PRP Records

Probable Primes Top 10000

(172142 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 ?
82514159^14747-14053370Enzo Doria07/2012
8252p(11586)#/2+3253357Robert Price12/2016
825315^45362-4653350Lelio R Paula01/2013
825414147^5892+5892^1414753338Hans Havermann07/2016
82557^63109+4653334Lelio R Paula10/2012
825620^40986-134353325Enzo Doria03/2013
825720^40977-888353313Enzo Doria03/2013
82583^111711+266053300Lelio R Paula10/2012
82592^177040-1186553295Enzo Doria10/2012
8260(7*10^53287+17)/353288Erik Branger03/2014
826135^34506-1075853280Enzo Doria03/2013
8262(11*10^53274-17)/353275Erik Branger03/2014
8263(1017*2^176971-1)/33553275Lelio R Paula03/2015
82642^176961-283353271Yves Minet09/2014
82653^111642+11053267Lelio R Paula10/2012
826617^43290-9853267Lelio R Paula01/2013
82677^63028+3653265Lelio R Paula10/2012
82687^63023-3653261Lelio R Paula10/2012
826919783^492+492^1978353256Anatoly F. Selevich02/2007
827013350^9739+9739^1335053247Hans Havermann10/2015
827114394^4993+4993^1439453235Hans Havermann10/2015
82722^176823-11280753230Enzo Doria06/2014
82731684^16495+16495^168453219Serge Batalov05/2014
827415277^3042+3042^1527753213Hans Havermann06/2016
8275(50322^11317-1)/5032153206Serge Batalov04/2015
82762^176742-159553205Lelio R Paula10/2009
8277(27*2^176767-1)/2045505635553204Lelio R Paula01/2014
8278(3*2^176696-1)/29953189Lelio R Paula01/2014
8279(7*10^53185-1)/353186Erik Branger03/2014
82802^176629+46553171Lelio R Paula07/2012
8281(3*2^176604-1)/35953162Lelio R Paula01/2014
82825^76038-1436653149Enzo Doria02/2013
828315156^3209+3209^1515653143Hans Havermann06/2016
82842^176532-283753142Yves Minet09/2014
828552^30967-5153140Norbert Schneider08/2014
82869*5^76023-253139Lelio R Paula09/2014
8287(14283!+1)/46421617753135Michael Porter03/2016
82882^176461-16553121Lelio R Paula02/2011
8289(62*10^53111+1)/953112Serge Batalov05/2010
82902^176403-13953103Lelio R Paula02/2011
829155^30508-253095Lelio R Paula08/2013
8292(48591^11329-1)/4859053090Serge Batalov04/2015
82933^111254-8853082Lelio R Paula10/2012
829415^45129-5653076Lelio R Paula01/2013
82952^176293-7353070Lelio R Paula01/2011
8296(67*10^53068+41)/953069Robert Price09/2015
829715271^2986+2986^1527153069Hans Havermann06/2016
82982^176255-66753059Yves Minet01/2012
829936471*2^176221+864753053Paul Vanderveen04/2016
8300(19*10^53049-1)/953050Serge Batalov03/2009
83019*2^176203-553044Lelio R Paula03/2014
83022^176205-9439553043Lelio R Paula08/2011
8303(19*2^176224-1)/21791691353042Lelio R Paula01/2014
830417^43103+1453037Lelio R Paula01/2013
8305(31*2^176188-1)/355553036Lelio R Paula01/2014
83062^176177+6094753035David Broadhurst05/2002
8307(22*10^53033-7)/353034Erik Branger09/2014
830813810^6909+6909^1381053023Hans Havermann06/2016
83102^176108+1609553014Lelio R Paula10/2009
83092^176107+1891553014Lelio R Paula07/2012
83113^111080-962852999Enzo Doria02/2013
83122^176047-155152996Yves Minet08/2012
83132^176042+7351952994Enzo Doria04/2016
8314lucasV(1715,1,2^14)/6553752986Mike Oakes04/2009
83152^175984-11225952977Enzo Doria06/2014
831611^50870+1052976Lelio R Paula01/2013
8317(11*10^52956+19)/352957Robert Price03/2016
8318gcd(V(949965),5*F(189993)*(F(189993)+1)+1)52941Serge Batalov04/2015
8319(98*10^52931-89)/9952931Ray Chandler11/2010
832013774^6963+6963^1377452931Hans Havermann06/2016
83212^175812-136752925Yves Minet05/2013
83222^175801+1155*17580152922Henri Lifchitz01/2005
832311^50801-909052904Enzo Doria02/2013
832443^32374+1252882Robert Price11/2013
83252^175628+1352870Lelio R Paula01/2011
83262^175615-174752866Yves Minet09/2012
83279*2^175586-752858Lelio R Paula03/2014
832812174^12937+12937^1217452854Norbert Schneider04/2016
8329(15*2^175565+1)/835952848Lelio R Paula07/2012
8330(2^175631-1)/330463093135534238072561/9273316952839Robert Kinser03/2017
833114256^5077+5077^1425652828Hans Havermann06/2016
83322^175467+8287552821Lelio R Paula07/2012
8333(67607*2^175426+1)/352813Lelio R Paula05/2014
833413^47400-6052801Lelio R Paula01/2013
83354*10^52792+6352793Robert Price06/2016
8337(78557*2^175360+1)/308752791Lelio R Paula06/2014
833618^42055-292952791Enzo Doria03/2013
83389*5^75521+252788Lelio R Paula09/2014
83396^67814+3152770Lelio R Paula10/2012
834070^28600+6952770Norbert Schneider10/2012
834114^46038+9752766Lelio R Paula01/2013
8342(61*10^52763-7)/952764Serge Batalov02/2009
83432*5^75474+952755Lelio R Paula09/2014
834410^52753+282643060952754Robert Price05/2015
834510^52753+18399752754Patrick De Geest01/2016
834610^52753-5015352753Patrick De Geest03/2016
834719846^455+455^1984652751Anatoly F. Selevich02/2007
83482^175217+7297752746Enzo Doria04/2016
8349(4*10^52740+41)/952740Robert Price11/2014
83502^175189+538552738Lelio R Paula08/2009
83512^175160+938552729Lelio R Paula07/2008
835212356^12885+12885^1235652724Norbert Schneider03/2016
83532^175137+1152722Lelio R Paula01/2011
835465^29077-64^2907752715Robert Price08/2013
83552*10^52713-8752714Robert Price06/2016
83562^175106-46552713Lelio R Paula08/2009
83572^175089-5869552708Lelio R Paula08/2009
83582^175045+19552694Lelio R Paula02/2011
83592^175025+14952688Lelio R Paula02/2011
8360(19^41201+1)/2052685Paul Bourdelais03/2010
83612*12^48815-5^4881552681Mike Oakes10/2010
8362335^20862-20862^33552678Norbert Schneider09/2015
83632^174983-760552676Lelio R Paula07/2009
83644*10^52667+1952668Robert Price04/2016
8365(10^52667+77)/352667Robert Price01/2017
836611434^12977+12977^1143452664Norbert Schneider04/2016
83672^174941-120352663Lelio R Paula07/2009
83682^174910+1270552654Lelio R Paula07/2012
83693^110338+7452645Lelio R Paula10/2012
83705^75303+1252635Lelio R Paula10/2012
83712^174836+25525552631Lelio R Paula07/2009
837220^40443+952618Lelio R Paula01/2013
8373(11*2^174788+1)/952617Lelio R Paula01/2012
8374(11*2^174786-1)/70352615Lelio R Paula01/2014
837511^50520-129052612Enzo Doria11/2012
8376(9913*2^174736-1)/33352603Lelio R Paula03/2015
837713145^10024+10024^1314552594Hans Havermann05/2016
83785003^14217-15052592Enzo Doria07/2012
837919^41123+1052587Lelio R Paula01/2013
83802^174683+1290952585Lelio R Paula01/2011
83812^174643+5952573Lelio R Paula01/2011
8382(1017*2^174640-1)/77352572Lelio R Paula03/2015
838313529^7662+7662^1352952552Hans Havermann06/2016
8384121421#+18876752548Makoto Morimoto02/2016
838520^40375-592352530Enzo Doria03/2013
8386(67607*2^174503+1)/9094807952528Lelio R Paula05/2014
8387(-lucasV(1,2,349014)+2)/(7*50873*1047043)52521Mike Oakes03/2017
83882^174462+34552519Lelio R Paula07/2009
8389t(178863)52509Robert Price10/2014
83902^174416+85552505Lelio R Paula07/2009
83916^67467-10352500Lelio R Paula10/2012
83922^174329-1126552479Enzo Doria06/2014
83932^174314-124152474Yves Minet05/2009
839452^30577-5152471Norbert Schneider08/2014
839515692^2205+2205^1569252465Hans Havermann06/2016
8396(2^174281-7)/62881702961552453Lelio R Paula02/2012
8397(2^174240+5)/352451Lelio R Paula02/2012
8398(15*2^174221+1)/40352445Lelio R Paula07/2012
839926313!2-3252443Robert Price10/2015
8400(3*2^174214-1)/374872952438Lelio R Paula01/2014
84012*3^109900-552436Lelio R Paula03/2014
84034159^14488-15052432Enzo Doria07/2012
8402(89*10^52431-71)/952432Robert Price11/2015
8404(7*2^174171-1)/68552429Lelio R Paula01/2014
8405(260137^9679+1)/26013852409Faysal YAtim03/2008
84062^174098+7952409Lelio R Paula01/2011
840735^33940-221452406Enzo Doria03/2013
840815^44557+252404Ray Chandler07/2011
84092^174049-43952394Yves Minet01/2012
84106^67329+11552393Lelio R Paula10/2012
84122^174041+26214552392Lelio R Paula07/2009
8411141^24377+252392Lelio R Paula05/2013
8413lucasU(285,1,21339)-lucasU(285,1,21338)52382Mike Oakes05/2009
84142^174001-595552380Lelio R Paula07/2009
8415lucasV(-1,2,347969)52375Mike Oakes02/2017
84163^109764-14052371Lelio R Paula10/2012
84172*3^109761+752370Lelio R Paula03/2014
84182^173944-11225352363Enzo Doria06/2014
84202^173940+111152362Lelio R Paula01/2011
8419(3126^14983-1)/312552362Richard Fischer03/2015
842115214^2763+2763^1521452358Hans Havermann05/2016
842213200^9247+9247^1320052352Hans Havermann05/2016
8423(1017*2^173867-1)/717552339Lelio R Paula03/2015
842413732^6465+6465^1373252327Hans Havermann05/2016
8425(2^173867-1)/5253663750268952326Donovan Johnson06/2005
84262^173811-68487752323Paul Bourdelais11/2012
84272^173807-595552322Lelio R Paula06/2009
84282^173796-104468952318Paul Bourdelais11/2012
842910^52317+6449752318Patrick De Geest12/2012
843010^52317+6474352318Patrick De Geest12/2012
843210^52317-7152317Robert Price05/2011
843110821^12968+12968^1082152317Norbert Schneider04/2016
8433(2^173778-3)/5795952308Lelio R Paula02/2012
84352^173727+952298Lelio R Paula01/2011
8434(14^45631+13^45631)/2752298Robert Price04/2013
843637856!3+656152293Robert Price11/2015
84374*3^109596+552292Lelio R Paula03/2014
843815436^2441+2441^1543652291Hans Havermann05/2016
843943^32005+2452280Robert Price11/2013
84402^173650-16552274Lelio R Paula02/2011
84414*10^52272+9352273Robert Price01/2017
844219^40873+8452267Lelio R Paula01/2013
84432^173621+424242952266Jason Earls09/2008
844414^45579-3152240Lelio R Paula01/2013
8445(10223*2^173518+1)/90352236Lelio R Paula05/2014
844620^40147-612352233Enzo Doria03/2013
84474^86754-3^(86754+1)52232Robert Price04/2016
84482^173477-343352222Yves Minet04/2009
8449(25*2^173446+1)/6152213Lelio R Paula07/2012
84503^109431-3852212Lelio R Paula10/2012
845113^46861-7252201Lelio R Paula01/2013
84522^173373-136352191Yves Minet03/2009
845311^50114-174052189Enzo Doria11/2012
845413735^6304+6304^1373552188Hans Havermann05/2016
845511^50111-111052186Enzo Doria11/2012
8456lucasU(46,1,31387)+lucasU(46,1,31386)52181Mike Oakes04/2009
845720^40105-858352178Enzo Doria03/2013
8458(10322^13001+2679^13001)/13001^252175Lelio R Paula08/2008
84592^173294+115552167Lelio R Paula07/2012
8461(19*2^173301-1)/2348952166Lelio R Paula01/2014
846015146^2781+2781^1514652166Hans Havermann06/2016
846211^50088-3252162Lelio R Paula01/2013
84633^109320+23652159Lelio R Paula10/2012
84642^173246-2863552153Lelio R Paula06/2009
84652*10^52147+1152148Robert Price01/2015
84662^173208-11262552141Enzo Doria06/2014
8467(9179*2^173206-1)/203552141Lelio R Paula03/2015
846815^44333-7652140Lelio R Paula01/2013
84692^173187-318952135Yves Minet10/2014
84702^173167+7557952129Enzo Doria04/2016
8471(2^173169+7)/9279352125Lelio R Paula02/2012
84729*7^61671+452119Lelio R Paula09/2014
84742^173130-922152118Lelio R Paula07/2008
8473(17*2^173129-1)/352118Lelio R Paula01/2014
84752^173100-11255952109Enzo Doria06/2014
84762^173091-11233952106Enzo Doria06/2014
847711^50030+2852101Lelio R Paula01/2013
8478(59*10^52099+13)/952100Robert Price09/2015
84792^173064-182952098Yves Minet09/2012
84802^173062-136152097Yves Minet08/2012
84813^109190-7052097Lelio R Paula10/2012
84822^173059+9019552096Lelio R Paula07/2012
84832^173048-11262552093Enzo Doria06/2014
848492^26524+9152088Norbert Schneider04/2013
848541^32295-4052085Theodore Burton02/2007
84862^173002+17752079Lelio R Paula02/2011
8487p(11334)#/2+852075Robert Price01/2017
84882^172965-11236352068Enzo Doria06/2014
84899*2^172935+752060Lelio R Paula03/2014
849011^49978-819052047Enzo Doria02/2013
849110^52041+63352042Patrick De Geest11/2012
849210^52041-9352041Robert Price05/2011
8493(21*2^172815-1)/86952021Lelio R Paula01/2014
8494(182*10^52018+1)/352020Robert Price02/2017
84954*6^66843-552015Lelio R Paula09/2014
849619^40670-5452007Lelio R Paula01/2013
84972^172756-11288352005Enzo Doria06/2014
849811832^12763-12763^1183251985Norbert Schneider02/2017
84997^61511-3651983Lelio R Paula10/2012
85002^172640-7551970Lelio R Paula01/2011


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Created by  Henri Lifchitz & Renaud Lifchitz : October, 26 2000, last modification: March, 18 2017 12:02 (Time in France)

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