PRP Records

Probable Primes Top 10000

(174961 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 ?
57512^238389-11090571763Enzo Doria05/2014
5752(145*10^71760-1)/971762Serge Batalov12/2014
57537^84913+506271760Mike Oakes02/2010
5754(F(11446)^31-F(11445)^31)/F(11444)71753Wayne Halsdorf03/2012
57552^238268-9730571726Lelio R Paula05/2012
5756gcd(V(1330365),5*F(266073)*(F(266073)-1)+1)71724Serge Batalov04/2015
57572^238235-11324771716Enzo Doria07/2014
57582*12^66450-5^6645071712Mike Oakes11/2010
5759(2^238213+lucasV(1,2,238213)+1)/471709Mike Oakes11/2016
57602^238199-11181771706Enzo Doria05/2014
5761lucasU(46,1,43125)+lucasU(46,1,43124)71696Mike Oakes04/2009
57622^238144+9876533171689Jason Earls01/2009
576318^57102-426571679Enzo Doria03/2013
5764(73*10^71670-1)/971671Robert Price01/2015
57652^238081+1155*23808171670Henri Lifchitz02/2005
57662^238067-11192571666Enzo Doria05/2014
576736^46030+3571637Norbert Schneider04/2014
57682^237905-9171617Lelio R Paula02/2012
5769(31*2^237902-1)/12371616Lelio R Paula01/2014
5770(15185*2^237866-1)/4396771605Lelio R Paula04/2015
5771(24737*2^237841+1)/2571601Lelio R Paula06/2014
57722^237846+129971599Lelio R Paula05/2012
57736^92004+19980171594Mike Oakes02/2011
5774159^32516+271581Lelio R Paula05/2013
57752^237781+85571580Lelio R Paula05/2012
57762^237720-407971561Yves Minet06/2011
57772^237698-11094571555Enzo Doria05/2014
57782^237695-11323971554Enzo Doria07/2014
57798*5^102362-971549Lelio R Paula10/2014
5780(4*10^71546-31)/971546Erik Branger05/2011
57812^237650+3771540Lelio R Paula02/2012
578218^56977-439171522Enzo Doria03/2013
5783(22699*2^237565+1)/413663771512Lelio R Paula06/2014
5784((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
5785(26*10^71503+7)/371504Erik Branger11/2013
5786(4*10^71498+173)/371499Robert Price01/2017
57873^149848+11071496Lelio R Paula11/2014
57882^237498+51371495Lelio R Paula05/2012
57892^237485+10771491Lelio R Paula02/2012
5790(2^237465+9)/241971481Lelio R Paula05/2012
57912^237439-11223771477Enzo Doria06/2014
57922^237407-978771467Lelio R Paula11/2009
57932^237383+7295371460Enzo Doria04/2016
579482^37337-81^3733771457Robert Price01/2015
5795(1017*2^237313-1)/1971441Lelio R Paula04/2015
57962^237311+19171438Lelio R Paula02/2012
57972^237280-5971429Lelio R Paula02/2012
579811^68564-9871403Lelio R Paula01/2015
57992^237173+7480171397Enzo Doria04/2016
580015^60697+5671386Lelio R Paula01/2015
58012^237118+17771380Lelio R Paula02/2012
58022^237110+6971378Lelio R Paula02/2012
580315^60690-5871377Lelio R Paula01/2015
5804(5*2^237125-1)/59985119171374Lelio R Paula01/2014
5805(3^149567+2)/53971359Lelio R Paula06/2012
5806(5*10^71357-143)/371358Robert Price04/2016
58072^237039-11462171356Enzo Doria05/2015
580812^66116-3771352Lelio R Paula02/2015
5809(3^149497+2^149497)/571328Jean-Louis Charton10/2010
58102^236941-6694571327Lelio R Paula05/2012
58112^236911-114771318Yves Minet10/2009
581265^39337+4271315Lelio R Paula01/2016
58136*10^71299+771300Dmitry Domanov11/2010
5814(25*2^236843+1)/375371295Lelio R Paula06/2012
581510^71291+1518771292Patrick De Geest03/2016
581710^71291-558730911971291Robert Price03/2015
581610^71291-27358171291Patrick De Geest03/2016
5818-numer(bernoulli(22808)/22808)71290T. D. Noe09/2005
5819(2^236738+9)/1371265Lelio R Paula05/2012
58205^101949+4271260Lelio R Paula07/2014
58215*10^71237+971238Dmitry Domanov11/2010
58222^236634-1602571234Enzo Doria04/2013
582371^38478+7071233Norbert Schneider12/2014
58249*7^84280+871226Lelio R Paula10/2014
5825(10^71223+59)/371223Serge Batalov12/2014
5826(15185*2^236569-1)/45371216Lelio R Paula04/2015
582751829#+(216091#)/(51829#)71208Makoto Morimoto03/2016
58282^236528-17371203Lelio R Paula02/2012
58293*2^236511-571198Lelio R Paula04/2014
58302^236477-9971187Lelio R Paula02/2012
583111^68356-213071186Enzo Doria12/2012
583211^68355-312071185Enzo Doria12/2012
583336^45737-35^4573771181Robert Price10/2012
58342^236432+2571174Lelio R Paula02/2012
58355^101818-1280671168Enzo Doria02/2013
583665^39253+6271163Lelio R Paula01/2016
583739^44718+3871150Norbert Schneider05/2014
58382^236296-40771133Yves Minet02/2012
58392^236286-11771130Lelio R Paula02/2012
58402^236257-11119371121Enzo Doria05/2014
58417^84149-3671115Lelio R Paula08/2014
58422^236209-11212371106Enzo Doria06/2014
584318^56644-498571104Enzo Doria03/2013
584421^53753+271074Ray Chandler08/2011
58452^236081-11092371068Enzo Doria05/2014
5846(293*27^49642-1736)/1371058Curtis Bright05/2015
584765^39192+2271052Lelio R Paula01/2016
5848(439#+1)^397-439#^39771038Mike Oakes11/2010
58497^84050-271031Lelio R Paula09/2013
585020^54558-2370982Lelio R Paula01/2015
58512^235793-11255570981Enzo Doria06/2014
585249936!3-3^4993670981Robert Price08/2015
58532^235787-7879570979Lelio R Paula05/2012
5854Perrin(581132)70970Eric W. Weisstein02/2011
585514^61913-9770961Lelio R Paula01/2015
58562^235720+1632170959Yves Minet03/2010
58572^235718+1609570959Lelio R Paula05/2012
5858163841#+34993370957Nicolas PALAU11/2016
58592^235710+770956Lelio R Paula02/2012
58602^235635-11208770934Enzo Doria06/2014
58622^235575-196570916Lelio R Paula05/2012
58616^91133+10170916Lelio R Paula01/2015
5863(21181*2^235505+1)/370898Lelio R Paula06/2014
58645^101425+8470894Lelio R Paula07/2014
5865177^31536+270893Lelio R Paula05/2013
586643*71^38292+470891Serge Batalov03/2016
5867(29*2^235506-1)/11202978570888Lelio R Paula01/2014
586811^68045-153070862Enzo Doria12/2012
58695*10^70858+2170859Robert Price01/2017
58712^235326+370841Donovan Johnson02/2006
587034523!2+470841Robert Price02/2015
5872(31*2^235307+1)/370836Lelio R Paula06/2012
58732^235308+13570835Lelio R Paula02/2012
5874r(35414,90)*1000+91170831Patrick De Geest07/2004
58752^235274+15970825Lelio R Paula02/2012
58763^148409+7070810Lelio R Paula11/2014
5877(19*10^70794+17)/970795Robert Price03/2015
58782^235108-23270970775Paul Bourdelais03/2013
5879(2^235099-2^117550+1)/57077211/2006
588019^55325-670748Lelio R Paula08/2014
5881257^29356+29356^25770746Norbert Schneider10/2014
58822^234956+1171570729Lelio R Paula05/2012
5883(7*10^70727-43)/970727Robert Price10/2014
58842^234890-3034170709Enzo Doria11/2012
588517^57461+1470703Lelio R Paula01/2015
5886(9179*2^234834-1)/570696Lelio R Paula04/2015
5887123^33822-12270685Norbert Schneider01/2015
5888(21*2^234772-1)/209570672Lelio R Paula01/2014
5889(29*2^234686-1)/2114570645Lelio R Paula01/2014
5890(15*2^234688-1)/527814170643Lelio R Paula01/2014
58922^234655-6770639Lelio R Paula02/2012
5891(79*10^70638-61)/970639Robert Price10/2015
58932^234652-17370638Lelio R Paula02/2012
58942^234618-364570628Lelio R Paula05/2012
5895(2^234610-5)/1970624Lelio R Paula05/2012
58964*5^101038+970624Lelio R Paula10/2014
58972^234603+7196370623Enzo Doria04/2016
58982^234600-11312970622Enzo Doria07/2014
58992^234586+970618Lelio R Paula02/2012
59003^148008+2670618Robert Price11/2013
590165^38947+3270608Lelio R Paula01/2016
5902(2^234488-3)/1170587Lelio R Paula05/2012
5903(3*2^234451+1)/3570576Lelio R Paula08/2012
5904Phi(159495,10)70560Maksym Voznyy09/2015
59052^234383-403570557Lelio R Paula05/2012
59062^234315-11124170536Enzo Doria05/2014
590714^61526+9770517Lelio R Paula01/2015
5908(3*2^234170+1)/1370492Lelio R Paula08/2012
590951^41281-50^4128170491Robert Price02/2013
59102^234141-11212370484Enzo Doria06/2014
59112^234139+1228570483Lelio R Paula04/2012
59122^234133-316370482Yves Minet04/2009
59132^234115+8370476Lelio R Paula02/2012
59142^234114-159570476Lelio R Paula05/2012
591524^51061-23^5106170475Robert Price07/2012
591619471^16428-270467Faysal YAtim09/2005
59177^83381+1270466Robert Price01/2014
59182^234067-11142770462Enzo Doria05/2014
5919(266*10^70457+1)/370459Robert Price02/2016
5920(31*2^234041-1)/9770453Lelio R Paula01/2014
59212^234026+1290970449Lelio R Paula04/2012
59222^233965-1970431Lelio R Paula02/2012
5923(5*2^233932-1)/17970419Lelio R Paula01/2014
59242^233908-1710970414Enzo Doria05/2013
5925695^24772+24772^69570402Norbert Schneider09/2016
59263*5^100719-270401Lelio R Paula10/2014
59272^233829-11135570390Enzo Doria05/2014
5928(19775^16384+1)/270388Henri Lifchitz03/2007
59297*3^147519+870386Lelio R Paula04/2014
59305*7^83265+270368Lelio R Paula10/2014
5931(23*10^70363+97)/370364Robert Price02/2017
5932(23*2^233749-1)/3532570363Lelio R Paula01/2014
59345^100652-1391670353Enzo Doria02/2013
593345^42555-270353Lelio R Paula08/2013
59352^233661-6170339Lelio R Paula02/2012
59362^233523-11224970298Enzo Doria06/2014
59375*3^147324-870293Lelio R Paula04/2014
59382^233488-1306570287Enzo Doria11/2012
5939(3^147322+8)/4285170286Lelio R Paula06/2012
5940(22*10^70259+161)/370260Robert Price02/2017
59412^233388+46570257Lelio R Paula11/2012
594214^61299+5970257Lelio R Paula01/2015
59432^233383+9406570256Lelio R Paula04/2012
594449471!3-656170253Robert Price11/2015
59457^83121+6^(83121-1)70246Robert Price03/2016
594623*10^70240-770242Robert Price03/2016
5947(71*10^70227-53)/970228Robert Price10/2015
5948(2^233247-9)/1770214Lelio R Paula05/2012
5949(11^67421-2^67421)/970211Robert Price01/2013
5950(23*10^70209-41)/970210Robert Price03/2015
5951(29*10^70194-11)/970195Robert Price04/2015
59523^147109+19670189Lelio R Paula05/2014
5953(34*10^70191-7)/9/3/40583/57304770181Makoto Morimoto05/2016
59549^73538+8^(73538+1)70174Robert Price06/2016
59552*5^100391+770171Lelio R Paula10/2014
595699^35156-270159Lelio R Paula08/2013
5957(68*10^70148+7)/370150Robert Price03/2016
595811^67360-603070149Enzo Doria01/2013
595949391!3+3^4939170128Robert Price09/2015
5960(229*10^70122-1)/370124Robert Price12/2016
59617^82975-9270123Lelio R Paula07/2014
596265^38670+5870106Lelio R Paula01/2016
5963105^34684+34684^10570103Serge Batalov05/2014
5964134^32955-13370099Norbert Schneider03/2015
59662^232836-22790370091Enzo Doria12/2012
59652^232837-185917370091Enzo Doria03/2016
59673*2^232820+570087Lelio R Paula04/2014
59692^232799+9019570080Lelio R Paula02/2013
59682^232799-11223770080Enzo Doria06/2014
59702^232759+26214570068Lelio R Paula04/2012
59713*2^232750+770066Lelio R Paula04/2014
597212^64918-1170059Lelio R Paula01/2015
59737^82899-1270058Lelio R Paula09/2013
5974(22*10^70051-13)/970052Robert Price03/2015
5975(2^232685-7)/251462570039Lelio R Paula04/2012
597618^55786-536370027Enzo Doria03/2013
5977(2^(77537*3+1)+243)/770023Kevin Acres11/2013
59782^232602+16970021Lelio R Paula02/2012
59792^232580+7213370014Enzo Doria04/2016
59804*6^89958-770002Lelio R Paula09/2014
598110^70000+8048770001Milton L. Brown05/2006
598210^69999+13485770000Patrick De Geest02/2007
598410^70000-927370000Patrick De Geest08/2009
5983(79*10^69999-7)/970000Robert Price01/2015
5987((2^43112609)/10^38420)%10^7000070000Michael Vang10/2016
5985(2^756839/10^36014)%10^7000070000Michael Vang12/2016
5986(2^74207281/10^32641)%10^7000070000Michael Vang12/2016
598810^69999-8825169999Patrick De Geest08/2009
59892^232507+108969992Lelio R Paula04/2012
5990(17*2^232445+1)/569974Lelio R Paula08/2012
59917^82778+4869956Lelio R Paula09/2013
59927*2^232381+369955Lelio R Paula04/2014
59932^232362-11054169948Enzo Doria05/2014
59942^232326-11239169938Enzo Doria06/2014
59953^146575+23669935Lelio R Paula09/2013
599630^47341-2969929Norbert Schneider02/2014
59975^100040-6869925Lelio R Paula09/2013
59982^232045-1729569853Lelio R Paula04/2012
5999(2^231987+78557)/9569834Lelio R Paula05/2012
60002^231955+7424369826Yves Minet03/2011


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Created by  Henri Lifchitz & Renaud Lifchitz : October, 26 2000, last modification: June, 22 2017 08:34 (Time in France)

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