PRP Records

Probable Primes Top 10000

(172751 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 ?
57512^235793-11255570981Enzo Doria06/2014
575249936!3-3^4993670981Robert Price08/2015
57532^235787-7879570979Lelio R Paula05/2012
5754Perrin(581132)70970Eric W. Weisstein02/2011
575514^61913-9770961Lelio R Paula01/2015
57572^235720+1632170959Yves Minet03/2010
57562^235718+1609570959Lelio R Paula05/2012
5758163841#+34993370957Nicolas PALAU11/2016
57592^235710+770956Lelio R Paula02/2012
57602^235635-11208770934Enzo Doria06/2014
57622^235575-196570916Lelio R Paula05/2012
57616^91133+10170916Lelio R Paula01/2015
5763(21181*2^235505+1)/370898Lelio R Paula06/2014
57645^101425+8470894Lelio R Paula07/2014
5765177^31536+270893Lelio R Paula05/2013
576643*71^38292+470891Serge Batalov03/2016
5767(29*2^235506-1)/11202978570888Lelio R Paula01/2014
576811^68045-153070862Enzo Doria12/2012
57695*10^70858+2170859Robert Price01/2017
57712^235326+370841Donovan Johnson02/2006
577034523!2+470841Robert Price02/2015
5772(31*2^235307+1)/370836Lelio R Paula06/2012
57732^235308+13570835Lelio R Paula02/2012
5774r(35414,90)*1000+91170831Patrick De Geest07/2004
57752^235274+15970825Lelio R Paula02/2012
57763^148409+7070810Lelio R Paula11/2014
5777(19*10^70794+17)/970795Robert Price03/2015
57782^235108-23270970775Paul Bourdelais03/2013
5779(2^235099-2^117550+1)/57077211/2006
578019^55325-670748Lelio R Paula08/2014
5781257^29356+29356^25770746Norbert Schneider10/2014
57822^234956+1171570729Lelio R Paula05/2012
5783(7*10^70727-43)/970727Robert Price10/2014
57842^234890-3034170709Enzo Doria11/2012
578517^57461+1470703Lelio R Paula01/2015
5786(9179*2^234834-1)/570696Lelio R Paula04/2015
5787123^33822-12270685Norbert Schneider01/2015
5788(21*2^234772-1)/209570672Lelio R Paula01/2014
5789(29*2^234686-1)/2114570645Lelio R Paula01/2014
5790(15*2^234688-1)/527814170643Lelio R Paula01/2014
57922^234655-6770639Lelio R Paula02/2012
5791(79*10^70638-61)/970639Robert Price10/2015
57932^234652-17370638Lelio R Paula02/2012
57942^234618-364570628Lelio R Paula05/2012
5795(2^234610-5)/1970624Lelio R Paula05/2012
57964*5^101038+970624Lelio R Paula10/2014
57972^234603+7196370623Enzo Doria04/2016
57982^234600-11312970622Enzo Doria07/2014
57992^234586+970618Lelio R Paula02/2012
58003^148008+2670618Robert Price11/2013
580165^38947+3270608Lelio R Paula01/2016
5802(2^234488-3)/1170587Lelio R Paula05/2012
5803(3*2^234451+1)/3570576Lelio R Paula08/2012
5804Phi(159495,10)70560Maksym Voznyy09/2015
58052^234383-403570557Lelio R Paula05/2012
58062^234315-11124170536Enzo Doria05/2014
580714^61526+9770517Lelio R Paula01/2015
5808(3*2^234170+1)/1370492Lelio R Paula08/2012
580951^41281-50^4128170491Robert Price02/2013
58102^234141-11212370484Enzo Doria06/2014
58112^234139+1228570483Lelio R Paula04/2012
58122^234133-316370482Yves Minet04/2009
58132^234115+8370476Lelio R Paula02/2012
58142^234114-159570476Lelio R Paula05/2012
581524^51061-23^5106170475Robert Price07/2012
581619471^16428-270467Faysal YAtim09/2005
58177^83381+1270466Robert Price01/2014
58182^234067-11142770462Enzo Doria05/2014
5819(266*10^70457+1)/370459Robert Price02/2016
5820(31*2^234041-1)/9770453Lelio R Paula01/2014
58212^234026+1290970449Lelio R Paula04/2012
58222^233965-1970431Lelio R Paula02/2012
5823(5*2^233932-1)/17970419Lelio R Paula01/2014
58242^233908-1710970414Enzo Doria05/2013
5825695^24772+24772^69570402Norbert Schneider09/2016
58263*5^100719-270401Lelio R Paula10/2014
58272^233829-11135570390Enzo Doria05/2014
5828(19775^16384+1)/270388Henri Lifchitz03/2007
58297*3^147519+870386Lelio R Paula04/2014
58305*7^83265+270368Lelio R Paula10/2014
5831(23*10^70363+97)/370364Robert Price02/2017
5832(23*2^233749-1)/3532570363Lelio R Paula01/2014
58345^100652-1391670353Enzo Doria02/2013
583345^42555-270353Lelio R Paula08/2013
58352^233661-6170339Lelio R Paula02/2012
58362^233523-11224970298Enzo Doria06/2014
58375*3^147324-870293Lelio R Paula04/2014
58382^233488-1306570287Enzo Doria11/2012
5839(3^147322+8)/4285170286Lelio R Paula06/2012
5840(22*10^70259+161)/370260Robert Price02/2017
58412^233388+46570257Lelio R Paula11/2012
584214^61299+5970257Lelio R Paula01/2015
58432^233383+9406570256Lelio R Paula04/2012
584449471!3-656170253Robert Price11/2015
58457^83121+6^(83121-1)70246Robert Price03/2016
584623*10^70240-770242Robert Price03/2016
5847(71*10^70227-53)/970228Robert Price10/2015
5848(2^233247-9)/1770214Lelio R Paula05/2012
5849(11^67421-2^67421)/970211Robert Price01/2013
5850(23*10^70209-41)/970210Robert Price03/2015
5851(29*10^70194-11)/970195Robert Price04/2015
58523^147109+19670189Lelio R Paula05/2014
5853(34*10^70191-7)/9/3/40583/57304770181Makoto Morimoto05/2016
58549^73538+8^(73538+1)70174Robert Price06/2016
58552*5^100391+770171Lelio R Paula10/2014
585699^35156-270159Lelio R Paula08/2013
5857(68*10^70148+7)/370150Robert Price03/2016
585811^67360-603070149Enzo Doria01/2013
585949391!3+3^4939170128Robert Price09/2015
5860(229*10^70122-1)/370124Robert Price12/2016
58617^82975-9270123Lelio R Paula07/2014
586265^38670+5870106Lelio R Paula01/2016
5863105^34684+34684^10570103Serge Batalov05/2014
5864134^32955-13370099Norbert Schneider03/2015
58662^232836-22790370091Enzo Doria12/2012
58652^232837-185917370091Enzo Doria03/2016
58673*2^232820+570087Lelio R Paula04/2014
58692^232799+9019570080Lelio R Paula02/2013
58682^232799-11223770080Enzo Doria06/2014
58702^232759+26214570068Lelio R Paula04/2012
58713*2^232750+770066Lelio R Paula04/2014
587212^64918-1170059Lelio R Paula01/2015
58737^82899-1270058Lelio R Paula09/2013
5874(22*10^70051-13)/970052Robert Price03/2015
5875(2^232685-7)/251462570039Lelio R Paula04/2012
587618^55786-536370027Enzo Doria03/2013
5877(2^(77537*3+1)+243)/770023Kevin Acres11/2013
58782^232602+16970021Lelio R Paula02/2012
58792^232580+7213370014Enzo Doria04/2016
58804*6^89958-770002Lelio R Paula09/2014
588110^70000+8048770001Milton L. Brown05/2006
588210^69999+13485770000Patrick De Geest02/2007
588710^70000-927370000Patrick De Geest08/2009
5883(79*10^69999-7)/970000Robert Price01/2015
5884((2^43112609)/10^38420)%10^7000070000Michael Vang10/2016
5885(2^756839/10^36014)%10^7000070000Michael Vang12/2016
5886(2^74207281/10^32641)%10^7000070000Michael Vang12/2016
588810^69999-8825169999Patrick De Geest08/2009
58892^232507+108969992Lelio R Paula04/2012
5890(17*2^232445+1)/569974Lelio R Paula08/2012
58917^82778+4869956Lelio R Paula09/2013
58927*2^232381+369955Lelio R Paula04/2014
58932^232362-11054169948Enzo Doria05/2014
58942^232326-11239169938Enzo Doria06/2014
58953^146575+23669935Lelio R Paula09/2013
589630^47341-2969929Norbert Schneider02/2014
58975^100040-6869925Lelio R Paula09/2013
58982^232045-1729569853Lelio R Paula04/2012
5899(2^231987+78557)/9569834Lelio R Paula05/2012
59002^231955+7424369826Yves Minet03/2011
59012^231946-1587369823Enzo Doria04/2013
590218^55618+9569816Lelio R Paula09/2013
59036^89712+5^(89712-1)69810Robert Price02/2016
59042^231870+13569800Lelio R Paula02/2012
5905(23*2^231827-1)/417969785Lelio R Paula01/2014
59062^231778+5461569773Lelio R Paula04/2012
5907(19*2^231780+1)/23569772Lelio R Paula08/2012
590814^60866+2769761Lelio R Paula09/2013
590913^62619-4469755Lelio R Paula09/2013
5910(2^231715-509203)/3569752Lelio R Paula05/2012
59112^231711-11046769752Enzo Doria05/2014
5912(19^54547+18^54547)/3769751Robert Price08/2013
5913(23*2^231697-1)/4569748Lelio R Paula01/2014
59142^231696-186149969748Enzo Doria03/2016
59152^231684-14769744Lelio R Paula02/2012
5916(23*2^231686-1)/118369743Lelio R Paula01/2014
59172^231591-47739769716Paul Bourdelais03/2013
591811^66916-42069686Enzo Doria08/2012
59195^99680-1370669674Enzo Doria02/2013
5920(8*10^69674-53)/969674Robert Price11/2014
5921(77*10^69656-23)/969657Robert Price10/2015
59226^89509+13169652Lelio R Paula09/2013
5923(78557*2^231349+1)/3569647Lelio R Paula06/2014
5924(11*10^69645+19)/369646Robert Price03/2016
592511^66875-2869644Lelio R Paula09/2013
59262^231347+7148369643Enzo Doria04/2016
5927(14^60763+3^60763)/1769641Robert Price04/2013
5928(4*10^69626+173)/369627Robert Price01/2017
59292^231289+25569625Lelio R Paula04/2012
59302^231234-11291369609Enzo Doria06/2014
5931(265*10^69602-7)/369604Robert Price07/2016
59322^231182-11284169593Enzo Doria06/2014
5933(15*2^231129+1)/2369577Lelio R Paula08/2012
59343^145806-2869568Lelio R Paula09/2013
5935(265*10^69554-7)/369556Robert Price07/2016
59362^231052-11315969554Enzo Doria07/2014
593711^66784-869549Lelio R Paula09/2013
5938Phi(104409,10)/229699969546Maksym Voznyy07/2015
59392^231016-11052369543Enzo Doria05/2014
59402^231014+57729457569543Lelio R Paula02/2016
594114^60658+6769522Lelio R Paula09/2013
59425^99418+3669491Lelio R Paula06/2013
59437^82203-3069470Lelio R Paula09/2013
59445^99359-2^9936069449Mike Oakes12/2010
5945(29*2^230684+1)/139569442Lelio R Paula08/2012
5946(19*10^69424+77)/369425Robert Price08/2016
594719^54287-9669420Lelio R Paula09/2013
59482^230541+5890569400Lelio R Paula04/2012
59492^230506+1270569390Lelio R Paula02/2013
59508*6^89156-569378Lelio R Paula09/2014
59512^230438-11134769369Enzo Doria05/2014
59522^230428-9969366Lelio R Paula02/2012
59533*10^69354+1769355Robert Price03/2017
5954(493*10^69340-7)/969342Robert Price07/2016
5955(41*10^69321+373)/969322Robert Price04/2017
59566^89072+5369312Lelio R Paula09/2013
5957155^31639+269300Lelio R Paula05/2013
59583*7^81965-469269Lelio R Paula09/2014
5959(86*10^69260-77)/969261Robert Price05/2016
59609*5^99087+469260Lelio R Paula09/2014
59613^145145+266069252Lelio R Paula09/2013
596311^66492-114069245Enzo Doria11/2012
59625*3^145129-469245Lelio R Paula04/2014
59647*3^145126+869244Lelio R Paula04/2014
596511^66480-237069232Enzo Doria12/2012
59662^229962-6569226Lelio R Paula02/2012
59672^229958-11073369225Enzo Doria05/2014
5968V(332407)69225Serge Batalov03/2015
59696^88959+769224Lelio R Paula09/2013
597015^58855-9469219Lelio R Paula09/2013
5971(2^229838+47)/1208169185Lelio R Paula04/2012
59723^144952+9869160Lelio R Paula09/2013
59735^98941-7269157Lelio R Paula06/2013
5974(17*2^229604-1)/22969117Lelio R Paula01/2014
59752^229585-106369112Yves Minet11/2012
5976(13*2^229567-1)/1969107Lelio R Paula01/2014
5977(13*2^229393-1)/569055Lelio R Paula01/2014
5978(53*10^69050-17)/969051Robert Price09/2015
59792^229305-186853369028Enzo Doria04/2016
59802^229297+138569026Lelio R Paula04/2012
598118^54986-244169023Enzo Doria03/2013
5982(34*10^69021-7)/9/3/6769020Makoto Morimoto04/2016
59835^98736-1463669014Enzo Doria02/2013
5984(13^61949-5^61949)/869007Robert Price03/2013
5985(2^229227+5)/61169002Lelio R Paula04/2012
59862^229216-11327969001Enzo Doria07/2014
598710^68994+5191368995Patrick De Geest03/2016
598910^68994-10^5814-168994Serge Batalov01/2011
598810^68994-8294768994Patrick De Geest03/2016
5990(17*2^229136-1)/238168975Lelio R Paula01/2014
59912^229113+10768970Lelio R Paula02/2012
599211^66202-441068943Enzo Doria01/2013
599312^63883+568942Lelio R Paula07/2013
5994(9913*2^229002-1)/39990368935Lelio R Paula04/2015
59952^228962-11158168925Enzo Doria05/2014
59962^228944+8168920Henri Lifchitz01/2007
599711^66174-5468914Lelio R Paula09/2013
59982^228913-11126568910Enzo Doria05/2014
59992^228902+7351968907Enzo Doria04/2016
6000(47*2^228884+1)/6368901Lelio R Paula04/2015


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Created by  Henri Lifchitz & Renaud Lifchitz : October, 26 2000, last modification: April, 24 2017 22:44 (Time in France)

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