PRP Records

Probable Primes Top 10000

(172742 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 ?
8501(67607*2^174503+1)/9094807952528Lelio R Paula05/2014
8502(-lucasV(1,2,349014)+2)/(7*50873*1047043)52521Mike Oakes03/2017
85032^174462+34552519Lelio R Paula07/2009
8504t(178863)52509Robert Price10/2014
85052^174416+85552505Lelio R Paula07/2009
85066^67467-10352500Lelio R Paula10/2012
85072^174329-1126552479Enzo Doria06/2014
85082^174314-124152474Yves Minet05/2009
850952^30577-5152471Norbert Schneider08/2014
851015692^2205+2205^1569252465Hans Havermann06/2016
8511(2^174281-7)/62881702961552453Lelio R Paula02/2012
8512(2^174240+5)/352451Lelio R Paula02/2012
8513(15*2^174221+1)/40352445Lelio R Paula07/2012
851426313!2-3252443Robert Price10/2015
8515(3*2^174214-1)/374872952438Lelio R Paula01/2014
85162*3^109900-552436Lelio R Paula03/2014
85184159^14488-15052432Enzo Doria07/2012
8517(89*10^52431-71)/952432Robert Price11/2015
8519(7*2^174171-1)/68552429Lelio R Paula01/2014
8521(260137^9679+1)/26013852409Faysal YAtim03/2008
85202^174098+7952409Lelio R Paula01/2011
852235^33940-221452406Enzo Doria03/2013
852315^44557+252404Ray Chandler07/2011
85242^174049-43952394Yves Minet01/2012
85256^67329+11552393Lelio R Paula10/2012
85272^174041+26214552392Lelio R Paula07/2009
8526141^24377+252392Lelio R Paula05/2013
8528lucasU(285,1,21339)-lucasU(285,1,21338)52382Mike Oakes05/2009
85292^174001-595552380Lelio R Paula07/2009
8530lucasV(-1,2,347969)52375Mike Oakes02/2017
85313^109764-14052371Lelio R Paula10/2012
85322*3^109761+752370Lelio R Paula03/2014
85332^173944-11225352363Enzo Doria06/2014
85352^173940+111152362Lelio R Paula01/2011
8534(3126^14983-1)/312552362Richard Fischer03/2015
853615214^2763+2763^1521452358Hans Havermann05/2016
853713200^9247+9247^1320052352Hans Havermann05/2016
8538(1017*2^173867-1)/717552339Lelio R Paula03/2015
853913732^6465+6465^1373252327Hans Havermann05/2016
8540(2^173867-1)/5253663750268952326Donovan Johnson06/2005
85412^173811-68487752323Paul Bourdelais11/2012
85422^173807-595552322Lelio R Paula06/2009
85432^173796-104468952318Paul Bourdelais11/2012
854410^52317+6449752318Patrick De Geest12/2012
854510^52317+6474352318Patrick De Geest12/2012
854710^52317-7152317Robert Price05/2011
854610821^12968+12968^1082152317Norbert Schneider04/2016
8548(2^173778-3)/5795952308Lelio R Paula02/2012
85502^173727+952298Lelio R Paula01/2011
8549(14^45631+13^45631)/2752298Robert Price04/2013
855137856!3+656152293Robert Price11/2015
85524*3^109596+552292Lelio R Paula03/2014
855315436^2441+2441^1543652291Hans Havermann05/2016
855443^32005+2452280Robert Price11/2013
85552^173650-16552274Lelio R Paula02/2011
85564*10^52272+9352273Robert Price01/2017
855719^40873+8452267Lelio R Paula01/2013
85582^173621+424242952266Jason Earls09/2008
8559numbpart(46909^2-1)52247Serge Batalov04/2017
856014^45579-3152240Lelio R Paula01/2013
8561(10223*2^173518+1)/90352236Lelio R Paula05/2014
856220^40147-612352233Enzo Doria03/2013
85634^86754-3^(86754+1)52232Robert Price04/2016
85642^173477-343352222Yves Minet04/2009
8565(25*2^173446+1)/6152213Lelio R Paula07/2012
85663^109431-3852212Lelio R Paula10/2012
856713^46861-7252201Lelio R Paula01/2013
85682^173373-136352191Yves Minet03/2009
856911^50114-174052189Enzo Doria11/2012
857013735^6304+6304^1373552188Hans Havermann05/2016
857111^50111-111052186Enzo Doria11/2012
8572lucasU(46,1,31387)+lucasU(46,1,31386)52181Mike Oakes04/2009
857320^40105-858352178Enzo Doria03/2013
8574(10322^13001+2679^13001)/13001^252175Lelio R Paula08/2008
85752^173294+115552167Lelio R Paula07/2012
8576(19*2^173301-1)/2348952166Lelio R Paula01/2014
857715146^2781+2781^1514652166Hans Havermann06/2016
857811^50088-3252162Lelio R Paula01/2013
85793^109320+23652159Lelio R Paula10/2012
85802^173246-2863552153Lelio R Paula06/2009
85812*10^52147+1152148Robert Price01/2015
85822^173208-11262552141Enzo Doria06/2014
8583(9179*2^173206-1)/203552141Lelio R Paula03/2015
858415^44333-7652140Lelio R Paula01/2013
85852^173187-318952135Yves Minet10/2014
85862^173167+7557952129Enzo Doria04/2016
8587(2^173169+7)/9279352125Lelio R Paula02/2012
85889*7^61671+452119Lelio R Paula09/2014
85902^173130-922152118Lelio R Paula07/2008
8589(17*2^173129-1)/352118Lelio R Paula01/2014
85912^173100-11255952109Enzo Doria06/2014
85922^173091-11233952106Enzo Doria06/2014
859311^50030+2852101Lelio R Paula01/2013
8594(59*10^52099+13)/952100Robert Price09/2015
85952^173064-182952098Yves Minet09/2012
85962^173062-136152097Yves Minet08/2012
85973^109190-7052097Lelio R Paula10/2012
85982^173059+9019552096Lelio R Paula07/2012
85992^173048-11262552093Enzo Doria06/2014
860092^26524+9152088Norbert Schneider04/2013
860141^32295-4052085Theodore Burton02/2007
86022^173002+17752079Lelio R Paula02/2011
8603p(11334)#/2+852075Robert Price01/2017
86042^172965-11236352068Enzo Doria06/2014
86059*2^172935+752060Lelio R Paula03/2014
860611^49978-819052047Enzo Doria02/2013
860710^52041+63352042Patrick De Geest11/2012
860810^52041-9352041Robert Price05/2011
8609(21*2^172815-1)/86952021Lelio R Paula01/2014
8610(182*10^52018+1)/352020Robert Price02/2017
86114*6^66843-552015Lelio R Paula09/2014
861219^40670-5452007Lelio R Paula01/2013
86132^172756-11288352005Enzo Doria06/2014
861411832^12763-12763^1183251985Norbert Schneider02/2017
86157^61511-3651983Lelio R Paula10/2012
86162^172640-7551970Lelio R Paula01/2011
8617gcd(V(932265),5*F(186453)*(F(186453)-1)+1)51953Serge Batalov04/2015
861812240^12709-12709^1224051952Norbert Schneider01/2017
8619t(173589)51951Robert Price12/2014
86207^61469+3451948Lelio R Paula10/2012
86219*2^172553-751945Lelio R Paula03/2014
862211542^12787+12787^1154251945Norbert Schneider01/2016
862335^33640-708651943Enzo Doria03/2013
8624(7*2^172534+1)/247951936Lelio R Paula07/2012
8625(2^86243+43467)^2+(2^86243+43467)+4151924Makoto Morimoto05/2016
8626(2^86243+84085)^2+(2^86243+84085)+4151924Makoto Morimoto05/2016
8627((2^86243+75146)^2+(2^86243+75146)+41)/6151922Makoto Morimoto05/2016
8628((2^86243+8692)^2+(2^86243+8692)+41)/301151920Makoto Morimoto05/2016
8629((2^86243+30085)^2+(2^86243+30085)+41)/41/19951920Makoto Morimoto05/2016
8630((2^86243+36540)^2+(2^86243+36540)+41)/43/64751920Makoto Morimoto05/2016
86322^172470+751919Lelio R Paula01/2011
8631((2^86243+76136)^2+(2^86243+76136)+41)/6050951919Makoto Morimoto05/2016
8633((2^86243+50999)^2+(2^86243+50999)+41)/249686951918Makoto Morimoto05/2016
8634((2^86243+80760)^2+(2^86243+80760)+41)/93048151918Makoto Morimoto05/2016
8635((2^86243+26732)^2+(2^86243+26732)+41)/223/9651751917Makoto Morimoto05/2016
8636((2^86243+51479)^2+(2^86243+51479)+41)/1607/2202751916Makoto Morimoto05/2016
86392^172455+1551915Lelio R Paula01/2011
8637((2^86243+27637)^2+(2^86243+27637)+41)/2693/51843151915Makoto Morimoto05/2016
8638((2^86243+82275)^2+(2^86243+82275)+41)/71/930992951915Makoto Morimoto05/2016
8640((2^86243+57757)^2+(2^86243+57757)+41)/30871/62272951914Makoto Morimoto05/2016
8641((2^86243+18643)^2+(2^86243+18643)+41)/47/23071/6529351913Makoto Morimoto05/2016
8642((2^86243+8693)^2+(2^86243+8693)+41)/494107/293389151912Makoto Morimoto05/2016
8643((2^86243+8250)^2+(2^86243+8250)+41)/223/34877/147262351911Makoto Morimoto05/2016
8644((2^86243+51745)^2+(2^86243+51745)+41)/71/95891/217129351911Makoto Morimoto05/2016
8645((2^86243+29592)^2+(2^86243+29592)+41)/7717/11933/1256650951909Makoto Morimoto05/2016
86465^74263+5451908Lelio R Paula10/2012
864713804^5755+5755^1380451904Hans Havermann05/2016
86487*2^172403-351900Henri Lifchitz06/2003
8649t(196078)51892Robert Price02/2014
86502*3^108759-751892Lelio R Paula03/2014
8651(94*10^51889+11)/351891Robert Price02/2017
8652(73*10^51889+17)/951890Robert Price10/2015
865335^33603-402651886Enzo Doria03/2013
86542^172350-10751883Lelio R Paula02/2011
865514419^3960+3960^1441951876Hans Havermann05/2016
86562^172325-11318551875Enzo Doria07/2014
865710^51872+10068351873Patrick De Geest06/2016
865810^51872-100000000151872Robert Price05/2016
865910^51872-10014951872Patrick De Geest06/2016
86602147092^8192+6351871Jens K. Andersen04/2009
866113^46564-2451870Lelio R Paula01/2013
866213981^5110+5110^1398151848Hans Havermann05/2016
86632^172228+7626151846Enzo Doria04/2016
866411^49772-126051833Enzo Doria11/2012
8665(11*2^172157-1)/35151823Lelio R Paula01/2014
86669001^13102-11451810Enzo Doria07/2012
8667(80051^10567+1)/8005251809Faysal YAtim07/2007
86692^172101-6151808Lelio R Paula01/2011
8668(2^172125+3)/3112550551808Lelio R Paula02/2012
86709*7^61301+451807Lelio R Paula09/2014
8671(23*2^172090-1)/3650951802Lelio R Paula01/2014
86722^172074+145951800Lelio R Paula07/2008
86732^172063+16551797Lelio R Paula02/2011
8674(21181*2^172061+1)/1814751796Lelio R Paula05/2014
867528^35785-2751787Norbert Schneider01/2014
8676(65*10^51778+43)/951779Ray Chandler09/2010
8677(15185*2^171975-1)/351774Lelio R Paula03/2015
86782^171978-11329751771Enzo Doria07/2014
867911^49708+7851766Lelio R Paula01/2013
8680(26*10^51764-107)/951765Robert Price07/2016
868112^47956-9751754Lelio R Paula12/2012
86822^171907-351151750Yves Minet03/2017
8683(12611^12611+311)/2/13/1357790351707Makoto Morimoto07/2016
8684(3*2^171761+1)/2951705Lelio R Paula07/2012
8685t(195346)51699Robert Price07/2014
868613^46409+4651697Lelio R Paula01/2013
86872^171663+1155*17166351676Henri Lifchitz01/2005
868815^43937+2651674Lelio R Paula01/2013
8689(3^108312-7)/12452651673Lelio R Paula03/2012
8690(12601^12601+465)/2/13151667Makoto Morimoto07/2016
8691(79*10^51663-97)/9951663Ray Chandler11/2010
8693(10^51652-31)/351652Serge Batalov12/2014
86922^171583+7379351652Enzo Doria04/2016
869412^47861-3551651Lelio R Paula12/2012
86956^66369-2681351646Enzo Doria03/2013
8696Phi(83967,10)/227248288951639Maksym Voznyy01/2010
86972^171524+15351634Lelio R Paula02/2011
8698(2^171516-509203)/486951628Lelio R Paula05/2012
8699(12589^12589+323)/2^5/351613Makoto Morimoto07/2016
87005*10^51608-8151609Robert Price04/2017
8701(lucasV(1,2,342870)+2)/(13*25933*242617)51597Mike Oakes03/2017
87022^171351-11267751582Enzo Doria06/2014
8703(12583^12583+1695)/2/11^2/753508951579Makoto Morimoto07/2016
8704(3^108091+7)/38251570Lelio R Paula03/2012
87052^171287-318751563Yves Minet04/2009
8706-lucasV(-1,2,342569)51563Mike Oakes02/2017
87072^171280-103070951561Paul Bourdelais11/2012
870813300^7527+7527^1330051560Hans Havermann05/2016
87092^171268+7371151557Enzo Doria04/2016
8710(17*2^171266+1)/696351554Lelio R Paula01/2012
8711(1964814^8192+1)/6553751551Lelio R Paula06/2013
87124*10^51530-6351531Robert Price12/2016
87133*6^66216-551527Lelio R Paula09/2014
871412569^12569+54051525Makoto Morimoto07/2016
87152^171152-245951522Yves Minet07/2014
8716(13*10^51511-1)/351512Robert Price12/2014
87175*10^51508+351509Dmitry Domanov11/2010
87183^107919-4651491Lelio R Paula07/2012
87194*10^51489+8751490Robert Price05/2016
8720(22699*2^171030+1)/302951487Lelio R Paula05/2014
87212^171028-323951485Yves Minet12/2014
87222^170992-95420951474Paul Bourdelais11/2012
872376^27367+7551473Norbert Schneider11/2012
87246007^13620-10251466Enzo Doria07/2012
8725gcd(V(923445),5*F(184689)*(F(184689)-1)+1)51462Serge Batalov04/2015
8726t(194442)51459Robert Price08/2014
8727(22*10^51457+161)/351458Robert Price02/2017
87289^53921+8^(53921+1)51454Robert Price06/2016
87292^170921-1699551453Lelio R Paula08/2011
87302^170922-213551453Yves Minet06/2013
87314357^14138-12051451Enzo Doria06/2012
8732153^23550+251450Lelio R Paula05/2013
8733(3^107833+2)/2551449Lelio R Paula03/2012
87347*10^51440-4751441Robert Price02/2017
8735(10^51431-3^51431)/751431Robert Price06/2011
8736U(250849)51425Michael Porter08/2007
8737(86*10^51424-41)/951425Robert Price11/2015
873912^47649+751422Lelio R Paula12/2012
8738(25*10^51421+11)/951422Robert Price03/2015
87403^107768+266051419Lelio R Paula07/2012
87422^170784-655551412Lelio R Paula05/2009
8741(-lucasV(1,2,341584)-2)/7951412Mike Oakes03/2017
874351^30106+251409Lelio R Paula05/2013
87445^73546-1280651407Enzo Doria02/2013
8745(12545^12545+12546^12546)/(1584571*19137767639)51404Walter Nissen09/2014
8746(3^107735-4)/43151401Lelio R Paula03/2012
874720^39505-648351398Enzo Doria03/2013
87482^170736-1519751397Enzo Doria04/2013
8749(12541^12541+393)/2/56351395Makoto Morimoto07/2016
87509^53857-8^5385751393Jean-Louis Charton11/2004


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Created by  Henri Lifchitz & Renaud Lifchitz : October, 26 2000, last modification: April, 21 2017 08:01 (Time in France)

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