PRP Records

Probable Primes Top 10000

(202632 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 ?
92512^173940+111152362Lelio R Paula01/2011
925215214^2763+2763^1521452358Hans Havermann05/2016
925313200^9247+9247^1320052352Hans Havermann05/2016
9254(1017*2^173867-1)/717552339Lelio R Paula03/2015
925513732^6465+6465^1373252327Hans Havermann05/2016
9256(2^173867-1)/5253663750268952326Donovan Johnson06/2005
92572^173811-68487752323Paul Bourdelais11/2012
92582^173807-595552322Lelio R Paula06/2009
92592^173796-104468952318Paul Bourdelais11/2012
926010^52317+6449752318Patrick De Geest12/2012
926110^52317+6474352318Patrick De Geest12/2012
926310^52317-7152317Robert Price05/2011
926210821^12968+12968^1082152317Norbert Schneider04/2016
9264(298*10^52308-7)/352310Robert Price06/2017
9265(2^173778-3)/5795952308Lelio R Paula02/2012
926610232^13043-13043^1023252302Norbert Schneider08/2017
92682^173727+952298Lelio R Paula01/2011
9267(14^45631+13^45631)/2752298Robert Price04/2013
926937856!3+656152293Robert Price11/2015
92704*3^109596+552292Lelio R Paula03/2014
927115436^2441+2441^1543652291Hans Havermann05/2016
927243^32005+2452280Robert Price11/2013
92732^173650-16552274Lelio R Paula02/2011
92744*10^52272+9352273Robert Price01/2017
927519^40873+8452267Lelio R Paula01/2013
92762^173621+424242952266Jason Earls09/2008
92779999^13064-13064^999952256Norbert Schneider09/2017
9278numbpart(46909^2-1)52247Serge Batalov04/2017
927914^45579-3152240Lelio R Paula01/2013
9280(10223*2^173518+1)/90352236Lelio R Paula05/2014
928120^40147-612352233Enzo Doria03/2013
92824^86754-3^(86754+1)52232Robert Price04/2016
92832^173477-343352222Yves Minet04/2009
9284(22*10^52217-73)/352218Robert Price09/2017
9285(25*2^173446+1)/6152213Lelio R Paula07/2012
92863^109431-3852212Lelio R Paula10/2012
92872^173424-395952206Yves Minet04/2017
928813^46861-7252201Lelio R Paula01/2013
92892^173373-136352191Yves Minet03/2009
929011^50114-174052189Enzo Doria11/2012
929113735^6304+6304^1373552188Hans Havermann05/2016
929211^50111-111052186Enzo Doria11/2012
9293lucasU(46,1,31387)+lucasU(46,1,31386)52181Mike Oakes04/2009
929420^40105-858352178Enzo Doria03/2013
9295(10322^13001+2679^13001)/13001^252175Lelio R Paula08/2008
92962^173314-394152173Yves Minet04/2017
92972^173294+115552167Lelio R Paula07/2012
9298(19*2^173301-1)/2348952166Lelio R Paula01/2014
929915146^2781+2781^1514652166Hans Havermann06/2016
930011^50088-3252162Lelio R Paula01/2013
93013^109320+23652159Lelio R Paula10/2012
93022^173246-2863552153Lelio R Paula06/2009
93032*10^52147+1152148Robert Price01/2015
93042^173208-11262552141Enzo Doria06/2014
9305(9179*2^173206-1)/203552141Lelio R Paula03/2015
930615^44333-7652140Lelio R Paula01/2013
93072^173187-318952135Yves Minet10/2014
93082^173167+7557952129Enzo Doria04/2016
9309(2^173169+7)/9279352125Lelio R Paula02/2012
9310(25*10^52119+23)/352120Robert Price06/2017
93119*7^61671+452119Lelio R Paula09/2014
93132^173130-922152118Lelio R Paula07/2008
9312(17*2^173129-1)/352118Lelio R Paula01/2014
93142^173100-11255952109Enzo Doria06/2014
93152^173091-11233952106Enzo Doria06/2014
931611^50030+2852101Lelio R Paula01/2013
9317(59*10^52099+13)/952100Robert Price09/2015
93182^173064-182952098Yves Minet09/2012
93192^173062-136152097Yves Minet08/2012
93203^109190-7052097Lelio R Paula10/2012
93212^173059+9019552096Lelio R Paula07/2012
93222^173048-11262552093Enzo Doria06/2014
932392^26524+9152088Norbert Schneider04/2013
932441^32295-4052085Theodore Burton02/2007
93252^173002+17752079Lelio R Paula02/2011
9326p(11334)#/2+852075Robert Price01/2017
93272^172965-11236352068Enzo Doria06/2014
93289*2^172935+752060Lelio R Paula03/2014
932911^49978-819052047Enzo Doria02/2013
933010^52041+63352042Patrick De Geest11/2012
93318494^13245-13245^849452042Norbert Schneider01/2018
933210^52041-9352041Robert Price05/2011
9333(21*2^172815-1)/86952021Lelio R Paula01/2014
9334(182*10^52018+1)/352020Robert Price02/2017
93354*6^66843-552015Lelio R Paula09/2014
933619^40670-5452007Lelio R Paula01/2013
93372^172756-11288352005Enzo Doria06/2014
933811832^12763-12763^1183251985Norbert Schneider02/2017
93397^61511-3651983Lelio R Paula10/2012
934010591^12914-12914^1059151979Norbert Schneider05/2017
93412^172640-7551970Lelio R Paula01/2011
9342gcd(V(932265),5*F(186453)*(F(186453)-1)+1)51953Serge Batalov04/2015
934312240^12709-12709^1224051952Norbert Schneider01/2017
9344t(173589)51951Robert Price12/2014
93457^61469+3451948Lelio R Paula10/2012
93469*2^172553-751945Lelio R Paula03/2014
934711542^12787+12787^1154251945Norbert Schneider01/2016
934835^33640-708651943Enzo Doria03/2013
9349(7*2^172534+1)/247951936Lelio R Paula07/2012
9350(2^86243+43467)^2+(2^86243+43467)+4151924Makoto Morimoto05/2016
9351(2^86243+84085)^2+(2^86243+84085)+4151924Makoto Morimoto05/2016
9352((2^86243+75146)^2+(2^86243+75146)+41)/6151922Makoto Morimoto05/2016
9353((2^86243+8692)^2+(2^86243+8692)+41)/301151920Makoto Morimoto05/2016
9354((2^86243+30085)^2+(2^86243+30085)+41)/41/19951920Makoto Morimoto05/2016
9355((2^86243+36540)^2+(2^86243+36540)+41)/43/64751920Makoto Morimoto05/2016
93572^172470+751919Lelio R Paula01/2011
9356((2^86243+76136)^2+(2^86243+76136)+41)/6050951919Makoto Morimoto05/2016
9358((2^86243+50999)^2+(2^86243+50999)+41)/249686951918Makoto Morimoto05/2016
9359((2^86243+80760)^2+(2^86243+80760)+41)/93048151918Makoto Morimoto05/2016
9360((2^86243+26732)^2+(2^86243+26732)+41)/223/9651751917Makoto Morimoto05/2016
9361((2^86243+51479)^2+(2^86243+51479)+41)/1607/2202751916Makoto Morimoto05/2016
93642^172455+1551915Lelio R Paula01/2011
9362((2^86243+27637)^2+(2^86243+27637)+41)/2693/51843151915Makoto Morimoto05/2016
9363((2^86243+82275)^2+(2^86243+82275)+41)/71/930992951915Makoto Morimoto05/2016
9365((2^86243+57757)^2+(2^86243+57757)+41)/30871/62272951914Makoto Morimoto05/2016
9366((2^86243+18643)^2+(2^86243+18643)+41)/47/23071/6529351913Makoto Morimoto05/2016
9367((2^86243+8693)^2+(2^86243+8693)+41)/494107/293389151912Makoto Morimoto05/2016
9368((2^86243+8250)^2+(2^86243+8250)+41)/223/34877/147262351911Makoto Morimoto05/2016
9369((2^86243+51745)^2+(2^86243+51745)+41)/71/95891/217129351911Makoto Morimoto05/2016
9370((2^86243+29592)^2+(2^86243+29592)+41)/7717/11933/1256650951909Makoto Morimoto05/2016
93715^74263+5451908Lelio R Paula10/2012
937213804^5755+5755^1380451904Hans Havermann05/2016
93737*2^172403-351900Henri Lifchitz06/2003
9374t(196078)51892Robert Price02/2014
93752*3^108759-751892Lelio R Paula03/2014
9376(94*10^51889+11)/351891Robert Price02/2017
9377(73*10^51889+17)/951890Robert Price10/2015
937835^33603-402651886Enzo Doria03/2013
93792^172350-10751883Lelio R Paula02/2011
938014419^3960+3960^1441951876Hans Havermann05/2016
93812^172325-11318551875Enzo Doria07/2014
938210^51872+10068351873Patrick De Geest06/2016
938310^51872-100000000151872Robert Price05/2016
938410^51872-10014951872Patrick De Geest06/2016
93852147092^8192+6351871Jens K. Andersen04/2009
938613^46564-2451870Lelio R Paula01/2013
938710524^12893-12893^1052451858Norbert Schneider05/2017
938813981^5110+5110^1398151848Hans Havermann05/2016
93892^172228+7626151846Enzo Doria04/2016
939011^49772-126051833Enzo Doria11/2012
9391(11*2^172157-1)/35151823Lelio R Paula01/2014
9392(43*10^51816-403)/951817Robert Price04/2017
93939001^13102-11451810Enzo Doria07/2012
9394(80051^10567+1)/8005251809Faysal YAtim07/2007
93962^172101-6151808Lelio R Paula01/2011
9395(2^172125+3)/3112550551808Lelio R Paula02/2012
93979*7^61301+451807Lelio R Paula09/2014
9398(23*2^172090-1)/3650951802Lelio R Paula01/2014
93992^172074+145951800Lelio R Paula07/2008
94002^172063+16551797Lelio R Paula02/2011
9401(21181*2^172061+1)/1814751796Lelio R Paula05/2014
9402(56*10^51793+367)/951794Robert Price10/2017
940328^35785-2751787Norbert Schneider01/2014
9404(65*10^51778+43)/951779Ray Chandler09/2010
9405(15185*2^171975-1)/351774Lelio R Paula03/2015
94062^171978-11329751771Enzo Doria07/2014
940711^49708+7851766Lelio R Paula01/2013
9408(26*10^51764-107)/951765Robert Price07/2016
940912^47956-9751754Lelio R Paula12/2012
94102^171907-351151750Yves Minet03/2017
94118203^13220-13220^820351743Norbert Schneider12/2017
94128*10^51721+8751722Robert Price10/2017
941310306^12885-12885^1030651709Norbert Schneider05/2017
9414(12611^12611+311)/2/13/1357790351707Makoto Morimoto07/2016
9415(3*2^171761+1)/2951705Lelio R Paula07/2012
9416t(195346)51699Robert Price07/2014
941713^46409+4651697Lelio R Paula01/2013
94182^171663+1155*17166351676Henri Lifchitz01/2005
941915^43937+2651674Lelio R Paula01/2013
9420(3^108312-7)/12452651673Lelio R Paula03/2012
9421(12601^12601+465)/2/13151667Makoto Morimoto07/2016
9422(79*10^51663-97)/9951663Ray Chandler11/2010
942348589!4+102451656Robert Price08/2017
9425(10^51652-31)/351652Serge Batalov12/2014
94262^171583+7379351652Enzo Doria04/2016
9424(28*10^51651-31)/351652Robert Price10/2017
942712^47861-3551651Lelio R Paula12/2012
94286^66369-2681351646Enzo Doria03/2013
9429Phi(83967,10)/227248288951639Maksym Voznyy01/2010
94302^171524+15351634Lelio R Paula02/2011
9431(2^171516-509203)/486951628Lelio R Paula05/2012
9432(12589^12589+323)/2^5/351613Makoto Morimoto07/2016
94335*10^51608-8151609Robert Price04/2017
9434(lucasV(1,2,342870)+2)/(13*25933*242617)51597Mike Oakes03/2017
9435(2*10^51597-23)/351597Robert Price09/2017
943610171^12872-12872^1017151583Norbert Schneider04/2017
94372^171351-11267751582Enzo Doria06/2014
9438(12583^12583+1695)/2/11^2/753508951579Makoto Morimoto07/2016
94399818^12919-12919^981851573Norbert Schneider05/2017
9440(3^108091+7)/38251570Lelio R Paula03/2012
94422^171287-318751563Yves Minet04/2009
9441-lucasV(-1,2,342569)51563Mike Oakes02/2017
94432^171280-103070951561Paul Bourdelais11/2012
944413300^7527+7527^1330051560Hans Havermann05/2016
94452^171268+7371151557Enzo Doria04/2016
9446(17*2^171266+1)/696351554Lelio R Paula01/2012
9447(1964814^8192+1)/6553751551Lelio R Paula06/2013
9448(26*10^51537-503)/951538Robert Price12/2017
94494*10^51530-6351531Robert Price12/2016
94503*6^66216-551527Lelio R Paula09/2014
945112569^12569+54051525Makoto Morimoto07/2016
94522^171152-245951522Yves Minet07/2014
9453(13*10^51511-1)/351512Robert Price12/2014
94545*10^51508+351509Dmitry Domanov11/2010
94553^107919-4651491Lelio R Paula07/2012
94564*10^51489+8751490Robert Price05/2016
9457(22699*2^171030+1)/302951487Lelio R Paula05/2014
94582^171028-323951485Yves Minet12/2014
94592^170992-95420951474Paul Bourdelais11/2012
946076^27367+7551473Norbert Schneider11/2012
94616007^13620-10251466Enzo Doria07/2012
9462gcd(V(923445),5*F(184689)*(F(184689)-1)+1)51462Serge Batalov04/2015
9463t(194442)51459Robert Price08/2014
9464(22*10^51457+161)/351458Robert Price02/2017
94659^53921+8^(53921+1)51454Robert Price06/2016
94672^170921-1699551453Lelio R Paula08/2011
94662^170922-213551453Yves Minet06/2013
94684357^14138-12051451Enzo Doria06/2012
9469153^23550+251450Lelio R Paula05/2013
9470(3^107833+2)/2551449Lelio R Paula03/2012
9471(159^23369+1)/16051443Eric Chen12/2017
94727*10^51440-4751441Robert Price02/2017
9473(10^51431-3^51431)/751431Robert Price06/2011
9475U(250849)51425Michael Porter08/2007
9474(86*10^51424-41)/951425Robert Price11/2015
947712^47649+751422Lelio R Paula12/2012
9476(25*10^51421+11)/951422Robert Price03/2015
94783^107768+266051419Lelio R Paula07/2012
94802^170784-655551412Lelio R Paula05/2009
9479(-lucasV(1,2,341584)-2)/7951412Mike Oakes03/2017
948151^30106+251409Lelio R Paula05/2013
94825^73546-1280651407Enzo Doria02/2013
9483(12545^12545+12546^12546)/(1584571*19137767639)51404Walter Nissen09/2014
9484(3^107735-4)/43151401Lelio R Paula03/2012
948520^39505-648351398Enzo Doria03/2013
94862^170736-1519751397Enzo Doria04/2013
94872^170737-382351397Yves Minet04/2017
9488(12541^12541+393)/2/56351395Makoto Morimoto07/2016
94899^53857-8^5385751393Jean-Louis Charton11/2004
94905^73524-1442651392Enzo Doria02/2013
94912^170712+24351390Lelio R Paula10/2011
9492(15*2^170713+1)/179351388Lelio R Paula07/2012
9493(2^170702+9)/126151384Lelio R Paula01/2012
9494283^20956+20956^28351380Norbert Schneider08/2014
94952^170665-3151376Lelio R Paula01/2011
949611^49330-1251372Lelio R Paula01/2013
9497(25*10^51366-73)/351367Robert Price09/2016
94985^73486-2^7348751365Mike Oakes10/2010
9499(10^51364+119)/351364Serge Batalov12/2014
950015^43672+6851363Lelio R Paula01/2013


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Created by  Henri Lifchitz & Renaud Lifchitz : October, 26 2000, last modification: February, 20 2018 10:36 (Time in France)

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