PRP Records

Probable Primes Top 10000

(174961 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 ?
85017^63109+4653334Lelio R Paula10/2012
850220^40986-134353325Enzo Doria03/2013
850320^40977-888353313Enzo Doria03/2013
85043^111711+266053300Lelio R Paula10/2012
85052^177040-1186553295Enzo Doria10/2012
8506(7*10^53287+17)/353288Erik Branger03/2014
850735^34506-1075853280Enzo Doria03/2013
8508(11*10^53274-17)/353275Erik Branger03/2014
8509(1017*2^176971-1)/33553275Lelio R Paula03/2015
85102^176961-283353271Yves Minet09/2014
85113^111642+11053267Lelio R Paula10/2012
851217^43290-9853267Lelio R Paula01/2013
85137^63028+3653265Lelio R Paula10/2012
8514(22*10^53264+71)/353265Robert Price05/2017
85157^63023-3653261Lelio R Paula10/2012
851619783^492+492^1978353256Anatoly F. Selevich02/2007
851713350^9739+9739^1335053247Hans Havermann10/2015
851814394^4993+4993^1439453235Hans Havermann10/2015
85192^176823-11280753230Enzo Doria06/2014
85201684^16495+16495^168453219Serge Batalov05/2014
852115277^3042+3042^1527753213Hans Havermann06/2016
8522(50322^11317-1)/5032153206Serge Batalov04/2015
85232^176742-159553205Lelio R Paula10/2009
8524(27*2^176767-1)/2045505635553204Lelio R Paula01/2014
8525(-lucasV(1,2,353460)-2)/(3^2*5^2)53199Mike Oakes03/2017
8526(3*2^176696-1)/29953189Lelio R Paula01/2014
8527(7*10^53185-1)/353186Erik Branger03/2014
85282^176629+46553171Lelio R Paula07/2012
8529(3*2^176604-1)/35953162Lelio R Paula01/2014
85305^76038-1436653149Enzo Doria02/2013
853115156^3209+3209^1515653143Hans Havermann06/2016
85322^176532-283753142Yves Minet09/2014
853352^30967-5153140Norbert Schneider08/2014
85349*5^76023-253139Lelio R Paula09/2014
8535(14283!+1)/46421617753135Michael Porter03/2016
85362^176461-16553121Lelio R Paula02/2011
8537(62*10^53111+1)/953112Serge Batalov05/2010
85382^176403-13953103Lelio R Paula02/2011
853955^30508-253095Lelio R Paula08/2013
8540(48591^11329-1)/4859053090Serge Batalov04/2015
85413^111254-8853082Lelio R Paula10/2012
854215^45129-5653076Lelio R Paula01/2013
85432^176293-7353070Lelio R Paula01/2011
8545(67*10^53068+41)/953069Robert Price09/2015
854415271^2986+2986^1527153069Hans Havermann06/2016
85462^176255-66753059Yves Minet01/2012
854736471*2^176221+864753053Paul Vanderveen04/2016
8548(19*10^53049-1)/953050Serge Batalov03/2009
85499*2^176203-553044Lelio R Paula03/2014
85502^176205-9439553043Lelio R Paula08/2011
8551(19*2^176224-1)/21791691353042Lelio R Paula01/2014
855217^43103+1453037Lelio R Paula01/2013
8553(31*2^176188-1)/355553036Lelio R Paula01/2014
85542^176177+6094753035David Broadhurst05/2002
8555(22*10^53033-7)/353034Erik Branger09/2014
855613810^6909+6909^1381053023Hans Havermann06/2016
85582^176108+1609553014Lelio R Paula10/2009
85572^176107+1891553014Lelio R Paula07/2012
85593^111080-962852999Enzo Doria02/2013
85602^176047-155152996Yves Minet08/2012
85612^176042+7351952994Enzo Doria04/2016
8562lucasV(1715,1,2^14)/6553752986Mike Oakes04/2009
85632^175984-11225952977Enzo Doria06/2014
856411^50870+1052976Lelio R Paula01/2013
8565(11*10^52956+19)/352957Robert Price03/2016
8566gcd(V(949965),5*F(189993)*(F(189993)+1)+1)52941Serge Batalov04/2015
8567(-lucasV(1,2,351735)+2)/(3*7*263)52938Mike Oakes03/2017
8569(98*10^52931-89)/9952931Ray Chandler11/2010
856813774^6963+6963^1377452931Hans Havermann06/2016
85702^175812-136752925Yves Minet05/2013
85712^175801+1155*17580152922Henri Lifchitz01/2005
857211^50801-909052904Enzo Doria02/2013
857343^32374+1252882Robert Price11/2013
85742^175628+1352870Lelio R Paula01/2011
85752^175615-174752866Yves Minet09/2012
85769*2^175586-752858Lelio R Paula03/2014
857712174^12937+12937^1217452854Norbert Schneider04/2016
8578(15*2^175565+1)/835952848Lelio R Paula07/2012
8579(2^175631-1)/330463093135534238072561/9273316952839Robert Kinser03/2017
858014256^5077+5077^1425652828Hans Havermann06/2016
85812^175467+8287552821Lelio R Paula07/2012
8582(67607*2^175426+1)/352813Lelio R Paula05/2014
858313^47400-6052801Lelio R Paula01/2013
85844*10^52792+6352793Robert Price06/2016
8586(78557*2^175360+1)/308752791Lelio R Paula06/2014
858518^42055-292952791Enzo Doria03/2013
85879*5^75521+252788Lelio R Paula09/2014
85886^67814+3152770Lelio R Paula10/2012
858970^28600+6952770Norbert Schneider10/2012
859014^46038+9752766Lelio R Paula01/2013
8591(61*10^52763-7)/952764Serge Batalov02/2009
85922*5^75474+952755Lelio R Paula09/2014
859310^52753+282643060952754Robert Price05/2015
859410^52753+18399752754Patrick De Geest01/2016
859510^52753-5015352753Patrick De Geest03/2016
859619846^455+455^1984652751Anatoly F. Selevich02/2007
85972^175217+7297752746Enzo Doria04/2016
8598p(11466)#/2-25652746Robert Price05/2017
8599(4*10^52740+41)/952740Robert Price11/2014
86002^175189+538552738Lelio R Paula08/2009
86012^175160+938552729Lelio R Paula07/2008
860212356^12885+12885^1235652724Norbert Schneider03/2016
86032^175137+1152722Lelio R Paula01/2011
860465^29077-64^2907752715Robert Price08/2013
86052*10^52713-8752714Robert Price06/2016
86062^175106-46552713Lelio R Paula08/2009
86072^175089-5869552708Lelio R Paula08/2009
86082^175045+19552694Lelio R Paula02/2011
86092^175025+14952688Lelio R Paula02/2011
8610(19^41201+1)/2052685Paul Bourdelais03/2010
86112*12^48815-5^4881552681Mike Oakes10/2010
8612335^20862-20862^33552678Norbert Schneider09/2015
86132^174983-760552676Lelio R Paula07/2009
86144*10^52667+1952668Robert Price04/2016
8615(10^52667+77)/352667Robert Price01/2017
861611434^12977+12977^1143452664Norbert Schneider04/2016
86172^174941-120352663Lelio R Paula07/2009
86182^174910+1270552654Lelio R Paula07/2012
86193^110338+7452645Lelio R Paula10/2012
86205^75303+1252635Lelio R Paula10/2012
86212^174836+25525552631Lelio R Paula07/2009
862220^40443+952618Lelio R Paula01/2013
8623(11*2^174788+1)/952617Lelio R Paula01/2012
8624(11*2^174786-1)/70352615Lelio R Paula01/2014
862511^50520-129052612Enzo Doria11/2012
8626(9913*2^174736-1)/33352603Lelio R Paula03/2015
862713145^10024+10024^1314552594Hans Havermann05/2016
86285003^14217-15052592Enzo Doria07/2012
862919^41123+1052587Lelio R Paula01/2013
86302^174683+1290952585Lelio R Paula01/2011
86312^174643+5952573Lelio R Paula01/2011
8632(1017*2^174640-1)/77352572Lelio R Paula03/2015
863313529^7662+7662^1352952552Hans Havermann06/2016
8634121421#+18876752548Makoto Morimoto02/2016
863520^40375-592352530Enzo Doria03/2013
8636(67607*2^174503+1)/9094807952528Lelio R Paula05/2014
8637(-lucasV(1,2,349014)+2)/(7*50873*1047043)52521Mike Oakes03/2017
86382^174462+34552519Lelio R Paula07/2009
8639t(178863)52509Robert Price10/2014
86402^174416+85552505Lelio R Paula07/2009
86416^67467-10352500Lelio R Paula10/2012
8642(2^174533-1)/(193594572654550537*91917886778031629891960890057)52494Dario Alpern06/2017
86432^174329-1126552479Enzo Doria06/2014
86442^174314-124152474Yves Minet05/2009
864552^30577-5152471Norbert Schneider08/2014
864615692^2205+2205^1569252465Hans Havermann06/2016
8647(2^174281-7)/62881702961552453Lelio R Paula02/2012
8648(2^174240+5)/352451Lelio R Paula02/2012
8649(86*10^52450-221)/952451Robert Price06/2017
8650(15*2^174221+1)/40352445Lelio R Paula07/2012
865126313!2-3252443Robert Price10/2015
8652(3*2^174214-1)/374872952438Lelio R Paula01/2014
86532*3^109900-552436Lelio R Paula03/2014
86554159^14488-15052432Enzo Doria07/2012
8654(89*10^52431-71)/952432Robert Price11/2015
86562^174170-394152431Yves Minet04/2017
8657(7*2^174171-1)/68552429Lelio R Paula01/2014
8659(260137^9679+1)/26013852409Faysal YAtim03/2008
86582^174098+7952409Lelio R Paula01/2011
866035^33940-221452406Enzo Doria03/2013
866115^44557+252404Ray Chandler07/2011
86622^174049-43952394Yves Minet01/2012
86636^67329+11552393Lelio R Paula10/2012
86652^174041+26214552392Lelio R Paula07/2009
8664141^24377+252392Lelio R Paula05/2013
8666lucasU(285,1,21339)-lucasU(285,1,21338)52382Mike Oakes05/2009
86672^174001-595552380Lelio R Paula07/2009
8668lucasV(-1,2,347969)52375Mike Oakes02/2017
86693^109764-14052371Lelio R Paula10/2012
86702*3^109761+752370Lelio R Paula03/2014
86712^173944-11225352363Enzo Doria06/2014
86732^173940+111152362Lelio R Paula01/2011
8672(3126^14983-1)/312552362Richard Fischer03/2015
867415214^2763+2763^1521452358Hans Havermann05/2016
867513200^9247+9247^1320052352Hans Havermann05/2016
8676(1017*2^173867-1)/717552339Lelio R Paula03/2015
867713732^6465+6465^1373252327Hans Havermann05/2016
8678(2^173867-1)/5253663750268952326Donovan Johnson06/2005
86792^173811-68487752323Paul Bourdelais11/2012
86802^173807-595552322Lelio R Paula06/2009
86812^173796-104468952318Paul Bourdelais11/2012
868210^52317+6449752318Patrick De Geest12/2012
868310^52317+6474352318Patrick De Geest12/2012
868510^52317-7152317Robert Price05/2011
868410821^12968+12968^1082152317Norbert Schneider04/2016
8686(298*10^52308-7)/352310Robert Price06/2017
8687(2^173778-3)/5795952308Lelio R Paula02/2012
86882^173727+952298Lelio R Paula01/2011
8689(14^45631+13^45631)/2752298Robert Price04/2013
869037856!3+656152293Robert Price11/2015
86914*3^109596+552292Lelio R Paula03/2014
869215436^2441+2441^1543652291Hans Havermann05/2016
869343^32005+2452280Robert Price11/2013
86942^173650-16552274Lelio R Paula02/2011
86954*10^52272+9352273Robert Price01/2017
869619^40873+8452267Lelio R Paula01/2013
86972^173621+424242952266Jason Earls09/2008
8698numbpart(46909^2-1)52247Serge Batalov04/2017
869914^45579-3152240Lelio R Paula01/2013
8700(10223*2^173518+1)/90352236Lelio R Paula05/2014
870120^40147-612352233Enzo Doria03/2013
87024^86754-3^(86754+1)52232Robert Price04/2016
87032^173477-343352222Yves Minet04/2009
8704(25*2^173446+1)/6152213Lelio R Paula07/2012
87053^109431-3852212Lelio R Paula10/2012
87062^173424-395952206Yves Minet04/2017
870713^46861-7252201Lelio R Paula01/2013
87082^173373-136352191Yves Minet03/2009
870911^50114-174052189Enzo Doria11/2012
871013735^6304+6304^1373552188Hans Havermann05/2016
871111^50111-111052186Enzo Doria11/2012
8712lucasU(46,1,31387)+lucasU(46,1,31386)52181Mike Oakes04/2009
871320^40105-858352178Enzo Doria03/2013
8714(10322^13001+2679^13001)/13001^252175Lelio R Paula08/2008
87152^173314-394152173Yves Minet04/2017
87162^173294+115552167Lelio R Paula07/2012
8717(19*2^173301-1)/2348952166Lelio R Paula01/2014
871815146^2781+2781^1514652166Hans Havermann06/2016
871911^50088-3252162Lelio R Paula01/2013
87203^109320+23652159Lelio R Paula10/2012
87212^173246-2863552153Lelio R Paula06/2009
87222*10^52147+1152148Robert Price01/2015
87232^173208-11262552141Enzo Doria06/2014
8724(9179*2^173206-1)/203552141Lelio R Paula03/2015
872515^44333-7652140Lelio R Paula01/2013
87262^173187-318952135Yves Minet10/2014
87272^173167+7557952129Enzo Doria04/2016
8728(2^173169+7)/9279352125Lelio R Paula02/2012
8729(25*10^52119+23)/352120Robert Price06/2017
87309*7^61671+452119Lelio R Paula09/2014
87322^173130-922152118Lelio R Paula07/2008
8731(17*2^173129-1)/352118Lelio R Paula01/2014
87332^173100-11255952109Enzo Doria06/2014
87342^173091-11233952106Enzo Doria06/2014
873511^50030+2852101Lelio R Paula01/2013
8736(59*10^52099+13)/952100Robert Price09/2015
87372^173064-182952098Yves Minet09/2012
87382^173062-136152097Yves Minet08/2012
87393^109190-7052097Lelio R Paula10/2012
87402^173059+9019552096Lelio R Paula07/2012
87412^173048-11262552093Enzo Doria06/2014
874292^26524+9152088Norbert Schneider04/2013
874341^32295-4052085Theodore Burton02/2007
87442^173002+17752079Lelio R Paula02/2011
8745p(11334)#/2+852075Robert Price01/2017
87462^172965-11236352068Enzo Doria06/2014
87479*2^172935+752060Lelio R Paula03/2014
874811^49978-819052047Enzo Doria02/2013
874910^52041+63352042Patrick De Geest11/2012
875010^52041-9352041Robert Price05/2011


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Created by  Henri Lifchitz & Renaud Lifchitz : October, 26 2000, last modification: June, 22 2017 08:34 (Time in France)

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