PRP Records

Probable Primes Top 10000

(255169 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 ?
725136^46030+3571637Norbert Schneider04/2014
7252(74*10^71621+313)/971622Robert Price11/2017
72532^237905-9171617Lelio R Paula02/2012
7254(31*2^237902-1)/12371616Lelio R Paula01/2014
7255(15185*2^237866-1)/4396771605Lelio R Paula04/2015
725616696^16957+16957^1669671603Norbert Schneider09/2019
7257(24737*2^237841+1)/2571601Lelio R Paula06/2014
72582^237846+129971599Lelio R Paula05/2012
72596^92004+19980171594Mike Oakes02/2011
7260159^32516+271581Lelio R Paula05/2013
72612^237781+85571580Lelio R Paula05/2012
72622^237720-407971561Yves Minet06/2011
72632^237698-11094571555Enzo Doria05/2014
72642^237695-11323971554Enzo Doria07/2014
72658*5^102362-971549Lelio R Paula10/2014
7266(4*10^71546-31)/971546Erik Branger05/2011
72672^237650+3771540Lelio R Paula02/2012
726818^56977-439171522Enzo Doria03/2013
7270(22699*2^237565+1)/413663771512Lelio R Paula06/2014
7269((1+sqrt(7)+sqrt(6))^48479-1)*((1+sqrt(7)-sqrt(6))^48479-1)*((1-sqrt(7)+sqrt(6))^48479-1)*((1-sqrt(771512Mike Oakes05/2009
7271(26*10^71503+7)/371504Erik Branger11/2013
7272(4*10^71498+173)/371499Robert Price01/2017
72733^149848+11071496Lelio R Paula11/2014
72742^237498+51371495Lelio R Paula05/2012
72752^237485+10771491Lelio R Paula02/2012
7276(2^237465+9)/241971481Lelio R Paula05/2012
72772^237439-11223771477Enzo Doria06/2014
72782^237407-978771467Lelio R Paula11/2009
72792^237383+7295371460Enzo Doria04/2016
728082^37337-81^3733771457Robert Price01/2015
7281(1017*2^237313-1)/1971441Lelio R Paula04/2015
72822^237311+19171438Lelio R Paula02/2012
728311699^17560+17560^1169971437Norbert Schneider09/2019
72842^237280-5971429Lelio R Paula02/2012
728511^68564-9871403Lelio R Paula01/2015
72862^237173+7480171397Enzo Doria04/2016
728715^60697+5671386Lelio R Paula01/2015
72882^237118+17771380Lelio R Paula02/2012
72892^237110+6971378Lelio R Paula02/2012
729015^60690-5871377Lelio R Paula01/2015
7291(5*2^237125-1)/59985119171374Lelio R Paula01/2014
7292(3^149567+2)/53971359Lelio R Paula06/2012
7293(5*10^71357-143)/371358Robert Price04/2016
72942^237039-11462171356Enzo Doria05/2015
729512^66116-3771352Lelio R Paula02/2015
7296(3^149497+2^149497)/571328Jean-Louis Charton10/2010
72972^236941-6694571327Lelio R Paula05/2012
72982^236911-114771318Yves Minet10/2009
729965^39337+4271315Lelio R Paula01/2016
73006*10^71299+771300Dmitry Domanov11/2010
7301(25*2^236843+1)/375371295Lelio R Paula06/2012
730210^71291+1518771292Patrick De Geest03/2016
730410^71291-558730911971291Robert Price03/2015
730310^71291-27358171291Patrick De Geest03/2016
7305-numer(bernoulli(22808)/22808)71290T. D. Noe09/2005
730615105^17054+17054^1510571271Norbert Schneider08/2018
7307(2^236738+9)/1371265Lelio R Paula05/2012
73085^101949+4271260Lelio R Paula07/2014
73095*10^71237+971238Dmitry Domanov11/2010
73102^236634-1602571234Enzo Doria04/2013
731171^38478+7071233Norbert Schneider12/2014
73129*7^84280+871226Lelio R Paula10/2014
7313(10^71223+59)/371223Serge Batalov12/2014
7314(15185*2^236569-1)/45371216Lelio R Paula04/2015
731551829#+(216091#)/(51829#)71208Makoto Morimoto03/2016
73162^236528-17371203Lelio R Paula02/2012
73173*2^236511-571198Lelio R Paula04/2014
73182^236477-9971187Lelio R Paula02/2012
731911^68356-213071186Enzo Doria12/2012
732015128^17031+17031^1512871186Norbert Schneider08/2018
732111^68355-312071185Enzo Doria12/2012
732236^45737-35^4573771181Robert Price10/2012
7323(3^149183-lucasV(1,3,149183)+1)/371178Paul Vanderveen12/2017
73242^236432+2571174Lelio R Paula02/2012
73255^101818-1280671168Enzo Doria02/2013
7326(7*10^71166-457)/971166Robert Price09/2017
732765^39253+6271163Lelio R Paula01/2016
732839^44718+3871150Norbert Schneider05/2014
73292^236296-40771133Yves Minet02/2012
73302^236286-11771130Lelio R Paula02/2012
73312^236257-11119371121Enzo Doria05/2014
73327^84149-3671115Lelio R Paula08/2014
7333164176#-p(164176)71108Henri Lifchitz12/2018
73342^236209-11212371106Enzo Doria06/2014
733518^56644-498571104Enzo Doria03/2013
7336(46*10^71077+521)/971078Robert Price08/2017
733721^53753+271074Ray Chandler08/2011
7338(86*10^71068-311)/971069Robert Price10/2017
73392^236081-11092371068Enzo Doria05/2014
7340(293*27^49642-1736)/1371058Curtis Bright05/2015
734165^39192+2271052Lelio R Paula01/2016
7342(439#+1)^397-439#^39771038Mike Oakes11/2010
73437^84050-271031Lelio R Paula09/2013
734415813^16916+16916^1581371031Norbert Schneider09/2019
734564877!4+12871007Robert Price09/2019
734620^54558-2370982Lelio R Paula01/2015
73472^235793-11255570981Enzo Doria06/2014
734849936!3-3^4993670981Robert Price08/2015
73492^235787-7879570979Lelio R Paula05/2012
7350Perrin(581132)70970Eric W. Weisstein02/2011
735114^61913-9770961Lelio R Paula01/2015
73532^235720+1632170959Yves Minet03/2010
73522^235718+1609570959Lelio R Paula05/2012
7354163841#+34993370957Nicolas PALAU11/2016
73552^235710+770956Lelio R Paula02/2012
7356(175^31627+1)/17670939Eric Chen10/2017
73572^235635-11208770934Enzo Doria06/2014
7358153^32467+15270931Norbert Schneider11/2018
73602^235575-196570916Lelio R Paula05/2012
73596^91133+10170916Lelio R Paula01/2015
7361(21181*2^235505+1)/370898Lelio R Paula06/2014
7362(14*10^70896+211)/970897Robert Price11/2017
73635^101425+8470894Lelio R Paula07/2014
7364177^31536+270893Lelio R Paula05/2013
736543*71^38292+470891Serge Batalov03/2016
7366(29*2^235506-1)/11202978570888Lelio R Paula01/2014
736711^68045-153070862Enzo Doria12/2012
73685*10^70858+2170859Robert Price01/2017
73702^235326+370841Donovan Johnson02/2006
736934523!2+470841Robert Price02/2015
7371(31*2^235307+1)/370836Lelio R Paula06/2012
73722^235308+13570835Lelio R Paula02/2012
7373r(35414,90)*1000+91170831Patrick De Geest07/2004
73742^235274+15970825Lelio R Paula02/2012
73753^148409+7070810Lelio R Paula11/2014
7376(19*10^70794+17)/970795Robert Price03/2015
73772^235108-23270970775Paul Bourdelais03/2013
7378(2^235099-2^117550+1)/57077211/2006
737919^55325-670748Lelio R Paula08/2014
7380257^29356+29356^25770746Norbert Schneider10/2014
738122*10^70729+370731Robert Price10/2017
73822^234956+1171570729Lelio R Paula05/2012
7383(7*10^70727-43)/970727Robert Price10/2014
73842^234890-3034170709Enzo Doria11/2012
738517^57461+1470703Lelio R Paula01/2015
738618281^7366+7366^1828170697Hans Havermann09/2019
7387(9179*2^234834-1)/570696Lelio R Paula04/2015
73882*10^70688+5170689Robert Price10/2017
7389123^33822-12270685Norbert Schneider01/2015
73907*10^70680-9970681Robert Price11/2017
7391(21*2^234772-1)/209570672Lelio R Paula01/2014
7392(29*2^234686-1)/2114570645Lelio R Paula01/2014
7393(15*2^234688-1)/527814170643Lelio R Paula01/2014
73952^234655-6770639Lelio R Paula02/2012
7394(79*10^70638-61)/970639Robert Price10/2015
73962^234652-17370638Lelio R Paula02/2012
73972^234618-364570628Lelio R Paula05/2012
7398(2^234610-5)/1970624Lelio R Paula05/2012
73994*5^101038+970624Lelio R Paula10/2014
74002^234603+7196370623Enzo Doria04/2016
74012^234600-11312970622Enzo Doria07/2014
74022^234586+970618Lelio R Paula02/2012
74033^148008+2670618Robert Price11/2013
7404(7*10^70616-151)/970616Robert Price09/2017
740565^38947+3270608Lelio R Paula01/2016
7406(2^234488-3)/1170587Lelio R Paula05/2012
7407(3*2^234451+1)/3570576Lelio R Paula08/2012
7408Phi(159495,10)70560Maksym Voznyy09/2015
74092^234383-403570557Lelio R Paula05/2012
74102^234315-11124170536Enzo Doria05/2014
741114^61526+9770517Lelio R Paula01/2015
741214742^16915+16915^1474270512Norbert Schneider10/2019
7413(3*2^234170+1)/1370492Lelio R Paula08/2012
741451^41281-50^4128170491Robert Price02/2013
74152^234141-11212370484Enzo Doria06/2014
74162^234139+1228570483Lelio R Paula04/2012
74172^234133-316370482Yves Minet04/2009
74182^234115+8370476Lelio R Paula02/2012
74192^234114-159570476Lelio R Paula05/2012
742024^51061-23^5106170475Robert Price07/2012
742119471^16428-270467Faysal YAtim09/2005
74227^83381+1270466Robert Price01/2014
74232^234067-11142770462Enzo Doria05/2014
7424(266*10^70457+1)/370459Robert Price02/2016
7425(31*2^234041-1)/9770453Lelio R Paula01/2014
74262^234026+1290970449Lelio R Paula04/2012
74272^233965-1970431Lelio R Paula02/2012
7428(5*2^233932-1)/17970419Lelio R Paula01/2014
74292^233908-1710970414Enzo Doria05/2013
7430695^24772+24772^69570402Norbert Schneider09/2016
74313*5^100719-270401Lelio R Paula10/2014
74322^233829-11135570390Enzo Doria05/2014
7433(19775^16384+1)/270388Henri Lifchitz03/2007
74347*3^147519+870386Lelio R Paula04/2014
7435141^32749-270385Lelio R Paula10/2017
74365*7^83265+270368Lelio R Paula10/2014
7437(23*10^70363+97)/370364Robert Price02/2017
7438(23*2^233749-1)/3532570363Lelio R Paula01/2014
74395^100652-1391670353Enzo Doria02/2013
744045^42555-270353Lelio R Paula08/2013
74412^233661-6170339Lelio R Paula02/2012
74422^233523-11224970298Enzo Doria06/2014
74435*3^147324-870293Lelio R Paula04/2014
74442^233488-1306570287Enzo Doria11/2012
7445(3^147322+8)/4285170286Lelio R Paula06/2012
7446(22*10^70259+161)/370260Robert Price02/2017
74482^233388+46570257Lelio R Paula11/2012
744714^61299+5970257Lelio R Paula01/2015
74492^233383+9406570256Lelio R Paula04/2012
745049471!3-656170253Robert Price11/2015
74517^83121+6^(83121-1)70246Robert Price03/2016
7452(197*10^70241-11)/370243Robert Price10/2017
745323*10^70240-770242Robert Price03/2016
7454(71*10^70227-53)/970228Robert Price10/2015
745519825^3486+3486^1982570227Hans Havermann10/2019
745610815^17408+17408^1081570225Norbert Schneider05/2019
7457(2^233247-9)/1770214Lelio R Paula05/2012
7458(11^67421-2^67421)/970211Robert Price01/2013
7459(23*10^70209-41)/970210Robert Price03/2015
7460(29*10^70194-11)/970195Robert Price04/2015
74613^147109+19670189Lelio R Paula05/2014
7462(34*10^70191-7)/9/3/40583/57304770181Makoto Morimoto05/2016
74639^73538+8^(73538+1)70174Robert Price06/2016
74642*5^100391+770171Lelio R Paula10/2014
746599^35156-270159Lelio R Paula08/2013
7466(68*10^70148+7)/370150Robert Price03/2016
746711^67360-603070149Enzo Doria01/2013
7468(35*10^70130-377)/970131Robert Price12/2017
746949391!3+3^4939170128Robert Price09/2015
7470(229*10^70122-1)/370124Robert Price12/2016
74717^82975-9270123Lelio R Paula07/2014
747220294^2853+2853^2029470122Hans Havermann10/2019
747365^38670+5870106Lelio R Paula01/2016
7474105^34684+34684^10570103Serge Batalov05/2014
747518597^5882+5882^1859770102Hans Havermann10/2019
7476134^32955-13370099Norbert Schneider03/2015
74792^232836-22790370091Enzo Doria12/2012
74782^232837-185917370091Enzo Doria03/2016
747717778^8761+8761^1777870091Hans Havermann10/2019
74803*2^232820+570087Lelio R Paula04/2014
74822^232799+9019570080Lelio R Paula02/2013
74812^232799-11223770080Enzo Doria06/2014
748317894^8247+8247^1789470079Hans Havermann09/2019
74842^232759+26214570068Lelio R Paula04/2012
748516817^14670+14670^1681770067Hans Havermann09/2019
74863*2^232750+770066Lelio R Paula04/2014
748712^64918-1170059Lelio R Paula01/2015
74887^82899-1270058Lelio R Paula09/2013
7489(22*10^70051-13)/970052Robert Price03/2015
7490(2^232685-7)/251462570039Lelio R Paula04/2012
749118^55786-536370027Enzo Doria03/2013
7492(2^(77537*3+1)+243)/770023Kevin Acres11/2013
74932^232602+16970021Lelio R Paula02/2012
7494(137^32768+29^32768)/270016Jeppe Stig Nielsen04/2018
74952^232580+7213370014Enzo Doria04/2016
74964*6^89958-770002Lelio R Paula09/2014
749710^70000+8048770001Milton L. Brown05/2006
749810^69999+13485770000Patrick De Geest02/2007
749910^70000-927370000Patrick De Geest08/2009
7500(79*10^69999-7)/970000Robert Price01/2015


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Created by  Henri Lifchitz & Renaud Lifchitz : October, 26 2000, last modification: October, 13 2019 10:51 (Time in France)

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