PRP Records

Probable Primes Top 10000

(247113 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 ?
950135^34970-878653997Enzo Doria03/2013
95022^179371-163758753997Enzo Doria05/2015
950319^42225-9253996Lelio R Paula01/2013
950410190^13471-13471^1019053995Norbert Schneider05/2018
9505(3^113188+7)/7391767578453994Lelio R Paula03/2012
95067*3^113162+853993Lelio R Paula03/2014
9507(10^53991+179)/953991Serge Batalov12/2014
95092^179350-214553990Lelio R Paula10/2009
9508(-lucasV(1,2,358718)-2)/(5*17*19)53990Mike Oakes04/2017
95108^59782-6^59782-3^5978253989Mike Oakes11/2009
95113*7^63861+853970Lelio R Paula09/2014
95122^179274+7138953967Enzo Doria04/2016
95132^179259-5869553963Lelio R Paula10/2009
95146^69345+6153961Lelio R Paula10/2012
9515(-lucasV(1,2,358635)+2)/(7*179317*232171*960251*1716271)53957Mike Oakes04/2017
9516(40216^11719-1)/4021553955Serge Batalov04/2015
951789*10^53951-953953Robert Price05/2017
95186703^14100-14100^670353951Norbert Schneider11/2018
951914^47067-353945Lelio R Paula01/2013
9520p(11700)#/2-51253937Robert Price07/2017
9521(2^179168-5)/5953934Lelio R Paula02/2012
95222^179128+841553923Lelio R Paula07/2012
95232^179120+253353921Henri Lifchitz09/2004
9524(2^179126+78557)/464932118753913Lelio R Paula05/2012
952574^28842+7353913Norbert Schneider11/2012
95261271^17368+17368^127153913Serge Batalov05/2014
95272^179079+5353909Lelio R Paula02/2011
952817^43807+5453903Lelio R Paula01/2013
952917^43807+3053903Lelio R Paula01/2013
95303^112951-31053892Lelio R Paula10/2012
9531Phi(7,2957!)53888Robert Price05/2015
95328275^13754-13754^827553885Norbert Schneider10/2018
9533(10223*2^178975+1)/3398553877Lelio R Paula05/2014
95342^178944-21920953868Enzo Doria11/2012
9535(10^53859+149)/353859Serge Batalov12/2014
95362^178910-19153858Lelio R Paula02/2011
953716170^2141+2141^1617053857Hans Havermann07/2016
9538(5*10^53855-107)/353856Robert Price01/2017
9539(72*10^53847-27)/9953847Patrick De Geest08/2004
95402^178841-86968810553837Lelio R Paula06/2012
95412*10^53834-2753835Robert Price02/2017
95432^178821-101152353831Paul Bourdelais11/2012
954212601^13128-13128^1260153831Norbert Schneider10/2017
95442^178819-1553830Lelio R Paula02/2011
9545(14450!-1)/22529658153829Donovan Johnson04/2006
9546(124351#+125386)/(2^5*71*883*4489103*9820259)53826Makoto Morimoto10/2017
954710530^13381-13381^1053053825Norbert Schneider03/2018
95482^178761-46553813Lelio R Paula10/2009
954918900^703+703^1890053808Anatoly F. Selevich02/2007
955013918^7343+7343^1391853806Hans Havermann08/2016
955110^53804+3174953805Patrick De Geest12/2012
955210^53804-7153804Robert Price05/2011
9553t(178994)53804Robert Price03/2015
9554(2^178693-lucasV(1,2,178693)+1)/253792Mike Oakes11/2016
95552^178671-11321553786Enzo Doria07/2014
955615110^3621+3621^1511053774Hans Havermann07/2016
95572^178611+9553768Lelio R Paula02/2011
95582^178597+571153764Lelio R Paula10/2011
95592^178598+1291553764Lelio R Paula07/2012
9560(9179*2^178579-1)/30353760Lelio R Paula03/2015
956110671^13342-13342^1067153745Norbert Schneider02/2018
95625*7^63589+253740Lelio R Paula09/2014
95632^178516-11251553739Enzo Doria06/2014
956420^41302-2753736Lelio R Paula01/2013
95656^69054-3920953735Mike Oakes12/2010
956613086^12769+12769^1308653734Hans Havermann07/2016
95672^178455+7604353721Enzo Doria04/2016
9568(10^53718-7)/353718Makoto Kamada10/2004
9569(67607*2^178426+1)/353716Lelio R Paula05/2014
95709*10^53707+1153708Robert Kinser01/2017
957194601!8-253708Robert Price04/2017
957213214^11595+11595^1321453706Hans Havermann07/2016
9573Phi(134350,10)/537401/801196225153705Maksym Voznyy10/2011
95742^178367-37953694Yves Minet03/2013
9575(2^178364-5)/1153692Lelio R Paula02/2012
95764339^14760-16853688Enzo Doria06/2012
957712^49746-1153685Lelio R Paula01/2013
957812950^13051-13051^1295053670Norbert Schneider08/2017
9580(9913*2^178266-1)/224753665Lelio R Paula03/2015
957913725^8128+8128^1372553665Hans Havermann07/2016
95812^178250-11326153659Enzo Doria07/2014
95822^178226+1171553652Lelio R Paula10/2009
958335^34742-197653645Enzo Doria03/2013
958420^41228-56353639Enzo Doria03/2013
9585359^20992+20992^35953637Norbert Schneider08/2014
9586(27*2^178183-1)/2906553636Lelio R Paula01/2014
9587(3^112414+7)/3738169653628Lelio R Paula03/2012
958817994^955+955^1799453623Anatoly F. Selevich10/2006
95892^178117-155153619Yves Minet08/2012
95902^178099-1128753614Enzo Doria06/2014
959110751^13298-13298^1075153611Norbert Schneider01/2018
9592(15*2^178080-1)/30907153604Lelio R Paula01/2014
95935^76672-1376653592Enzo Doria02/2013
95946^68868-13753590Lelio R Paula10/2012
9595(5*2^178021+1)/817353587Lelio R Paula07/2012
95965^76654-2653579Lelio R Paula10/2012
9597(3^112297-2)/762753576Lelio R Paula03/2012
95983*2^177948-753569Lelio R Paula03/2014
959910^53558+1854353559Patrick De Geest12/2012
960010^53558-2153558Robert Price03/2011
96012^177792-9553521Lelio R Paula02/2011
960213392^9919+9919^1339253521Hans Havermann07/2016
960313105^12132+12132^1310553520Hans Havermann07/2016
960413^48042+8253517Lelio R Paula01/2013
96052^177768+3912153514Yves Minet10/2010
960613835^7366+7366^1383553504Hans Havermann07/2016
960717^43477+8453497Lelio R Paula01/2013
96085*10^53492+953493Dmitry Domanov11/2010
96092^177683+9553488Lelio R Paula01/2011
961011057^13226-13226^1105753482Norbert Schneider12/2017
9611(2^177678+3)/51462753481Lelio R Paula02/2012
96122^177641-25546353476Gary Barnes08/2009
9613p(11608)#/2+1653469Robert Price12/2016
9614(14*10^53465+211)/953466Robert Price11/2017
961537302#*10^(37302+52)+p(37302+1)53457Jason Earls08/2008
961612001^13104-13104^1200153455Norbert Schneider10/2017
96171829^16384+1828^1638453449Henri Lifchitz01/2007
961810^53442+1262153443Patrick De Geest06/2018
961910^53442-200753442Patrick De Geest06/2018
962035^34608-960253438Enzo Doria03/2013
9621(3^111992+8)/1486753430Lelio R Paula03/2012
96232^177480+186966153427Enzo Doria05/2016
962211791^13122-13122^1179153427Norbert Schneider10/2017
9624(8*10^53411+1)/953411Serge Batalov12/2008
96254*5^76410-353409Lelio R Paula09/2014
96262^177380-11304553397Enzo Doria07/2014
96285^76362-2*3^7636253375Mike Oakes11/2009
962772365!6-2453375Robert Price08/2018
96294159^14747-14053370Enzo Doria07/2012
9630(lucasV(1,2,354503)-2)/353358Mike Oakes03/2017
9631p(11586)#/2+3253357Robert Price12/2016
963215^45362-4653350Lelio R Paula01/2013
963314147^5892+5892^1414753338Hans Havermann07/2016
96347^63109+4653334Lelio R Paula10/2012
963520^40986-134353325Enzo Doria03/2013
96364*10^53324-8953325Robert Price08/2017
963720^40977-888353313Enzo Doria03/2013
96383^111711+266053300Lelio R Paula10/2012
96392^177040-1186553295Enzo Doria10/2012
9640(7*10^53287+17)/353288Erik Branger03/2014
964135^34506-1075853280Enzo Doria03/2013
9642(11*10^53274-17)/353275Erik Branger03/2014
9643(1017*2^176971-1)/33553275Lelio R Paula03/2015
96442^176961-283353271Yves Minet09/2014
96453^111642+11053267Lelio R Paula10/2012
964617^43290-9853267Lelio R Paula01/2013
96477^63028+3653265Lelio R Paula10/2012
9648(22*10^53264+71)/353265Robert Price05/2017
96497^63023-3653261Lelio R Paula10/2012
965019783^492+492^1978353256Anatoly F. Selevich02/2007
965113350^9739+9739^1335053247Hans Havermann10/2015
965214394^4993+4993^1439453235Hans Havermann10/2015
96532^176823-11280753230Enzo Doria06/2014
96541684^16495+16495^168453219Serge Batalov05/2014
965515277^3042+3042^1527753213Hans Havermann06/2016
9656(50322^11317-1)/5032153206Serge Batalov04/2015
96572^176742-159553205Lelio R Paula10/2009
9658(27*2^176767-1)/2045505635553204Lelio R Paula01/2014
965972149!6-1253200Robert Price08/2018
9660(-lucasV(1,2,353460)-2)/(3^2*5^2)53199Mike Oakes03/2017
9661(3*2^176696-1)/29953189Lelio R Paula01/2014
9662(7*10^53185-1)/353186Erik Branger03/2014
96632^176629+46553171Lelio R Paula07/2012
9664(3*2^176604-1)/35953162Lelio R Paula01/2014
966510955^13158-13158^1095553154Norbert Schneider11/2017
96665^76038-1436653149Enzo Doria02/2013
966715156^3209+3209^1515653143Hans Havermann06/2016
96682^176532-283753142Yves Minet09/2014
966952^30967-5153140Norbert Schneider08/2014
96709*5^76023-253139Lelio R Paula09/2014
9671(14283!+1)/46421617753135Michael Porter03/2016
96722^176461-16553121Lelio R Paula02/2011
9673(62*10^53111+1)/953112Serge Batalov05/2010
96742^176403-13953103Lelio R Paula02/2011
967555^30508-253095Lelio R Paula08/2013
9676(48591^11329-1)/4859053090Serge Batalov04/2015
96773^111254-8853082Lelio R Paula10/2012
967815^45129-5653076Lelio R Paula01/2013
9679(640^18913-1)/63953071Eric Chen09/2018
96802^176293-7353070Lelio R Paula01/2011
9681(67*10^53068+41)/953069Robert Price09/2015
968215271^2986+2986^1527153069Hans Havermann06/2016
96832^176255-66753059Yves Minet01/2012
968436471*2^176221+864753053Paul Vanderveen04/2016
9685(19*10^53049-1)/953050Serge Batalov03/2009
96869*2^176203-553044Lelio R Paula03/2014
96872^176205-9439553043Lelio R Paula08/2011
9688(19*2^176224-1)/21791691353042Lelio R Paula01/2014
96898600^13481-13481^860053041Norbert Schneider05/2018
969017^43103+1453037Lelio R Paula01/2013
9691(31*2^176188-1)/355553036Lelio R Paula01/2014
96922^176177+6094753035David Broadhurst05/2002
9693(22*10^53033-7)/353034Erik Branger09/2014
969413810^6909+6909^1381053023Hans Havermann06/2016
96952^176108+1609553014Lelio R Paula10/2009
96962^176107+1891553014Lelio R Paula07/2012
96973^111080-962852999Enzo Doria02/2013
96982^176047-155152996Yves Minet08/2012
96992^176042+7351952994Enzo Doria04/2016
9700lucasV(1715,1,2^14)/6553752986Mike Oakes04/2009
97012^175984-11225952977Enzo Doria06/2014
970211^50870+1052976Lelio R Paula01/2013
9703(11*10^52956+19)/352957Robert Price03/2016
97046773^13820-13820^677352942Norbert Schneider11/2018
9705gcd(V(949965),5*F(189993)*(F(189993)+1)+1)52941Serge Batalov04/2015
9706(-lucasV(1,2,351735)+2)/(3*7*263)52938Mike Oakes03/2017
9708(98*10^52931-89)/9952931Ray Chandler11/2010
970713774^6963+6963^1377452931Hans Havermann06/2016
97092^175812-136752925Yves Minet05/2013
97102^175801+1155*17580152922Henri Lifchitz01/2005
971111^50801-909052904Enzo Doria02/2013
97127803^13592-13592^780352904Norbert Schneider07/2018
971343^32374+1252882Robert Price11/2013
97142^175628+1352870Lelio R Paula01/2011
97152^175615-174752866Yves Minet09/2012
9716(13*10^52861+107)/352862Robert Price11/2017
97179*2^175586-752858Lelio R Paula03/2014
971812174^12937+12937^1217452854Norbert Schneider04/2016
9719(15*2^175565+1)/835952848Lelio R Paula07/2012
9720(2^175631-1)/330463093135534238072561/9273316952839Robert Kinser03/2017
972114256^5077+5077^1425652828Hans Havermann06/2016
97222^175467+8287552821Lelio R Paula07/2012
9723(7*10^52819+167)/352820Robert Kinser10/2017
9725(67607*2^175426+1)/352813Lelio R Paula05/2014
972471671!6-3252813Robert Price08/2018
972613^47400-6052801Lelio R Paula01/2013
97274*10^52792+6352793Robert Price06/2016
9729(78557*2^175360+1)/308752791Lelio R Paula06/2014
972818^42055-292952791Enzo Doria03/2013
97309*5^75521+252788Lelio R Paula09/2014
97316^67814+3152770Lelio R Paula10/2012
973270^28600+6952770Norbert Schneider10/2012
973314^46038+9752766Lelio R Paula01/2013
9734(61*10^52763-7)/952764Serge Batalov02/2009
97352*5^75474+952755Lelio R Paula09/2014
973610^52753+282643060952754Robert Price05/2015
973710^52753+18399752754Patrick De Geest01/2016
973810^52753-5015352753Patrick De Geest03/2016
973919846^455+455^1984652751Anatoly F. Selevich02/2007
97412^175217+7297752746Enzo Doria04/2016
9740p(11466)#/2-25652746Robert Price05/2017
9742(4*10^52740+41)/952740Robert Price11/2014
97432^175189+538552738Lelio R Paula08/2009
97442^175160+938552729Lelio R Paula07/2008
974512356^12885+12885^1235652724Norbert Schneider03/2016
97462^175137+1152722Lelio R Paula01/2011
974765^29077-64^2907752715Robert Price08/2013
97482*10^52713-8752714Robert Price06/2016
97492^175106-46552713Lelio R Paula08/2009
97502^175089-5869552708Lelio R Paula08/2009


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Created by  Henri Lifchitz & Renaud Lifchitz : October, 26 2000, last modification: December, 11 2018 05:54 (Time in France)

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