PRP Records

Probable Primes Top 10000

(173006 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 ?
57512^237485+10771491Lelio R Paula02/2012
5752(2^237465+9)/241971481Lelio R Paula05/2012
57532^237439-11223771477Enzo Doria06/2014
57542^237407-978771467Lelio R Paula11/2009
57552^237383+7295371460Enzo Doria04/2016
575682^37337-81^3733771457Robert Price01/2015
5757(1017*2^237313-1)/1971441Lelio R Paula04/2015
57582^237311+19171438Lelio R Paula02/2012
57592^237280-5971429Lelio R Paula02/2012
576011^68564-9871403Lelio R Paula01/2015
57612^237173+7480171397Enzo Doria04/2016
576215^60697+5671386Lelio R Paula01/2015
57632^237118+17771380Lelio R Paula02/2012
57642^237110+6971378Lelio R Paula02/2012
576515^60690-5871377Lelio R Paula01/2015
5766(5*2^237125-1)/59985119171374Lelio R Paula01/2014
5767(3^149567+2)/53971359Lelio R Paula06/2012
5768(5*10^71357-143)/371358Robert Price04/2016
57692^237039-11462171356Enzo Doria05/2015
577012^66116-3771352Lelio R Paula02/2015
5771(3^149497+2^149497)/571328Jean-Louis Charton10/2010
57722^236941-6694571327Lelio R Paula05/2012
57732^236911-114771318Yves Minet10/2009
577465^39337+4271315Lelio R Paula01/2016
57756*10^71299+771300Dmitry Domanov11/2010
5776(25*2^236843+1)/375371295Lelio R Paula06/2012
577710^71291+1518771292Patrick De Geest03/2016
577910^71291-558730911971291Robert Price03/2015
577810^71291-27358171291Patrick De Geest03/2016
5780-numer(bernoulli(22808)/22808)71290T. D. Noe09/2005
5781(2^236738+9)/1371265Lelio R Paula05/2012
57825^101949+4271260Lelio R Paula07/2014
57835*10^71237+971238Dmitry Domanov11/2010
57842^236634-1602571234Enzo Doria04/2013
578571^38478+7071233Norbert Schneider12/2014
57869*7^84280+871226Lelio R Paula10/2014
5787(10^71223+59)/371223Serge Batalov12/2014
5788(15185*2^236569-1)/45371216Lelio R Paula04/2015
578951829#+(216091#)/(51829#)71208Makoto Morimoto03/2016
57902^236528-17371203Lelio R Paula02/2012
57913*2^236511-571198Lelio R Paula04/2014
57922^236477-9971187Lelio R Paula02/2012
579311^68356-213071186Enzo Doria12/2012
579411^68355-312071185Enzo Doria12/2012
579536^45737-35^4573771181Robert Price10/2012
57962^236432+2571174Lelio R Paula02/2012
57975^101818-1280671168Enzo Doria02/2013
579865^39253+6271163Lelio R Paula01/2016
579939^44718+3871150Norbert Schneider05/2014
58002^236296-40771133Yves Minet02/2012
58012^236286-11771130Lelio R Paula02/2012
58022^236257-11119371121Enzo Doria05/2014
58037^84149-3671115Lelio R Paula08/2014
58042^236209-11212371106Enzo Doria06/2014
580518^56644-498571104Enzo Doria03/2013
580621^53753+271074Ray Chandler08/2011
58072^236081-11092371068Enzo Doria05/2014
5808(293*27^49642-1736)/1371058Curtis Bright05/2015
580965^39192+2271052Lelio R Paula01/2016
5810(439#+1)^397-439#^39771038Mike Oakes11/2010
58117^84050-271031Lelio R Paula09/2013
581220^54558-2370982Lelio R Paula01/2015
58132^235793-11255570981Enzo Doria06/2014
581449936!3-3^4993670981Robert Price08/2015
58152^235787-7879570979Lelio R Paula05/2012
5816Perrin(581132)70970Eric W. Weisstein02/2011
581714^61913-9770961Lelio R Paula01/2015
58192^235720+1632170959Yves Minet03/2010
58182^235718+1609570959Lelio R Paula05/2012
5820163841#+34993370957Nicolas PALAU11/2016
58212^235710+770956Lelio R Paula02/2012
58222^235635-11208770934Enzo Doria06/2014
58242^235575-196570916Lelio R Paula05/2012
58236^91133+10170916Lelio R Paula01/2015
5825(21181*2^235505+1)/370898Lelio R Paula06/2014
58265^101425+8470894Lelio R Paula07/2014
5827177^31536+270893Lelio R Paula05/2013
582843*71^38292+470891Serge Batalov03/2016
5829(29*2^235506-1)/11202978570888Lelio R Paula01/2014
583011^68045-153070862Enzo Doria12/2012
58315*10^70858+2170859Robert Price01/2017
58332^235326+370841Donovan Johnson02/2006
583234523!2+470841Robert Price02/2015
5834(31*2^235307+1)/370836Lelio R Paula06/2012
58352^235308+13570835Lelio R Paula02/2012
5836r(35414,90)*1000+91170831Patrick De Geest07/2004
58372^235274+15970825Lelio R Paula02/2012
58383^148409+7070810Lelio R Paula11/2014
5839(19*10^70794+17)/970795Robert Price03/2015
58402^235108-23270970775Paul Bourdelais03/2013
5841(2^235099-2^117550+1)/57077211/2006
584219^55325-670748Lelio R Paula08/2014
5843257^29356+29356^25770746Norbert Schneider10/2014
58442^234956+1171570729Lelio R Paula05/2012
5845(7*10^70727-43)/970727Robert Price10/2014
58462^234890-3034170709Enzo Doria11/2012
584717^57461+1470703Lelio R Paula01/2015
5848(9179*2^234834-1)/570696Lelio R Paula04/2015
5849123^33822-12270685Norbert Schneider01/2015
5850(21*2^234772-1)/209570672Lelio R Paula01/2014
5851(29*2^234686-1)/2114570645Lelio R Paula01/2014
5852(15*2^234688-1)/527814170643Lelio R Paula01/2014
58542^234655-6770639Lelio R Paula02/2012
5853(79*10^70638-61)/970639Robert Price10/2015
58552^234652-17370638Lelio R Paula02/2012
58562^234618-364570628Lelio R Paula05/2012
5857(2^234610-5)/1970624Lelio R Paula05/2012
58584*5^101038+970624Lelio R Paula10/2014
58592^234603+7196370623Enzo Doria04/2016
58602^234600-11312970622Enzo Doria07/2014
58612^234586+970618Lelio R Paula02/2012
58623^148008+2670618Robert Price11/2013
586365^38947+3270608Lelio R Paula01/2016
5864(2^234488-3)/1170587Lelio R Paula05/2012
5865(3*2^234451+1)/3570576Lelio R Paula08/2012
5866Phi(159495,10)70560Maksym Voznyy09/2015
58672^234383-403570557Lelio R Paula05/2012
58682^234315-11124170536Enzo Doria05/2014
586914^61526+9770517Lelio R Paula01/2015
5870(3*2^234170+1)/1370492Lelio R Paula08/2012
587151^41281-50^4128170491Robert Price02/2013
58722^234141-11212370484Enzo Doria06/2014
58732^234139+1228570483Lelio R Paula04/2012
58742^234133-316370482Yves Minet04/2009
58752^234115+8370476Lelio R Paula02/2012
58762^234114-159570476Lelio R Paula05/2012
587724^51061-23^5106170475Robert Price07/2012
587819471^16428-270467Faysal YAtim09/2005
58797^83381+1270466Robert Price01/2014
58802^234067-11142770462Enzo Doria05/2014
5881(266*10^70457+1)/370459Robert Price02/2016
5882(31*2^234041-1)/9770453Lelio R Paula01/2014
58832^234026+1290970449Lelio R Paula04/2012
58842^233965-1970431Lelio R Paula02/2012
5885(5*2^233932-1)/17970419Lelio R Paula01/2014
58862^233908-1710970414Enzo Doria05/2013
5887695^24772+24772^69570402Norbert Schneider09/2016
58883*5^100719-270401Lelio R Paula10/2014
58892^233829-11135570390Enzo Doria05/2014
5890(19775^16384+1)/270388Henri Lifchitz03/2007
58917*3^147519+870386Lelio R Paula04/2014
58925*7^83265+270368Lelio R Paula10/2014
5893(23*10^70363+97)/370364Robert Price02/2017
5894(23*2^233749-1)/3532570363Lelio R Paula01/2014
58965^100652-1391670353Enzo Doria02/2013
589545^42555-270353Lelio R Paula08/2013
58972^233661-6170339Lelio R Paula02/2012
58982^233523-11224970298Enzo Doria06/2014
58995*3^147324-870293Lelio R Paula04/2014
59002^233488-1306570287Enzo Doria11/2012
5901(3^147322+8)/4285170286Lelio R Paula06/2012
5902(22*10^70259+161)/370260Robert Price02/2017
59032^233388+46570257Lelio R Paula11/2012
590414^61299+5970257Lelio R Paula01/2015
59052^233383+9406570256Lelio R Paula04/2012
590649471!3-656170253Robert Price11/2015
59077^83121+6^(83121-1)70246Robert Price03/2016
590823*10^70240-770242Robert Price03/2016
5909(71*10^70227-53)/970228Robert Price10/2015
5910(2^233247-9)/1770214Lelio R Paula05/2012
5911(11^67421-2^67421)/970211Robert Price01/2013
5912(23*10^70209-41)/970210Robert Price03/2015
5913(29*10^70194-11)/970195Robert Price04/2015
59143^147109+19670189Lelio R Paula05/2014
5915(34*10^70191-7)/9/3/40583/57304770181Makoto Morimoto05/2016
59169^73538+8^(73538+1)70174Robert Price06/2016
59172*5^100391+770171Lelio R Paula10/2014
591899^35156-270159Lelio R Paula08/2013
5919(68*10^70148+7)/370150Robert Price03/2016
592011^67360-603070149Enzo Doria01/2013
592149391!3+3^4939170128Robert Price09/2015
5922(229*10^70122-1)/370124Robert Price12/2016
59237^82975-9270123Lelio R Paula07/2014
592465^38670+5870106Lelio R Paula01/2016
5925105^34684+34684^10570103Serge Batalov05/2014
5926134^32955-13370099Norbert Schneider03/2015
59282^232836-22790370091Enzo Doria12/2012
59272^232837-185917370091Enzo Doria03/2016
59293*2^232820+570087Lelio R Paula04/2014
59312^232799+9019570080Lelio R Paula02/2013
59302^232799-11223770080Enzo Doria06/2014
59322^232759+26214570068Lelio R Paula04/2012
59333*2^232750+770066Lelio R Paula04/2014
593412^64918-1170059Lelio R Paula01/2015
59357^82899-1270058Lelio R Paula09/2013
5936(22*10^70051-13)/970052Robert Price03/2015
5937(2^232685-7)/251462570039Lelio R Paula04/2012
593818^55786-536370027Enzo Doria03/2013
5939(2^(77537*3+1)+243)/770023Kevin Acres11/2013
59402^232602+16970021Lelio R Paula02/2012
59412^232580+7213370014Enzo Doria04/2016
59424*6^89958-770002Lelio R Paula09/2014
594310^70000+8048770001Milton L. Brown05/2006
594410^69999+13485770000Patrick De Geest02/2007
594810^70000-927370000Patrick De Geest08/2009
5945(79*10^69999-7)/970000Robert Price01/2015
5949((2^43112609)/10^38420)%10^7000070000Michael Vang10/2016
5946(2^756839/10^36014)%10^7000070000Michael Vang12/2016
5947(2^74207281/10^32641)%10^7000070000Michael Vang12/2016
595010^69999-8825169999Patrick De Geest08/2009
59512^232507+108969992Lelio R Paula04/2012
5952(17*2^232445+1)/569974Lelio R Paula08/2012
59537^82778+4869956Lelio R Paula09/2013
59547*2^232381+369955Lelio R Paula04/2014
59552^232362-11054169948Enzo Doria05/2014
59562^232326-11239169938Enzo Doria06/2014
59573^146575+23669935Lelio R Paula09/2013
595830^47341-2969929Norbert Schneider02/2014
59595^100040-6869925Lelio R Paula09/2013
59602^232045-1729569853Lelio R Paula04/2012
5961(2^231987+78557)/9569834Lelio R Paula05/2012
59622^231955+7424369826Yves Minet03/2011
59632^231946-1587369823Enzo Doria04/2013
596418^55618+9569816Lelio R Paula09/2013
59656^89712+5^(89712-1)69810Robert Price02/2016
59662^231870+13569800Lelio R Paula02/2012
5967(23*2^231827-1)/417969785Lelio R Paula01/2014
59682^231778+5461569773Lelio R Paula04/2012
5969(19*2^231780+1)/23569772Lelio R Paula08/2012
597014^60866+2769761Lelio R Paula09/2013
597113^62619-4469755Lelio R Paula09/2013
5972(2^231715-509203)/3569752Lelio R Paula05/2012
59732^231711-11046769752Enzo Doria05/2014
5974(19^54547+18^54547)/3769751Robert Price08/2013
5975(23*2^231697-1)/4569748Lelio R Paula01/2014
59762^231696-186149969748Enzo Doria03/2016
59772^231684-14769744Lelio R Paula02/2012
5978(23*2^231686-1)/118369743Lelio R Paula01/2014
59792^231591-47739769716Paul Bourdelais03/2013
598011^66916-42069686Enzo Doria08/2012
59815^99680-1370669674Enzo Doria02/2013
5982(8*10^69674-53)/969674Robert Price11/2014
5983(77*10^69656-23)/969657Robert Price10/2015
59846^89509+13169652Lelio R Paula09/2013
5985(78557*2^231349+1)/3569647Lelio R Paula06/2014
5986(11*10^69645+19)/369646Robert Price03/2016
598711^66875-2869644Lelio R Paula09/2013
59882^231347+7148369643Enzo Doria04/2016
5989(14^60763+3^60763)/1769641Robert Price04/2013
5990(4*10^69626+173)/369627Robert Price01/2017
59912^231289+25569625Lelio R Paula04/2012
59922^231234-11291369609Enzo Doria06/2014
5993(265*10^69602-7)/369604Robert Price07/2016
59942^231182-11284169593Enzo Doria06/2014
5995(15*2^231129+1)/2369577Lelio R Paula08/2012
59963^145806-2869568Lelio R Paula09/2013
5997(265*10^69554-7)/369556Robert Price07/2016
59982^231052-11315969554Enzo Doria07/2014
599911^66784-869549Lelio R Paula09/2013
6000Phi(104409,10)/229699969546Maksym Voznyy07/2015


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Created by  Henri Lifchitz & Renaud Lifchitz : October, 26 2000, last modification: May, 25 2017 10:58 (Time in France)

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