Phi(3, - 712012262144)

At this site we maintain a list of the 5000 Largest Known Primes which is updated hourly. This list is the most important PrimePages database: a collection of research, records and results all about prime numbers. This page summarizes our information about one of these primes.

Description:Phi(3, - 712012262144)
Verification status (*):Proven
Official Comment (*):Generalized unique
Proof-code(s): (*):L4506 : Propper, Batalov, CycloSv, EMsieve, PIES, Prime95, LLR
Decimal Digits:3068389   (log10 is 3068388.86843421)
Rank (*):50 (digit rank is 1)
Entrance Rank (*):18
Currently on list? (*):short
Submitted:1/14/2017 19:48:18 CDT
Last modified:1/18/2017 04:20:09 CDT
Database id:122736
Status Flags:TrialDiv
Score (*):50.0702 (normalized score 344.5145)

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 5
Subcategory: "Generalized Unique"
(archival tag id 224081, tag last modified 2020-08-04 13:50:04)

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.
machineUsing: Xeon 4c+4c 3.5GHz
notesCommand: /home/caldwell/client/pfgw/pfgw64 -t -q"Phi(3,-712012^262144)" 2>&1 PFGW Version [GWNUM 27.11] Primality testing Phi(3,-712012^262144) [N-1, Brillhart-Lehmer-Selfridge] Running N-1 test using base 11 Calling Brillhart-Lehmer-Selfridge with factored part 37.64% Phi(3,-712012^262144) is prime! (288906.7776s+0.7367s) [Elapsed time: 3.34 days]
modified2020-07-07 17:30:16
created2017-01-14 19:51:01

Query times: 0.0018 seconds to select prime, 0.0006 seconds to seek comments.
Printed from the PrimePages <> © Chris Caldwell.