Phi(3, - 153865465536)
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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, - 153865465536)
Verification status (*):Proven
Official Comment:Generalized unique
Proof-code(s): (*):L4561 : Propper, Batalov, CycloSv, Cyclo, EMsieve, PIES, LLR
Decimal Digits:810961   (log10 is 810960.94124589)
Rank (*):483 (digit rank is 1)
Entrance Rank (*):472
Currently on list? (*):short
Submitted:10/28/2017 18:16:59 CDT
Last modified:10/28/2017 23:20:18 CDT
Database id:123968
Status Flags:TrialDiv
Score (*):45.99 (normalized score 9.3876)

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 20
Subcategory: "Generalized Unique"
(archival tag id 218907, tag last modified 2017-10-28 23:20:21)

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_id123968
person_id9
machineUsing: Xeon (pool) 4c+4c 3.5GHz
whatprime
notesCommand: /home/caldwell/clientpool/1/pfgw64 -t -q"Phi(3,-1538654^65536)" 2>&1
PFGW Version 3.7.7.64BIT.20130722.x86_Dev [GWNUM 27.11]
Primality testing Phi(3,-1538654^65536) [N-1, Brillhart-Lehmer-Selfridge]
Running N-1 test using base 7
Calling Brillhart-Lehmer-Selfridge with factored part 38.57%


Phi(3,-1538654^65536) is prime! (16487.3651s+0.0566s)
[Elapsed time: 4.58 hours]
modified2017-10-28 22:57:49
created2017-10-28 18:23:01
id169630

Query times: 0.0004 seconds to select prime, 0.0005 seconds to seek comments.