PRP Records

Probable Primes Top 10000

(259919 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 (> 50000) Who ? When ?
825115^60697+5671386Lelio R Paula01/2015
82522^237118+17771380Lelio R Paula02/2012
82532^237110+6971378Lelio R Paula02/2012
825415^60690-5871377Lelio R Paula01/2015
8255(5*2^237125-1)/59985119171374Lelio R Paula01/2014
825620311^3262+3262^2031171363Hans Havermann11/2019
8257(3^149567+2)/53971359Lelio R Paula06/2012
8258(5*10^71357-143)/371358Robert Price04/2016
82592^237039-11462171356Enzo Doria05/2015
8260(2^237037+3462)/271355Stefano Morozzi01/2020
826112^66116-3771352Lelio R Paula02/2015
8262(3^149497+2^149497)/571328Jean-Louis Charton10/2010
82632^236941-6694571327Lelio R Paula05/2012
82642^236911-114771318Yves Minet10/2009
826565^39337+4271315Lelio R Paula01/2016
8266(2^236863+3234)/271303Stefano Morozzi01/2020
82676*10^71299+771300Dmitry Domanov11/2010
8268(25*2^236843+1)/375371295Lelio R Paula06/2012
826910^71291+1518771292Patrick De Geest03/2016
827110^71291-558730911971291Robert Price03/2015
827010^71291-27358171291Patrick De Geest03/2016
8272-numer(bernoulli(22808)/22808)71290T. D. Noe09/2005
8273(2^236781+1514)/271278Stefano Morozzi01/2020
8274(2^236775+2886)/271277Stefano Morozzi01/2020
827515105^17054+17054^1510571271Norbert Schneider08/2018
8276(2^236738+9)/1371265Lelio R Paula05/2012
82775^101949+4271260Lelio R Paula07/2014
82785*10^71237+971238Dmitry Domanov11/2010
82792^236634-1602571234Enzo Doria04/2013
828071^38478+7071233Norbert Schneider12/2014
82819*7^84280+871226Lelio R Paula10/2014
8282(2^236603+2378)/271225Stefano Morozzi01/2020
8283(10^71223+59)/371223Serge Batalov12/2014
828423260^1153+1153^2326071219Hans Havermann10/2019
8285(15185*2^236569-1)/45371216Lelio R Paula04/2015
828651829#+(216091#)/(51829#)71208Makoto Morimoto03/2016
82872^236528-17371203Lelio R Paula02/2012
82883*2^236511-571198Lelio R Paula04/2014
82892^236477-9971187Lelio R Paula02/2012
829011^68356-213071186Enzo Doria12/2012
829115128^17031+17031^1512871186Norbert Schneider08/2018
829211^68355-312071185Enzo Doria12/2012
8293(2^236463+998)/271183Stefano Morozzi01/2020
829436^45737-35^4573771181Robert Price10/2012
8295(3^149183-lucasV(1,3,149183)+1)/371178Paul Vanderveen12/2017
82962^236432+2571174Lelio R Paula02/2012
82975^101818-1280671168Enzo Doria02/2013
8298(7*10^71166-457)/971166Robert Price09/2017
829965^39253+6271163Lelio R Paula01/2016
830039^44718+3871150Norbert Schneider05/2014
830118996^5557+5557^1899671137Hans Havermann10/2019
830264983!4-25671135Robert Price11/2019
83032^236296-40771133Yves Minet02/2012
83042^236286-11771130Lelio R Paula02/2012
8305(2^236283+1074)/271128Stefano Morozzi01/2020
83062^236257-11119371121Enzo Doria05/2014
83077^84149-3671115Lelio R Paula08/2014
8308164176#-p(164176)71108Henri Lifchitz12/2018
8309(2^236214+2934)/271108Stefano Morozzi01/2020
83102^236209-11212371106Enzo Doria06/2014
831118^56644-498571104Enzo Doria03/2013
8312(46*10^71077+521)/971078Robert Price08/2017
831321^53753+271074Ray Chandler08/2011
8314(86*10^71068-311)/971069Robert Price10/2017
83152^236081-11092371068Enzo Doria05/2014
8316(293*27^49642-1736)/1371058Curtis Bright05/2015
831765^39192+2271052Lelio R Paula01/2016
8318(2^236016+1246)/271048Stefano Morozzi01/2020
8319(439#+1)^397-439#^39771038Mike Oakes11/2010
83207^84050-271031Lelio R Paula09/2013
832115813^16916+16916^1581371031Norbert Schneider09/2019
8322(2^235956+3978)/271030Stefano Morozzi01/2020
832364877!4+12871007Robert Price09/2019
832418562^6681+6681^1856270997Hans Havermann10/2019
8325(2^235802+474)/270984Stefano Morozzi01/2020
832620^54558-2370982Lelio R Paula01/2015
83272^235793-11255570981Enzo Doria06/2014
832849936!3-3^4993670981Robert Price08/2015
83292^235787-7879570979Lelio R Paula05/2012
8330(2^235761+2930)/270971Stefano Morozzi01/2020
8331Perrin(581132)70970Eric W. Weisstein02/2011
8332(2^235748+3478)/270967Stefano Morozzi01/2020
833314^61913-9770961Lelio R Paula01/2015
83352^235720+1632170959Yves Minet03/2010
83342^235718+1609570959Lelio R Paula05/2012
8336163841#+34993370957Nicolas PALAU11/2016
83372^235710+770956Lelio R Paula02/2012
8338(175^31627+1)/17670939Eric Chen10/2017
8339(2^235644+670)/270936Stefano Morozzi01/2020
83402^235635-11208770934Enzo Doria06/2014
8341153^32467+15270931Norbert Schneider11/2018
83432^235575-196570916Lelio R Paula05/2012
83426^91133+10170916Lelio R Paula01/2015
8344(21181*2^235505+1)/370898Lelio R Paula06/2014
8345(14*10^70896+211)/970897Robert Price11/2017
83465^101425+8470894Lelio R Paula07/2014
8347177^31536+270893Lelio R Paula05/2013
834843*71^38292+470891Serge Batalov03/2016
8349(29*2^235506-1)/11202978570888Lelio R Paula01/2014
835011^68045-153070862Enzo Doria12/2012
83515*10^70858+2170859Robert Price01/2017
83532^235326+370841Donovan Johnson02/2006
835234523!2+470841Robert Price02/2015
8354(31*2^235307+1)/370836Lelio R Paula06/2012
8355(2^235310+1038)/270836Stefano Morozzi01/2020
83562^235308+13570835Lelio R Paula02/2012
8357r(35414,90)*1000+91170831Patrick De Geest07/2004
83582^235274+15970825Lelio R Paula02/2012
83593^148409+7070810Lelio R Paula11/2014
8360(19*10^70794+17)/970795Robert Price03/2015
8361(2^235144+1350)/270786Stefano Morozzi01/2020
83622^235108-23270970775Paul Bourdelais03/2013
836322995^1196+1196^2299570773Hans Havermann11/2019
8364(2^235099-2^117550+1)/57077211/2006
836519^55325-670748Lelio R Paula08/2014
8366257^29356+29356^25770746Norbert Schneider10/2014
836722*10^70729+370731Robert Price10/2017
83682^234956+1171570729Lelio R Paula05/2012
8369(7*10^70727-43)/970727Robert Price10/2014
8370(2^234897+3906)/270711Stefano Morozzi01/2020
83712^234890-3034170709Enzo Doria11/2012
837217^57461+1470703Lelio R Paula01/2015
837318281^7366+7366^1828170697Hans Havermann09/2019
8374(9179*2^234834-1)/570696Lelio R Paula04/2015
83752*10^70688+5170689Robert Price10/2017
8376123^33822-12270685Norbert Schneider01/2015
83777*10^70680-9970681Robert Price11/2017
8378(2^234784+3646)/270677Stefano Morozzi01/2020
8379(21*2^234772-1)/209570672Lelio R Paula01/2014
8380(2^234762+1498)/270671Stefano Morozzi01/2020
8381(2^234723+3690)/270659Stefano Morozzi01/2020
8382(2^234718+3798)/270657Stefano Morozzi01/2020
8383(2^234680+2902)/270646Stefano Morozzi01/2020
8384(29*2^234686-1)/2114570645Lelio R Paula01/2014
8385(15*2^234688-1)/527814170643Lelio R Paula01/2014
83872^234655-6770639Lelio R Paula02/2012
8386(79*10^70638-61)/970639Robert Price10/2015
83882^234652-17370638Lelio R Paula02/2012
83892^234618-364570628Lelio R Paula05/2012
8390(2^234610-5)/1970624Lelio R Paula05/2012
83914*5^101038+970624Lelio R Paula10/2014
83922^234603+7196370623Enzo Doria04/2016
83932^234600-11312970622Enzo Doria07/2014
8394(2^234601+1446)/270622Stefano Morozzi01/2020
83952^234586+970618Lelio R Paula02/2012
83963^148008+2670618Robert Price11/2013
8397(7*10^70616-151)/970616Robert Price09/2017
839865^38947+3270608Lelio R Paula01/2016
8399(2^234517+2750)/270597Stefano Morozzi01/2020
840018363^6988+6988^1836370594Hans Havermann10/2019
8401(2^234488-3)/1170587Lelio R Paula05/2012
8402(3*2^234451+1)/3570576Lelio R Paula08/2012
8403Phi(159495,10)70560Maksym Voznyy09/2015
84042^234383-403570557Lelio R Paula05/2012
8405(2^234364+3618)/270551Stefano Morozzi01/2020
8406(2^234333+3482)/270541Stefano Morozzi01/2020
84072^234315-11124170536Enzo Doria05/2014
840814^61526+9770517Lelio R Paula01/2015
840914742^16915+16915^1474270512Norbert Schneider10/2019
8410(2^234203+3306)/270502Stefano Morozzi01/2020
8411(3*2^234170+1)/1370492Lelio R Paula08/2012
841251^41281-50^4128170491Robert Price02/2013
84132^234141-11212370484Enzo Doria06/2014
84142^234139+1228570483Lelio R Paula04/2012
84152^234133-316370482Yves Minet04/2009
84162^234115+8370476Lelio R Paula02/2012
84172^234114-159570476Lelio R Paula05/2012
841824^51061-23^5106170475Robert Price07/2012
8419(2^234099+2538)/270471Stefano Morozzi01/2020
842019471^16428-270467Faysal YAtim09/2005
84217^83381+1270466Robert Price01/2014
8422(2^234080+3922)/270465Stefano Morozzi01/2020
84232^234067-11142770462Enzo Doria05/2014
8424(266*10^70457+1)/370459Robert Price02/2016
8425(31*2^234041-1)/9770453Lelio R Paula01/2014
8426(2^234030+642)/270450Stefano Morozzi01/2020
84272^234026+1290970449Lelio R Paula04/2012
8428(2^234021+3510)/270448Stefano Morozzi01/2020
84292^233965-1970431Lelio R Paula02/2012
8430(5*2^233932-1)/17970419Lelio R Paula01/2014
84312^233908-1710970414Enzo Doria05/2013
8432695^24772+24772^69570402Norbert Schneider09/2016
84333*5^100719-270401Lelio R Paula10/2014
8434(2^233862+1878)/270400Stefano Morozzi01/2020
8435(2^233843+3330)/270394Stefano Morozzi01/2020
84362^233829-11135570390Enzo Doria05/2014
8437(19775^16384+1)/270388Henri Lifchitz03/2007
84387*3^147519+870386Lelio R Paula04/2014
8439141^32749-270385Lelio R Paula10/2017
84405*7^83265+270368Lelio R Paula10/2014
8441(23*10^70363+97)/370364Robert Price02/2017
8442(23*2^233749-1)/3532570363Lelio R Paula01/2014
84435^100652-1391670353Enzo Doria02/2013
844445^42555-270353Lelio R Paula08/2013
84452^233661-6170339Lelio R Paula02/2012
8446(2^233641+1014)/270333Stefano Morozzi01/2020
8447(2^233614+1074)/270325Stefano Morozzi01/2020
8448(2^233592+2986)/270318Stefano Morozzi01/2020
84492^233523-11224970298Enzo Doria06/2014
84505*3^147324-870293Lelio R Paula04/2014
84512^233488-1306570287Enzo Doria11/2012
8452(3^147322+8)/4285170286Lelio R Paula06/2012
8453(22*10^70259+161)/370260Robert Price02/2017
84552^233388+46570257Lelio R Paula11/2012
845414^61299+5970257Lelio R Paula01/2015
84562^233383+9406570256Lelio R Paula04/2012
845749471!3-656170253Robert Price11/2015
84587^83121+6^(83121-1)70246Robert Price03/2016
8459(197*10^70241-11)/370243Robert Price10/2017
846023*10^70240-770242Robert Price03/2016
8461(2^233301+2730)/270231Stefano Morozzi01/2020
8462(71*10^70227-53)/970228Robert Price10/2015
846319825^3486+3486^1982570227Hans Havermann10/2019
846410815^17408+17408^1081570225Norbert Schneider05/2019
8465(2^233247-9)/1770214Lelio R Paula05/2012
8466(11^67421-2^67421)/970211Robert Price01/2013
8467(23*10^70209-41)/970210Robert Price03/2015
8468(29*10^70194-11)/970195Robert Price04/2015
84693^147109+19670189Lelio R Paula05/2014
8470(34*10^70191-7)/9/3/40583/57304770181Makoto Morimoto05/2016
84719^73538+8^(73538+1)70174Robert Price06/2016
84722*5^100391+770171Lelio R Paula10/2014
847399^35156-270159Lelio R Paula08/2013
8474(68*10^70148+7)/370150Robert Price03/2016
847511^67360-603070149Enzo Doria01/2013
8476(35*10^70130-377)/970131Robert Price12/2017
847749391!3+3^4939170128Robert Price09/2015
8478(229*10^70122-1)/370124Robert Price12/2016
84797^82975-9270123Lelio R Paula07/2014
848020294^2853+2853^2029470122Hans Havermann10/2019
848165^38670+5870106Lelio R Paula01/2016
8482105^34684+34684^10570103Serge Batalov05/2014
848318597^5882+5882^1859770102Hans Havermann10/2019
8484134^32955-13370099Norbert Schneider03/2015
84872^232836-22790370091Enzo Doria12/2012
84862^232837-185917370091Enzo Doria03/2016
848517778^8761+8761^1777870091Hans Havermann10/2019
84883*2^232820+570087Lelio R Paula04/2014
84902^232799+9019570080Lelio R Paula02/2013
84892^232799-11223770080Enzo Doria06/2014
849117894^8247+8247^1789470079Hans Havermann09/2019
8492(2^232766+954)/270070Stefano Morozzi01/2020
84932^232759+26214570068Lelio R Paula04/2012
849416817^14670+14670^1681770067Hans Havermann09/2019
84953*2^232750+770066Lelio R Paula04/2014
849612^64918-1170059Lelio R Paula01/2015
84977^82899-1270058Lelio R Paula09/2013
8498(22*10^70051-13)/970052Robert Price03/2015
849916428^16615-16615^1642870042Norbert Schneider11/2019
8500(2^232685-7)/251462570039Lelio R Paula04/2012


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Created by  Henri Lifchitz & Renaud Lifchitz : October, 26 2000, last modification: March, 29 2020 17:41 (Time in France)

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