Phi(3, 31118781 + 1)/3
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The hardware and software on this system was updated September 4th.  Please let me know of any problem you encounter. <caldwell@utm.edu>

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, 31118781 + 1)/3
Verification status (*):Proven
Official Comment:Generalized unique
Unofficial Comments:This prime has 2 user comments below.
Proof-code(s): (*):L3839 : Batalov, EMsieve, LLR
Decimal Digits:1067588   (log10 is 1067587.91183178)
Rank (*):84 (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 29.5477)

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 1
Subcategory: "Generalized Unique"
(archival tag id 217791, tag last modified 2014-08-18 06:50:07)

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.

Serge Batalov writes (11 Sep 2014): 
Eisenstein Mersenne Norm prime #26
This prime may also be written: 3^2237561+3^1118781+1

Serge Batalov writes (11 Sep 2014): 
In memoriam for my father, Vasiliy A. Batalov (1943-2014), who instilled in me love for math, science and discipline

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.
fieldvalue
prime_id117512
person_id9
machineXeon 4c+4c 3.5GHz
whatprime
notesCommand: ./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 [N-1/N+1, Brillhart-Lehmer-Selfridge]
Running N-1 test using base 3
Running N-1 test using base 5
Running N-1 test using base 13
Running N-1 test using base 17
Running N-1 test using base 59
Running N-1 test using base 61
Running N+1 test using discriminant 97, base 3+sqrt(97)
Calling N-1 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]
modified2014-08-20 21:16:36
created2014-08-20 21:16:36
id163949

fieldvalue
prime_id117512
person_id9
machineXeon 4c+4c 3.5GHz
whatrequested
notesUsing pfgw
modified2014-08-20 21:16:20
created2014-08-20 21:16:20
id163948

Query times: 0.0004 seconds to select prime, 0.0006 seconds to seek comments.