PRP Records

Probable Primes Top 10000

(172751 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 ?
825110^54084+3*3^5408454085Mike Oakes05/2010
82522^179613-179554069Lelio R Paula10/2009
82532^179589-101152354062Paul Bourdelais11/2012
82542^179574-253154058Yves Minet07/2014
8255(41*10^54051-23)/954052Robert Price05/2015
8256117^26131-11654044Norbert Schneider10/2013
8257(10^54038-31)/354038Serge Batalov12/2014
825811^51885-8454033Lelio R Paula01/2013
825914990^4011+4011^1499054013Hans Havermann07/2016
8260(19*2^179414+1)/754010Lelio R Paula07/2012
82613^113182-1040854002Enzo Doria02/2013
826235^34970-878653997Enzo Doria03/2013
82632^179371-163758753997Enzo Doria05/2015
826419^42225-9253996Lelio R Paula01/2013
8265(3^113188+7)/7391767578453994Lelio R Paula03/2012
82667*3^113162+853993Lelio R Paula03/2014
8267(10^53991+179)/953991Serge Batalov12/2014
82692^179350-214553990Lelio R Paula10/2009
8268(-lucasV(1,2,358718)-2)/(5*17*19)53990Mike Oakes04/2017
82708^59782-6^59782-3^5978253989Mike Oakes11/2009
82713*7^63861+853970Lelio R Paula09/2014
82722^179274+7138953967Enzo Doria04/2016
82732^179259-5869553963Lelio R Paula10/2009
82746^69345+6153961Lelio R Paula10/2012
8275(-lucasV(1,2,358635)+2)/(7*179317*232171*960251*1716271)53957Mike Oakes04/2017
8276(40216^11719-1)/4021553955Serge Batalov04/2015
827714^47067-353945Lelio R Paula01/2013
8278(2^179168-5)/5953934Lelio R Paula02/2012
82792^179128+841553923Lelio R Paula07/2012
82802^179120+253353921Henri Lifchitz09/2004
8281(2^179126+78557)/464932118753913Lelio R Paula05/2012
828374^28842+7353913Norbert Schneider11/2012
82821271^17368+17368^127153913Serge Batalov05/2014
82842^179079+5353909Lelio R Paula02/2011
828517^43807+5453903Lelio R Paula01/2013
828617^43807+3053903Lelio R Paula01/2013
82873^112951-31053892Lelio R Paula10/2012
8288Phi(7,2957!)53888Robert Price05/2015
8289(10223*2^178975+1)/3398553877Lelio R Paula05/2014
82902^178944-21920953868Enzo Doria11/2012
8291(10^53859+149)/353859Serge Batalov12/2014
82922^178910-19153858Lelio R Paula02/2011
829316170^2141+2141^1617053857Hans Havermann07/2016
8294(5*10^53855-107)/353856Robert Price01/2017
8295(72*10^53847-27)/9953847Patrick De Geest08/2004
82962^178841-86968810553837Lelio R Paula06/2012
82972*10^53834-2753835Robert Price02/2017
82982^178821-101152353831Paul Bourdelais11/2012
82992^178819-1553830Lelio R Paula02/2011
8300(14450!-1)/22529658153829Donovan Johnson04/2006
83012^178761-46553813Lelio R Paula10/2009
830218900^703+703^1890053808Anatoly F. Selevich02/2007
830313918^7343+7343^1391853806Hans Havermann08/2016
830410^53804+3174953805Patrick De Geest12/2012
830510^53804-7153804Robert Price05/2011
8306t(178994)53804Robert Price03/2015
8307(2^178693-lucasV(1,2,178693)+1)/253792Mike Oakes11/2016
83082^178671-11321553786Enzo Doria07/2014
830915110^3621+3621^1511053774Hans Havermann07/2016
83102^178611+9553768Lelio R Paula02/2011
83112^178597+571153764Lelio R Paula10/2011
83122^178598+1291553764Lelio R Paula07/2012
8313(9179*2^178579-1)/30353760Lelio R Paula03/2015
83145*7^63589+253740Lelio R Paula09/2014
83152^178516-11251553739Enzo Doria06/2014
831620^41302-2753736Lelio R Paula01/2013
83176^69054-3920953735Mike Oakes12/2010
831813086^12769+12769^1308653734Hans Havermann07/2016
83192^178455+7604353721Enzo Doria04/2016
8320(10^53718-7)/353718Makoto Kamada10/2004
8321(67607*2^178426+1)/353716Lelio R Paula05/2014
83229*10^53707+1153708Robert Kinser01/2017
832313214^11595+11595^1321453706Hans Havermann07/2016
8324Phi(134350,10)/537401/801196225153705Maksym Voznyy10/2011
83252^178367-37953694Yves Minet03/2013
8326(2^178364-5)/1153692Lelio R Paula02/2012
83274339^14760-16853688Enzo Doria06/2012
832812^49746-1153685Lelio R Paula01/2013
8330(9913*2^178266-1)/224753665Lelio R Paula03/2015
832913725^8128+8128^1372553665Hans Havermann07/2016
83312^178250-11326153659Enzo Doria07/2014
83322^178226+1171553652Lelio R Paula10/2009
833335^34742-197653645Enzo Doria03/2013
833420^41228-56353639Enzo Doria03/2013
8335359^20992+20992^35953637Norbert Schneider08/2014
8336(27*2^178183-1)/2906553636Lelio R Paula01/2014
8337(3^112414+7)/3738169653628Lelio R Paula03/2012
833817994^955+955^1799453623Anatoly F. Selevich10/2006
83392^178117-155153619Yves Minet08/2012
83402^178099-1128753614Enzo Doria06/2014
8341(15*2^178080-1)/30907153604Lelio R Paula01/2014
83425^76672-1376653592Enzo Doria02/2013
83436^68868-13753590Lelio R Paula10/2012
8344(5*2^178021+1)/817353587Lelio R Paula07/2012
83455^76654-2653579Lelio R Paula10/2012
8346(3^112297-2)/762753576Lelio R Paula03/2012
83473*2^177948-753569Lelio R Paula03/2014
834810^53558+1854353559Patrick De Geest12/2012
834910^53558-2153558Robert Price03/2011
83502^177792-9553521Lelio R Paula02/2011
835113392^9919+9919^1339253521Hans Havermann07/2016
835213105^12132+12132^1310553520Hans Havermann07/2016
835313^48042+8253517Lelio R Paula01/2013
83542^177768+3912153514Yves Minet10/2010
835513835^7366+7366^1383553504Hans Havermann07/2016
835617^43477+8453497Lelio R Paula01/2013
83575*10^53492+953493Dmitry Domanov11/2010
83582^177683+9553488Lelio R Paula01/2011
8359(2^177678+3)/51462753481Lelio R Paula02/2012
83602^177641-25546353476Gary Barnes08/2009
8361p(11608)#/2+1653469Robert Price12/2016
836237302#*10^(37302+52)+p(37302+1)53457Jason Earls08/2008
83631829^16384+1828^1638453449Henri Lifchitz01/2007
836435^34608-960253438Enzo Doria03/2013
8365(3^111992+8)/1486753430Lelio R Paula03/2012
83662^177480+186966153427Enzo Doria05/2016
8367(8*10^53411+1)/953411Serge Batalov12/2008
83684*5^76410-353409Lelio R Paula09/2014
83692^177380-11304553397Enzo Doria07/2014
83705^76362-2*3^7636253375Mike Oakes11/2009
83714159^14747-14053370Enzo Doria07/2012
8372(lucasV(1,2,354503)-2)/353358Mike Oakes03/2017
8373p(11586)#/2+3253357Robert Price12/2016
837415^45362-4653350Lelio R Paula01/2013
837514147^5892+5892^1414753338Hans Havermann07/2016
83767^63109+4653334Lelio R Paula10/2012
837720^40986-134353325Enzo Doria03/2013
837820^40977-888353313Enzo Doria03/2013
83793^111711+266053300Lelio R Paula10/2012
83802^177040-1186553295Enzo Doria10/2012
8381(7*10^53287+17)/353288Erik Branger03/2014
838235^34506-1075853280Enzo Doria03/2013
8383(11*10^53274-17)/353275Erik Branger03/2014
8384(1017*2^176971-1)/33553275Lelio R Paula03/2015
83852^176961-283353271Yves Minet09/2014
83863^111642+11053267Lelio R Paula10/2012
838717^43290-9853267Lelio R Paula01/2013
83887^63028+3653265Lelio R Paula10/2012
83897^63023-3653261Lelio R Paula10/2012
839019783^492+492^1978353256Anatoly F. Selevich02/2007
839113350^9739+9739^1335053247Hans Havermann10/2015
839214394^4993+4993^1439453235Hans Havermann10/2015
83932^176823-11280753230Enzo Doria06/2014
83941684^16495+16495^168453219Serge Batalov05/2014
839515277^3042+3042^1527753213Hans Havermann06/2016
8396(50322^11317-1)/5032153206Serge Batalov04/2015
83972^176742-159553205Lelio R Paula10/2009
8398(27*2^176767-1)/2045505635553204Lelio R Paula01/2014
8399(-lucasV(1,2,353460)-2)/(3^2*5^2)53199Mike Oakes03/2017
8400(3*2^176696-1)/29953189Lelio R Paula01/2014
8401(7*10^53185-1)/353186Erik Branger03/2014
84022^176629+46553171Lelio R Paula07/2012
8403(3*2^176604-1)/35953162Lelio R Paula01/2014
84045^76038-1436653149Enzo Doria02/2013
840515156^3209+3209^1515653143Hans Havermann06/2016
84062^176532-283753142Yves Minet09/2014
840752^30967-5153140Norbert Schneider08/2014
84089*5^76023-253139Lelio R Paula09/2014
8409(14283!+1)/46421617753135Michael Porter03/2016
84102^176461-16553121Lelio R Paula02/2011
8411(62*10^53111+1)/953112Serge Batalov05/2010
84122^176403-13953103Lelio R Paula02/2011
841355^30508-253095Lelio R Paula08/2013
8414(48591^11329-1)/4859053090Serge Batalov04/2015
84153^111254-8853082Lelio R Paula10/2012
841615^45129-5653076Lelio R Paula01/2013
84172^176293-7353070Lelio R Paula01/2011
8419(67*10^53068+41)/953069Robert Price09/2015
841815271^2986+2986^1527153069Hans Havermann06/2016
84202^176255-66753059Yves Minet01/2012
842136471*2^176221+864753053Paul Vanderveen04/2016
8422(19*10^53049-1)/953050Serge Batalov03/2009
84239*2^176203-553044Lelio R Paula03/2014
84242^176205-9439553043Lelio R Paula08/2011
8425(19*2^176224-1)/21791691353042Lelio R Paula01/2014
842617^43103+1453037Lelio R Paula01/2013
8427(31*2^176188-1)/355553036Lelio R Paula01/2014
84282^176177+6094753035David Broadhurst05/2002
8429(22*10^53033-7)/353034Erik Branger09/2014
843013810^6909+6909^1381053023Hans Havermann06/2016
84322^176108+1609553014Lelio R Paula10/2009
84312^176107+1891553014Lelio R Paula07/2012
84333^111080-962852999Enzo Doria02/2013
84342^176047-155152996Yves Minet08/2012
84352^176042+7351952994Enzo Doria04/2016
8436lucasV(1715,1,2^14)/6553752986Mike Oakes04/2009
84372^175984-11225952977Enzo Doria06/2014
843811^50870+1052976Lelio R Paula01/2013
8439(11*10^52956+19)/352957Robert Price03/2016
8440gcd(V(949965),5*F(189993)*(F(189993)+1)+1)52941Serge Batalov04/2015
8441(-lucasV(1,2,351735)+2)/(3*7*263)52938Mike Oakes03/2017
8443(98*10^52931-89)/9952931Ray Chandler11/2010
844213774^6963+6963^1377452931Hans Havermann06/2016
84442^175812-136752925Yves Minet05/2013
84452^175801+1155*17580152922Henri Lifchitz01/2005
844611^50801-909052904Enzo Doria02/2013
844743^32374+1252882Robert Price11/2013
84482^175628+1352870Lelio R Paula01/2011
84492^175615-174752866Yves Minet09/2012
84509*2^175586-752858Lelio R Paula03/2014
845112174^12937+12937^1217452854Norbert Schneider04/2016
8452(15*2^175565+1)/835952848Lelio R Paula07/2012
8453(2^175631-1)/330463093135534238072561/9273316952839Robert Kinser03/2017
845414256^5077+5077^1425652828Hans Havermann06/2016
84552^175467+8287552821Lelio R Paula07/2012
8456(67607*2^175426+1)/352813Lelio R Paula05/2014
845713^47400-6052801Lelio R Paula01/2013
84584*10^52792+6352793Robert Price06/2016
8460(78557*2^175360+1)/308752791Lelio R Paula06/2014
845918^42055-292952791Enzo Doria03/2013
84619*5^75521+252788Lelio R Paula09/2014
84626^67814+3152770Lelio R Paula10/2012
846370^28600+6952770Norbert Schneider10/2012
846414^46038+9752766Lelio R Paula01/2013
8465(61*10^52763-7)/952764Serge Batalov02/2009
84662*5^75474+952755Lelio R Paula09/2014
846710^52753+282643060952754Robert Price05/2015
846810^52753+18399752754Patrick De Geest01/2016
846910^52753-5015352753Patrick De Geest03/2016
847019846^455+455^1984652751Anatoly F. Selevich02/2007
84712^175217+7297752746Enzo Doria04/2016
8472(4*10^52740+41)/952740Robert Price11/2014
84732^175189+538552738Lelio R Paula08/2009
84742^175160+938552729Lelio R Paula07/2008
847512356^12885+12885^1235652724Norbert Schneider03/2016
84762^175137+1152722Lelio R Paula01/2011
847765^29077-64^2907752715Robert Price08/2013
84782*10^52713-8752714Robert Price06/2016
84792^175106-46552713Lelio R Paula08/2009
84802^175089-5869552708Lelio R Paula08/2009
84812^175045+19552694Lelio R Paula02/2011
84822^175025+14952688Lelio R Paula02/2011
8483(19^41201+1)/2052685Paul Bourdelais03/2010
84842*12^48815-5^4881552681Mike Oakes10/2010
8485335^20862-20862^33552678Norbert Schneider09/2015
84862^174983-760552676Lelio R Paula07/2009
84874*10^52667+1952668Robert Price04/2016
8488(10^52667+77)/352667Robert Price01/2017
848911434^12977+12977^1143452664Norbert Schneider04/2016
84902^174941-120352663Lelio R Paula07/2009
84912^174910+1270552654Lelio R Paula07/2012
84923^110338+7452645Lelio R Paula10/2012
84935^75303+1252635Lelio R Paula10/2012
84942^174836+25525552631Lelio R Paula07/2009
849520^40443+952618Lelio R Paula01/2013
8496(11*2^174788+1)/952617Lelio R Paula01/2012
8497(11*2^174786-1)/70352615Lelio R Paula01/2014
849811^50520-129052612Enzo Doria11/2012
8499(9913*2^174736-1)/33352603Lelio R Paula03/2015
850013145^10024+10024^1314552594Hans Havermann05/2016


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Created by  Henri Lifchitz & Renaud Lifchitz : October, 26 2000, last modification: April, 24 2017 22:44 (Time in France)

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