PRP Records

Probable Primes Top 10000

(180278 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) !!!


Submit your PRPs


See the Top discoverers
See the Latest PRPs
Search by form



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(5*10^53855-107)/353856Robert Price01/2017
8502(72*10^53847-27)/9953847Patrick De Geest08/2004
85032^178841-86968810553837Lelio R Paula06/2012
85042*10^53834-2753835Robert Price02/2017
85052^178821-101152353831Paul Bourdelais11/2012
85062^178819-1553830Lelio R Paula02/2011
8507(14450!-1)/22529658153829Donovan Johnson04/2006
85082^178761-46553813Lelio R Paula10/2009
850918900^703+703^1890053808Anatoly F. Selevich02/2007
851013918^7343+7343^1391853806Hans Havermann08/2016
851110^53804+3174953805Patrick De Geest12/2012
851210^53804-7153804Robert Price05/2011
8513t(178994)53804Robert Price03/2015
8514(2^178693-lucasV(1,2,178693)+1)/253792Mike Oakes11/2016
85152^178671-11321553786Enzo Doria07/2014
851615110^3621+3621^1511053774Hans Havermann07/2016
85172^178611+9553768Lelio R Paula02/2011
85182^178597+571153764Lelio R Paula10/2011
85192^178598+1291553764Lelio R Paula07/2012
8520(9179*2^178579-1)/30353760Lelio R Paula03/2015
85215*7^63589+253740Lelio R Paula09/2014
85222^178516-11251553739Enzo Doria06/2014
852320^41302-2753736Lelio R Paula01/2013
85246^69054-3920953735Mike Oakes12/2010
852513086^12769+12769^1308653734Hans Havermann07/2016
85262^178455+7604353721Enzo Doria04/2016
8527(10^53718-7)/353718Makoto Kamada10/2004
8528(67607*2^178426+1)/353716Lelio R Paula05/2014
85299*10^53707+1153708Robert Kinser01/2017
853094601!8-253708Robert Price04/2017
853113214^11595+11595^1321453706Hans Havermann07/2016
8532Phi(134350,10)/537401/801196225153705Maksym Voznyy10/2011
85332^178367-37953694Yves Minet03/2013
8534(2^178364-5)/1153692Lelio R Paula02/2012
85354339^14760-16853688Enzo Doria06/2012
853612^49746-1153685Lelio R Paula01/2013
8538(9913*2^178266-1)/224753665Lelio R Paula03/2015
853713725^8128+8128^1372553665Hans Havermann07/2016
85392^178250-11326153659Enzo Doria07/2014
85402^178226+1171553652Lelio R Paula10/2009
854135^34742-197653645Enzo Doria03/2013
854220^41228-56353639Enzo Doria03/2013
8543359^20992+20992^35953637Norbert Schneider08/2014
8544(27*2^178183-1)/2906553636Lelio R Paula01/2014
8545(3^112414+7)/3738169653628Lelio R Paula03/2012
854617994^955+955^1799453623Anatoly F. Selevich10/2006
85472^178117-155153619Yves Minet08/2012
85482^178099-1128753614Enzo Doria06/2014
8549(15*2^178080-1)/30907153604Lelio R Paula01/2014
85505^76672-1376653592Enzo Doria02/2013
85516^68868-13753590Lelio R Paula10/2012
8552(5*2^178021+1)/817353587Lelio R Paula07/2012
85535^76654-2653579Lelio R Paula10/2012
8554(3^112297-2)/762753576Lelio R Paula03/2012
85553*2^177948-753569Lelio R Paula03/2014
855610^53558+1854353559Patrick De Geest12/2012
855710^53558-2153558Robert Price03/2011
85582^177792-9553521Lelio R Paula02/2011
855913392^9919+9919^1339253521Hans Havermann07/2016
856013105^12132+12132^1310553520Hans Havermann07/2016
856113^48042+8253517Lelio R Paula01/2013
85622^177768+3912153514Yves Minet10/2010
856313835^7366+7366^1383553504Hans Havermann07/2016
856417^43477+8453497Lelio R Paula01/2013
85655*10^53492+953493Dmitry Domanov11/2010
85662^177683+9553488Lelio R Paula01/2011
8567(2^177678+3)/51462753481Lelio R Paula02/2012
85682^177641-25546353476Gary Barnes08/2009
8569p(11608)#/2+1653469Robert Price12/2016
857037302#*10^(37302+52)+p(37302+1)53457Jason Earls08/2008
85711829^16384+1828^1638453449Henri Lifchitz01/2007
857235^34608-960253438Enzo Doria03/2013
8573(3^111992+8)/1486753430Lelio R Paula03/2012
85742^177480+186966153427Enzo Doria05/2016
8575(8*10^53411+1)/953411Serge Batalov12/2008
85764*5^76410-353409Lelio R Paula09/2014
85772^177380-11304553397Enzo Doria07/2014
85785^76362-2*3^7636253375Mike Oakes11/2009
85794159^14747-14053370Enzo Doria07/2012
8580(lucasV(1,2,354503)-2)/353358Mike Oakes03/2017
8581p(11586)#/2+3253357Robert Price12/2016
858215^45362-4653350Lelio R Paula01/2013
858314147^5892+5892^1414753338Hans Havermann07/2016
85847^63109+4653334Lelio R Paula10/2012
858520^40986-134353325Enzo Doria03/2013
85864*10^53324-8953325Robert Price08/2017
858720^40977-888353313Enzo Doria03/2013
85883^111711+266053300Lelio R Paula10/2012
85892^177040-1186553295Enzo Doria10/2012
8590(7*10^53287+17)/353288Erik Branger03/2014
859135^34506-1075853280Enzo Doria03/2013
8592(11*10^53274-17)/353275Erik Branger03/2014
8593(1017*2^176971-1)/33553275Lelio R Paula03/2015
85942^176961-283353271Yves Minet09/2014
85953^111642+11053267Lelio R Paula10/2012
859617^43290-9853267Lelio R Paula01/2013
85977^63028+3653265Lelio R Paula10/2012
8598(22*10^53264+71)/353265Robert Price05/2017
85997^63023-3653261Lelio R Paula10/2012
860019783^492+492^1978353256Anatoly F. Selevich02/2007
860113350^9739+9739^1335053247Hans Havermann10/2015
860214394^4993+4993^1439453235Hans Havermann10/2015
86032^176823-11280753230Enzo Doria06/2014
86041684^16495+16495^168453219Serge Batalov05/2014
860515277^3042+3042^1527753213Hans Havermann06/2016
8606(50322^11317-1)/5032153206Serge Batalov04/2015
86072^176742-159553205Lelio R Paula10/2009
8608(27*2^176767-1)/2045505635553204Lelio R Paula01/2014
8609(-lucasV(1,2,353460)-2)/(3^2*5^2)53199Mike Oakes03/2017
8610(3*2^176696-1)/29953189Lelio R Paula01/2014
8611(7*10^53185-1)/353186Erik Branger03/2014
86122^176629+46553171Lelio R Paula07/2012
8613(3*2^176604-1)/35953162Lelio R Paula01/2014
86145^76038-1436653149Enzo Doria02/2013
861515156^3209+3209^1515653143Hans Havermann06/2016
86162^176532-283753142Yves Minet09/2014
861752^30967-5153140Norbert Schneider08/2014
86189*5^76023-253139Lelio R Paula09/2014
8619(14283!+1)/46421617753135Michael Porter03/2016
86202^176461-16553121Lelio R Paula02/2011
8621(62*10^53111+1)/953112Serge Batalov05/2010
86222^176403-13953103Lelio R Paula02/2011
862355^30508-253095Lelio R Paula08/2013
8624(48591^11329-1)/4859053090Serge Batalov04/2015
86253^111254-8853082Lelio R Paula10/2012
862615^45129-5653076Lelio R Paula01/2013
86272^176293-7353070Lelio R Paula01/2011
8628(67*10^53068+41)/953069Robert Price09/2015
862915271^2986+2986^1527153069Hans Havermann06/2016
86302^176255-66753059Yves Minet01/2012
863136471*2^176221+864753053Paul Vanderveen04/2016
8632(19*10^53049-1)/953050Serge Batalov03/2009
86339*2^176203-553044Lelio R Paula03/2014
86342^176205-9439553043Lelio R Paula08/2011
8635(19*2^176224-1)/21791691353042Lelio R Paula01/2014
863617^43103+1453037Lelio R Paula01/2013
8637(31*2^176188-1)/355553036Lelio R Paula01/2014
86382^176177+6094753035David Broadhurst05/2002
8639(22*10^53033-7)/353034Erik Branger09/2014
864013810^6909+6909^1381053023Hans Havermann06/2016
86422^176108+1609553014Lelio R Paula10/2009
86412^176107+1891553014Lelio R Paula07/2012
86433^111080-962852999Enzo Doria02/2013
86442^176047-155152996Yves Minet08/2012
86452^176042+7351952994Enzo Doria04/2016
8646lucasV(1715,1,2^14)/6553752986Mike Oakes04/2009
86472^175984-11225952977Enzo Doria06/2014
864811^50870+1052976Lelio R Paula01/2013
8649(11*10^52956+19)/352957Robert Price03/2016
8650gcd(V(949965),5*F(189993)*(F(189993)+1)+1)52941Serge Batalov04/2015
8651(-lucasV(1,2,351735)+2)/(3*7*263)52938Mike Oakes03/2017
8652(98*10^52931-89)/9952931Ray Chandler11/2010
865313774^6963+6963^1377452931Hans Havermann06/2016
86542^175812-136752925Yves Minet05/2013
86552^175801+1155*17580152922Henri Lifchitz01/2005
865611^50801-909052904Enzo Doria02/2013
865743^32374+1252882Robert Price11/2013
86582^175628+1352870Lelio R Paula01/2011
86592^175615-174752866Yves Minet09/2012
86609*2^175586-752858Lelio R Paula03/2014
866112174^12937+12937^1217452854Norbert Schneider04/2016
8662(15*2^175565+1)/835952848Lelio R Paula07/2012
8663(2^175631-1)/330463093135534238072561/9273316952839Robert Kinser03/2017
866414256^5077+5077^1425652828Hans Havermann06/2016
86652^175467+8287552821Lelio R Paula07/2012
8666(67607*2^175426+1)/352813Lelio R Paula05/2014
866713^47400-6052801Lelio R Paula01/2013
86684*10^52792+6352793Robert Price06/2016
8670(78557*2^175360+1)/308752791Lelio R Paula06/2014
866918^42055-292952791Enzo Doria03/2013
86719*5^75521+252788Lelio R Paula09/2014
86726^67814+3152770Lelio R Paula10/2012
867370^28600+6952770Norbert Schneider10/2012
867414^46038+9752766Lelio R Paula01/2013
8675(61*10^52763-7)/952764Serge Batalov02/2009
86762*5^75474+952755Lelio R Paula09/2014
867710^52753+282643060952754Robert Price05/2015
867810^52753+18399752754Patrick De Geest01/2016
867910^52753-5015352753Patrick De Geest03/2016
868019846^455+455^1984652751Anatoly F. Selevich02/2007
86812^175217+7297752746Enzo Doria04/2016
8682p(11466)#/2-25652746Robert Price05/2017
8683(4*10^52740+41)/952740Robert Price11/2014
86842^175189+538552738Lelio R Paula08/2009
86852^175160+938552729Lelio R Paula07/2008
868612356^12885+12885^1235652724Norbert Schneider03/2016
86872^175137+1152722Lelio R Paula01/2011
868865^29077-64^2907752715Robert Price08/2013
86892*10^52713-8752714Robert Price06/2016
86902^175106-46552713Lelio R Paula08/2009
86912^175089-5869552708Lelio R Paula08/2009
86922^175045+19552694Lelio R Paula02/2011
86932^175025+14952688Lelio R Paula02/2011
8694(19^41201+1)/2052685Paul Bourdelais03/2010
86952*12^48815-5^4881552681Mike Oakes10/2010
8696335^20862-20862^33552678Norbert Schneider09/2015
86972^174983-760552676Lelio R Paula07/2009
86984*10^52667+1952668Robert Price04/2016
8699(10^52667+77)/352667Robert Price01/2017
870011434^12977+12977^1143452664Norbert Schneider04/2016
87012^174941-120352663Lelio R Paula07/2009
87022^174910+1270552654Lelio R Paula07/2012
87033^110338+7452645Lelio R Paula10/2012
87045^75303+1252635Lelio R Paula10/2012
87052^174836+25525552631Lelio R Paula07/2009
870620^40443+952618Lelio R Paula01/2013
8707(11*2^174788+1)/952617Lelio R Paula01/2012
8708(11*2^174786-1)/70352615Lelio R Paula01/2014
870911^50520-129052612Enzo Doria11/2012
8710(9913*2^174736-1)/33352603Lelio R Paula03/2015
871113145^10024+10024^1314552594Hans Havermann05/2016
87125003^14217-15052592Enzo Doria07/2012
871319^41123+1052587Lelio R Paula01/2013
87142^174683+1290952585Lelio R Paula01/2011
87152^174643+5952573Lelio R Paula01/2011
8716(1017*2^174640-1)/77352572Lelio R Paula03/2015
871713529^7662+7662^1352952552Hans Havermann06/2016
8718121421#+18876752548Makoto Morimoto02/2016
871920^40375-592352530Enzo Doria03/2013
8720(67607*2^174503+1)/9094807952528Lelio R Paula05/2014
8721(-lucasV(1,2,349014)+2)/(7*50873*1047043)52521Mike Oakes03/2017
87222^174462+34552519Lelio R Paula07/2009
8723t(178863)52509Robert Price10/2014
87242^174416+85552505Lelio R Paula07/2009
87256^67467-10352500Lelio R Paula10/2012
8726(2^174533-1)/(193594572654550537*91917886778031629891960890057)52494Dario Alpern06/2017
87272^174329-1126552479Enzo Doria06/2014
87282^174314-124152474Yves Minet05/2009
872952^30577-5152471Norbert Schneider08/2014
873015692^2205+2205^1569252465Hans Havermann06/2016
8731(2^174281-7)/62881702961552453Lelio R Paula02/2012
8732(2^174240+5)/352451Lelio R Paula02/2012
8733(86*10^52450-221)/952451Robert Price06/2017
8734(15*2^174221+1)/40352445Lelio R Paula07/2012
873526313!2-3252443Robert Price10/2015
8736(3*2^174214-1)/374872952438Lelio R Paula01/2014
87372*3^109900-552436Lelio R Paula03/2014
87394159^14488-15052432Enzo Doria07/2012
8738(89*10^52431-71)/952432Robert Price11/2015
87402^174170-394152431Yves Minet04/2017
8741(7*2^174171-1)/68552429Lelio R Paula01/2014
8743(260137^9679+1)/26013852409Faysal YAtim03/2008
87422^174098+7952409Lelio R Paula01/2011
874435^33940-221452406Enzo Doria03/2013
874515^44557+252404Ray Chandler07/2011
87462^174049-43952394Yves Minet01/2012
87476^67329+11552393Lelio R Paula10/2012
87492^174041+26214552392Lelio R Paula07/2009
8748141^24377+252392Lelio R Paula05/2013
8750lucasU(285,1,21339)-lucasU(285,1,21338)52382Mike Oakes05/2009


Find by discoverer :


Created by  Henri Lifchitz & Renaud Lifchitz : October, 26 2000, last modification: August, 20 2017 08:36 (Time in France)

Go back
Valid XHTML 1.0!    Valid CSS!