
At this site we maintain a list of the 5000 Largest Known Primes which is updated hourly. This list is the most important databases at The Prime Pages: a collection of research, records and results all about prime numbers. This page summarizes our information about one of these primes. This prime's information:
field (help)  value 
Description:  Phi(3, 3^{1118781} + 1)/3 
Verification status (*):  Proven 
Official Comment:  Generalized unique 
Unofficial Comments:  This prime has 2 user comments below. 
Proofcode(s): (*):  L3839 : Batalov, EMsieve, LLR 
Decimal Digits:  1067588 (log_{10} is 1067587.91183178) 
Rank (*):  163 (digit rank is 1) 
Entrance Rank (*):  63 
Currently on list? (*):  short 
Submitted:  3/29/2014 04:39:12 CDT 
Last modified:  8/22/2014 08:37:26 CDT 
Database id:  117512 
Status Flags:  TrialDiv 
Score (*):  46.8336 (normalized score 22.3096) 

Archival tags:
There are certain forms classed as
archivable: these prime may (at times)
remain on this list even if they do not make
the Top 5000 proper. Such primes are tracked with archival
tags.
 Generalized Unique (archivable *)
 Prime on list: yes, rank 17
Subcategory: "Generalized Unique"
(archival tag id 217791, tag last modified 20170306 16:20:05)
User comments about this prime (disclaimer):
User comments are allowed to convey mathematical information about this number, how it was proven prime.... See our guidelines and restrictions.
Verification data:
The Top 5000 Primes is a list for proven primes only. In order to maintain the
integrity of this list, we seek to verify the primality of all submissions.
We are currently unable to check all proofs (ECPP, KP, ...), but we will at least trial
divide and PRP
check every entry before it is included in the list.
field  value 
prime_id  117512 
person_id  9 
machine  Xeon 4c+4c 3.5GHz 
what  prime 
notes  Command: ./pfgw64 tc q"Phi(3,3^1118781+1)/3" 2>&1 PFGW Version 3.7.7.64BIT.20130722.x86_Dev [GWNUM 27.11] Primality testing Phi(3,3^1118781+1)/3 [N1/N+1, BrillhartLehmerSelfridge] Running N1 test using base 3 Running N1 test using base 5 Running N1 test using base 13 Running N1 test using base 17 Running N1 test using base 59 Running N1 test using base 61 Running N+1 test using discriminant 97, base 3+sqrt(97) Calling N1 BLS with factored part 50.00% and helper 0.00% (150.01% proof)
Phi(3,3^1118781+1)/3 is prime! (255252.0424s+0.3649s) [Elapsed time: 2.95 days]

modified  20141215 15:47:32 
created  20140820 21:16:36 
id  163949 

Query times: 0.0004 seconds to select prime, 0.0007 seconds to seek comments.
