio R Paula04/2012
634329^45285+266225Ray Chandler08/2011
634415^56289+3866202Lelio R Paula08/2013
63453^138749+9866201Lelio R Paula06/2013
6346(21*2^219912-1)/566201Lelio R Paula01/2014
63472^219904-1699566198Lelio R Paula10/2011
6348(3^138712-2)/529766179Lelio R Paula04/2012
6349Phi(198552,10)66177Ray Chandler07/2010
63504*6^85041+766176Lelio R Paula09/2014
63512^219812-314966171Yves Minet10/2009
63522^219795-61116766165Paul Bourdelais03/2013
635332455!2+51266162Robert Price02/2015
6354(27*2^219760-1)/22766154Lelio R Paula01/2014
6356(11^63521-4^63521)/766150Robert Price03/2013
63555*7^78274-666150Lelio R Paula09/2014
6357(-lucasV(1,2,439441)-2)/(3*11927*81359)66134Mike Oakes04/2017
63582^219679-11201566130Enzo Doria05/2014
63592^219653+15015*21965366123Henri Lifchitz04/2005
63602^219600+7656166107Enzo Doria05/2016
63612^219594+25525566105Lelio R Paula10/2011
63624*7^78210-366096Lelio R Paula09/2014
6363(15185*2^219557-1)/6366096Lelio R Paula04/2015
6364(19*2^219499-1)/1366076Lelio R Paula01/2014
63652^219496+6661566075Lelio R Paula10/2011
6366(F(79021)^5-F(79020)^5)/F(79019)66057Wayne Halsdorf03/2012
6367(2^219414+7)/44365766045Lelio R Paula04/2012
6368(115*10^66043-1)/366045Serge Batalov12/2014
636910^66033+1966034Robert Price01/2011
637010^66033-7830966033Patrick De Geest05/2013
6371(lucasV(1,2,438701)+2)/759941966025Mike Oakes04/2017
63722^219304+45424566018Henri Lifchitz03/2007
6373(27*2^219293+1)/914566012Lelio R Paula08/2012
63742^219273-11263566008Enzo Doria06/2014
63752^219250+2566001Lelio R Paula08/2011
6376132^31123+13165999Norbert Schneider03/2015
6377V(319871)65987Serge Batalov03/2015
63782^219189-19565983Lelio R Paula08/2011
6379(7*2^219143-1)/5565968Lelio R Paula01/2014
63802^219112-1700965960Enzo Doria05/2013
63812^219093-11120165954Enzo Doria05/2014
63822^219089-11209965953Enzo Doria06/2014
638346714!3+8165950Robert Price09/2014
6384(11*10^65944-131)/365945Robert Price02/2017
63852^219021-355365932Yves Minet03/2017
6386Pell-LucasQ(172243)/265931Eric W. Weisstein01/2007
63872^218990+7351965923Enzo Doria04/2016
638858^37378-5765914Norbert Schneider09/2014
6389(2^218945-7)/167565906Lelio R Paula04/2012
6390(-lucasV(1,2,437845)-2)/167991765896Mike Oakes04/2017
63922^218897-11188965895Enzo Doria05/2014
63912^218896+186945165895Enzo Doria05/2016
639363^36616+265885Lelio R Paula05/2013
6394(3*2^218822-1)/1165872Lelio R Paula01/2014
63952^218796-11329765865Enzo Doria07/2014
63962^218797+7372765865Enzo Doria04/2016
63973^138040-11065862Lelio R Paula06/2013
639811^63240-195065858Enzo Doria12/2012
63992^218764-11187365855Enzo Doria05/2014
6400(34*10^65839-7)/9/3765839Makoto Morimoto04/2016
64013^137988+2665838Lelio R Paula06/2013
64022^218680-71965830Yves Minet05/2012
640318^52424+1765807Lelio R Paula08/2013
6404(2*15683^15683+1)/73238442565789David Broadhurst09/2010
6405(23*2^218517+1)/1900365778Lelio R Paula07/2012
6406(5*10^65773+1)/365774Erik Branger12/2013
64072^218457-1732965763Enzo Doria05/2013
6408151703#+22338165759Nicolas PALAU10/2016
64092^218436+4075565756Lelio R Paula10/2011
6410(F(44)^7433-F(43)^7433)/F(42)65744Wayne Halsdorf03/2012
6411157^29934+29934^15765733Serge Batalov05/2014
6412211^28273-265715Lelio R Paula09/2013
6413(59*10^65712+31)/965713Robert Price09/2015
6414611^23586+23586^61165712Norbert Schneider08/2016
6415p(13991)#/2+3265712Robert Price12/2016
64162^218282-1848565710Enzo Doria05/2013
64172^218274-11125165708Enzo Doria05/2014
64182*F(314335)-165693Henri Lifchitz12/2009
64192^218200+42765685Henri Lifchitz01/2005
642046532!3+365667Robert Price10/2014
64212^218120-14765661Lelio R Paula08/2011
6422452^24729+24729^45265659Norbert Schneider09/2016
64232^218102-11489365656Enzo Doria05/2015
6424(15*2^218083-1)/1765650Lelio R Paula01/2014
6425(15*2^218081+1)/1894165646Lelio R Paula08/2012
642719^51326+3665634Lelio R Paula08/2013
6426(21*2^218045-1)/45158365634Lelio R Paula01/2014
64282^217989-3365622Lelio R Paula08/2011
6429(13*2^217961+1)/365614Lelio R Paula06/2012
64304*6^84315-565611Lelio R Paula09/2014
6431(315047^11933+1)/31504865607Faysal YAtim06/2008
64326^84303+5565601Lelio R Paula07/2013
6433(-lucasV(1,2,435857)+2)/(173*859*8017)65595Mike Oakes04/2017
6434(9787*2^217873-1)/3765589Lelio R Paula04/2015
64355*2^217858+365583Lelio R Paula04/2014
6436(19*10^65572+119)/365573Robert Price02/2017
643720^50399+5165571Lelio R Paula08/2013
643811^62946-567065552Enzo Doria01/2013
64392^217742-391165547Yves Minet08/2009
6440(19*10^65545+77)/365546Robert Price08/2016
64412^217731+13165544Lelio R Paula08/2011
64422^217720-11128765541Enzo Doria05/2014
644310^65537+2765538Robert Price01/2011
644410^65537-7685965537Patrick De Geest05/2013
6445(10223*2^217676+1)/365531Lelio R Paula06/2014
6446PadovanNumber[536485]65518Eric W. Weisstein05/2009
64477*10^65492-4765493Robert Price02/2017
64482^217547-186840765489Enzo Doria04/2016
64492^217531-11176965484Enzo Doria05/2014
64507^77484-1865482Lelio R Paula06/2013
64512^217488-11328565471Enzo Doria07/2014
6452151153#/30-3065468Henri Lifchitz12/2011
64532^217466+425765464Lelio R Paula10/2011
645446396!3-8165455Robert Price09/2014
64552^217421-11318565451Enzo Doria07/2014
6456(6883*2^217440-1)/106119329589365448Lelio R Paula04/2015
64572^217408-214565447Lelio R Paula10/2011
64582^217398-1694765444Enzo Doria05/2013
64598*5^93613+365434Lelio R Paula09/2014
646011^62828-531065429Enzo Doria01/2013
646110^65426+1365427Robert Price01/2011
64622^217341-655565427Lelio R Paula10/2011
646310^65426-5484965426Patrick De Geest05/2013
6464(21*2^217363-1)/5600362666765424Lelio R Paula01/2014
646530011^14608-10865405Enzo Doria07/2012
6466(43^40031-1)/4265388Robert Price04/2014
64672^217190+9439565381Henri Lifchitz02/2005
646815^55587+4665376Lelio R Paula08/2013
64692^217088-11183365350Enzo Doria05/2014
6470(13*2^217069-1)/168294565340Lelio R Paula01/2014
6471(62*10^65331+1)/965332Serge Batalov11/2010
64722^216947-11135165308Enzo Doria05/2014
6473-E(18022)/77520184568268532294394923506835965307Thomas Ritschel02/2017
6474(13*10^65297+83)/365298Robert Price09/2016
64755^93400-865284Lelio R Paula06/2013
64762^216802-16565264Lelio R Paula08/2011
64772^216799-2863565264Lelio R Paula10/2011
64785*10^65255+5165256Robert Price01/2017
64792^216762-16765252Lelio R Paula08/2011
648011^62657-579065251Enzo Doria01/2013
64813^136756-11288065250Enzo Doria06/2014
64822^216752+2165249Lelio R Paula08/2011
648311^62651-270065245Enzo Doria12/2012
6485Pell-LucasQ(170413)/265230Eric W. Weisstein12/2006
6484gcd(V(790525),5*F(158105)*(F(158105)+1)+1)65230Serge Batalov04/2015
6486(2^216676-1017)/63765224Lelio R Paula04/2012
64872^216652-232765219Yves Minet10/2013
6488(9179*2^216648-1)/466765218Lelio R Paula04/2015
6489(5*10^65203-119)/365204Robert Price04/2016
64902^216555-11326965190Enzo Doria07/2014
6491(9513^16384+1)/265181Henri Lifchitz02/2007
64922^216474+1291565166Lelio R Paula02/2013
649319^50958-3265163Lelio R Paula08/2013
64942^216442-11213365156Enzo Doria06/2014
64952^216437-11221365155Enzo Doria06/2014
64962^216435-11276765154Enzo Doria06/2014
64972^216420+1270565149Lelio R Paula02/2013
64988*3^136507-765132Lelio R Paula04/2014
6499(-lucasV(1,2,432719)-2)/(5*461)65128Mike Oakes03/2017
65002^216197-11176965082Enzo Doria05/2014


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Created by  Henri Lifchitz & Renaud Lifchitz : October, 26 2000, last modification: April, 24 2017 22:44 (Time in France)

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