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 ?
85012^176255-66753059Yves Minet01/2012
850236471*2^176221+864753053Paul Vanderveen04/2016
8503(19*10^53049-1)/953050Serge Batalov03/2009
85049*2^176203-553044Lelio R Paula03/2014
85052^176205-9439553043Lelio R Paula08/2011
8506(19*2^176224-1)/21791691353042Lelio R Paula01/2014
850717^43103+1453037Lelio R Paula01/2013
8508(31*2^176188-1)/355553036Lelio R Paula01/2014
85092^176177+6094753035David Broadhurst05/2002
8510(22*10^53033-7)/353034Erik Branger09/2014
851113810^6909+6909^1381053023Hans Havermann06/2016
85132^176108+1609553014Lelio R Paula10/2009
85122^176107+1891553014Lelio R Paula07/2012
85143^111080-962852999Enzo Doria02/2013
85152^176047-155152996Yves Minet08/2012
85162^176042+7351952994Enzo Doria04/2016
8517lucasV(1715,1,2^14)/6553752986Mike Oakes04/2009
85182^175984-11225952977Enzo Doria06/2014
851911^50870+1052976Lelio R Paula01/2013
8520(11*10^52956+19)/352957Robert Price03/2016
8521gcd(V(949965),5*F(189993)*(F(189993)+1)+1)52941Serge Batalov04/2015
8522(-lucasV(1,2,351735)+2)/(3*7*263)52938Mike Oakes03/2017
8524(98*10^52931-89)/9952931Ray Chandler11/2010
852313774^6963+6963^1377452931Hans Havermann06/2016
85252^175812-136752925Yves Minet05/2013
85262^175801+1155*17580152922Henri Lifchitz01/2005
852711^50801-909052904Enzo Doria02/2013
852843^32374+1252882Robert Price11/2013
85292^175628+1352870Lelio R Paula01/2011
85302^175615-174752866Yves Minet09/2012
85319*2^175586-752858Lelio R Paula03/2014
853212174^12937+12937^1217452854Norbert Schneider04/2016
8533(15*2^175565+1)/835952848Lelio R Paula07/2012
8534(2^175631-1)/330463093135534238072561/9273316952839Robert Kinser03/2017
853514256^5077+5077^1425652828Hans Havermann06/2016
85362^175467+8287552821Lelio R Paula07/2012
8537(67607*2^175426+1)/352813Lelio R Paula05/2014
853813^47400-6052801Lelio R Paula01/2013
85394*10^52792+6352793Robert Price06/2016
8541(78557*2^175360+1)/308752791Lelio R Paula06/2014
854018^42055-292952791Enzo Doria03/2013
85429*5^75521+252788Lelio R Paula09/2014
85436^67814+3152770Lelio R Paula10/2012
854470^28600+6952770Norbert Schneider10/2012
854514^46038+9752766Lelio R Paula01/2013
8546(61*10^52763-7)/952764Serge Batalov02/2009
85472*5^75474+952755Lelio R Paula09/2014
854810^52753+282643060952754Robert Price05/2015
854910^52753+18399752754Patrick De Geest01/2016
855010^52753-5015352753Patrick De Geest03/2016
855119846^455+455^1984652751Anatoly F. Selevich02/2007
85522^175217+7297752746Enzo Doria04/2016
8553p(11466)#/2-25652746Robert Price05/2017
8554(4*10^52740+41)/952740Robert Price11/2014
85552^175189+538552738Lelio R Paula08/2009
85562^175160+938552729Lelio R Paula07/2008
855712356^12885+12885^1235652724Norbert Schneider03/2016
85582^175137+1152722Lelio R Paula01/2011
855965^29077-64^2907752715Robert Price08/2013
85602*10^52713-8752714Robert Price06/2016
85612^175106-46552713Lelio R Paula08/2009
85622^175089-5869552708Lelio R Paula08/2009
85632^175045+19552694Lelio R Paula02/2011
85642^175025+14952688Lelio R Paula02/2011
8565(19^41201+1)/2052685Paul Bourdelais03/2010
85662*12^48815-5^4881552681Mike Oakes10/2010
8567335^20862-20862^33552678Norbert Schneider09/2015
85682^174983-760552676Lelio R Paula07/2009
85694*10^52667+1952668Robert Price04/2016
8570(10^52667+77)/352667Robert Price01/2017
857111434^12977+12977^1143452664Norbert Schneider04/2016
85722^174941-120352663Lelio R Paula07/2009
85732^174910+1270552654Lelio R Paula07/2012
85743^110338+7452645Lelio R Paula10/2012
85755^75303+1252635Lelio R Paula10/2012
85762^174836+25525552631Lelio R Paula07/2009
857720^40443+952618Lelio R Paula01/2013
8578(11*2^174788+1)/952617Lelio R Paula01/2012
8579(11*2^174786-1)/70352615Lelio R Paula01/2014
858011^50520-129052612Enzo Doria11/2012
8581(9913*2^174736-1)/33352603Lelio R Paula03/2015
858213145^10024+10024^1314552594Hans Havermann05/2016
85835003^14217-15052592Enzo Doria07/2012
858419^41123+1052587Lelio R Paula01/2013
85852^174683+1290952585Lelio R Paula01/2011
85862^174643+5952573Lelio R Paula01/2011
8587(1017*2^174640-1)/77352572Lelio R Paula03/2015
858813529^7662+7662^1352952552Hans Havermann06/2016
8589121421#+18876752548Makoto Morimoto02/2016
859020^40375-592352530Enzo Doria03/2013
8591(67607*2^174503+1)/9094807952528Lelio R Paula05/2014
8592(-lucasV(1,2,349014)+2)/(7*50873*1047043)52521Mike Oakes03/2017
85932^174462+34552519Lelio R Paula07/2009
8594t(178863)52509Robert Price10/2014
85952^174416+85552505Lelio R Paula07/2009
85966^67467-10352500Lelio R Paula10/2012
85972^174329-1126552479Enzo Doria06/2014
85982^174314-124152474Yves Minet05/2009
859952^30577-5152471Norbert Schneider08/2014
860015692^2205+2205^1569252465Hans Havermann06/2016
8601(2^174281-7)/62881702961552453Lelio R Paula02/2012
8602(2^174240+5)/352451Lelio R Paula02/2012
8603(15*2^174221+1)/40352445Lelio R Paula07/2012
860426313!2-3252443Robert Price10/2015
8605(3*2^174214-1)/374872952438Lelio R Paula01/2014
86062*3^109900-552436Lelio R Paula03/2014
86084159^14488-15052432Enzo Doria07/2012
8607(89*10^52431-71)/952432Robert Price11/2015
86092^174170-394152431Yves Minet04/2017
8610(7*2^174171-1)/68552429Lelio R Paula01/2014
8612(260137^9679+1)/26013852409Faysal YAtim03/2008
86112^174098+7952409Lelio R Paula01/2011
861335^33940-221452406Enzo Doria03/2013
861415^44557+252404Ray Chandler07/2011
86152^174049-43952394Yves Minet01/2012
86166^67329+11552393Lelio R Paula10/2012
86182^174041+26214552392Lelio R Paula07/2009
8617141^24377+252392Lelio R Paula05/2013
8619lucasU(285,1,21339)-lucasU(285,1,21338)52382Mike Oakes05/2009
86202^174001-595552380Lelio R Paula07/2009
8621lucasV(-1,2,347969)52375Mike Oakes02/2017
86223^109764-14052371Lelio R Paula10/2012
86232*3^109761+752370Lelio R Paula03/2014
86242^173944-11225352363Enzo Doria06/2014
86262^173940+111152362Lelio R Paula01/2011
8625(3126^14983-1)/312552362Richard Fischer03/2015
862715214^2763+2763^1521452358Hans Havermann05/2016
862813200^9247+9247^1320052352Hans Havermann05/2016
8629(1017*2^173867-1)/717552339Lelio R Paula03/2015
863013732^6465+6465^1373252327Hans Havermann05/2016
8631(2^173867-1)/5253663750268952326Donovan Johnson06/2005
86322^173811-68487752323Paul Bourdelais11/2012
86332^173807-595552322Lelio R Paula06/2009
86342^173796-104468952318Paul Bourdelais11/2012
863510^52317+6449752318Patrick De Geest12/2012
863610^52317+6474352318Patrick De Geest12/2012
863810^52317-7152317Robert Price05/2011
863710821^12968+12968^1082152317Norbert Schneider04/2016
8639(2^173778-3)/5795952308Lelio R Paula02/2012
86412^173727+952298Lelio R Paula01/2011
8640(14^45631+13^45631)/2752298Robert Price04/2013
864237856!3+656152293Robert Price11/2015
86434*3^109596+552292Lelio R Paula03/2014
864415436^2441+2441^1543652291Hans Havermann05/2016
864543^32005+2452280Robert Price11/2013
86462^173650-16552274Lelio R Paula02/2011
86474*10^52272+9352273Robert Price01/2017
864819^40873+8452267Lelio R Paula01/2013
86492^173621+424242952266Jason Earls09/2008
8650numbpart(46909^2-1)52247Serge Batalov04/2017
865114^45579-3152240Lelio R Paula01/2013
8652(10223*2^173518+1)/90352236Lelio R Paula05/2014
865320^40147-612352233Enzo Doria03/2013
86544^86754-3^(86754+1)52232Robert Price04/2016
86552^173477-343352222Yves Minet04/2009
8656(25*2^173446+1)/6152213Lelio R Paula07/2012
86573^109431-3852212Lelio R Paula10/2012
86582^173424-395952206Yves Minet04/2017
865913^46861-7252201Lelio R Paula01/2013
86602^173373-136352191Yves Minet03/2009
866111^50114-174052189Enzo Doria11/2012
866213735^6304+6304^1373552188Hans Havermann05/2016
866311^50111-111052186Enzo Doria11/2012
8664lucasU(46,1,31387)+lucasU(46,1,31386)52181Mike Oakes04/2009
866520^40105-858352178Enzo Doria03/2013
8666(10322^13001+2679^13001)/13001^252175Lelio R Paula08/2008
86672^173314-394152173Yves Minet04/2017
86682^173294+115552167Lelio R Paula07/2012
8669(19*2^173301-1)/2348952166Lelio R Paula01/2014
867015146^2781+2781^1514652166Hans Havermann06/2016
867111^50088-3252162Lelio R Paula01/2013
86723^109320+23652159Lelio R Paula10/2012
86732^173246-2863552153Lelio R Paula06/2009
86742*10^52147+1152148Robert Price01/2015
86752^173208-11262552141Enzo Doria06/2014
8676(9179*2^173206-1)/203552141Lelio R Paula03/2015
867715^44333-7652140Lelio R Paula01/2013
86782^173187-318952135Yves Minet10/2014
86792^173167+7557952129Enzo Doria04/2016
8680(2^173169+7)/9279352125Lelio R Paula02/2012
86819*7^61671+452119Lelio R Paula09/2014
86832^173130-922152118Lelio R Paula07/2008
8682(17*2^173129-1)/352118Lelio R Paula01/2014
86842^173100-11255952109Enzo Doria06/2014
86852^173091-11233952106Enzo Doria06/2014
868611^50030+2852101Lelio R Paula01/2013
8687(59*10^52099+13)/952100Robert Price09/2015
86882^173064-182952098Yves Minet09/2012
86892^173062-136152097Yves Minet08/2012
86903^109190-7052097Lelio R Paula10/2012
86912^173059+9019552096Lelio R Paula07/2012
86922^173048-11262552093Enzo Doria06/2014
869392^26524+9152088Norbert Schneider04/2013
869441^32295-4052085Theodore Burton02/2007
86952^173002+17752079Lelio R Paula02/2011
8696p(11334)#/2+852075Robert Price01/2017
86972^172965-11236352068Enzo Doria06/2014
86989*2^172935+752060Lelio R Paula03/2014
869911^49978-819052047Enzo Doria02/2013
870010^52041+63352042Patrick De Geest11/2012
870110^52041-9352041Robert Price05/2011
8702(21*2^172815-1)/86952021Lelio R Paula01/2014
8703(182*10^52018+1)/352020Robert Price02/2017
87044*6^66843-552015Lelio R Paula09/2014
870519^40670-5452007Lelio R Paula01/2013
87062^172756-11288352005Enzo Doria06/2014
870711832^12763-12763^1183251985Norbert Schneider02/2017
87087^61511-3651983Lelio R Paula10/2012
87092^172640-7551970Lelio R Paula01/2011
8710gcd(V(932265),5*F(186453)*(F(186453)-1)+1)51953Serge Batalov04/2015
871112240^12709-12709^1224051952Norbert Schneider01/2017
8712t(173589)51951Robert Price12/2014
87137^61469+3451948Lelio R Paula10/2012
87149*2^172553-751945Lelio R Paula03/2014
871511542^12787+12787^1154251945Norbert Schneider01/2016
871635^33640-708651943Enzo Doria03/2013
8717(7*2^172534+1)/247951936Lelio R Paula07/2012
8718(2^86243+43467)^2+(2^86243+43467)+4151924Makoto Morimoto05/2016
8719(2^86243+84085)^2+(2^86243+84085)+4151924Makoto Morimoto05/2016
8720((2^86243+75146)^2+(2^86243+75146)+41)/6151922Makoto Morimoto05/2016
8721((2^86243+8692)^2+(2^86243+8692)+41)/301151920Makoto Morimoto05/2016
8722((2^86243+30085)^2+(2^86243+30085)+41)/41/19951920Makoto Morimoto05/2016
8723((2^86243+36540)^2+(2^86243+36540)+41)/43/64751920Makoto Morimoto05/2016
87252^172470+751919Lelio R Paula01/2011
8724((2^86243+76136)^2+(2^86243+76136)+41)/6050951919Makoto Morimoto05/2016
8726((2^86243+50999)^2+(2^86243+50999)+41)/249686951918Makoto Morimoto05/2016
8727((2^86243+80760)^2+(2^86243+80760)+41)/93048151918Makoto Morimoto05/2016
8728((2^86243+26732)^2+(2^86243+26732)+41)/223/9651751917Makoto Morimoto05/2016
8729((2^86243+51479)^2+(2^86243+51479)+41)/1607/2202751916Makoto Morimoto05/2016
87322^172455+1551915Lelio R Paula01/2011
8730((2^86243+27637)^2+(2^86243+27637)+41)/2693/51843151915Makoto Morimoto05/2016
8731((2^86243+82275)^2+(2^86243+82275)+41)/71/930992951915Makoto Morimoto05/2016
8733((2^86243+57757)^2+(2^86243+57757)+41)/30871/62272951914Makoto Morimoto05/2016
8734((2^86243+18643)^2+(2^86243+18643)+41)/47/23071/6529351913Makoto Morimoto05/2016
8735((2^86243+8693)^2+(2^86243+8693)+41)/494107/293389151912Makoto Morimoto05/2016
8736((2^86243+8250)^2+(2^86243+8250)+41)/223/34877/147262351911Makoto Morimoto05/2016
8737((2^86243+51745)^2+(2^86243+51745)+41)/71/95891/217129351911Makoto Morimoto05/2016
8738((2^86243+29592)^2+(2^86243+29592)+41)/7717/11933/1256650951909Makoto Morimoto05/2016
87395^74263+5451908Lelio R Paula10/2012
874013804^5755+5755^1380451904Hans Havermann05/2016
87417*2^172403-351900Henri Lifchitz06/2003
8742t(196078)51892Robert Price02/2014
87432*3^108759-751892Lelio R Paula03/2014
8744(94*10^51889+11)/351891Robert Price02/2017
8745(73*10^51889+17)/951890Robert Price10/2015
874635^33603-402651886Enzo Doria03/2013
87472^172350-10751883Lelio R Paula02/2011
874814419^3960+3960^1441951876Hans Havermann05/2016
87492^172325-11318551875Enzo Doria07/2014
875010^51872+10068351873Patrick De Geest06/2016


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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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