Phi(3, - 23125549152)

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, - 23125549152)
Verification status (*):Proven
Official Comment (*):Generalized unique
Proof-code(s): (*):L4142 : Batalov, CycloSv, EMsieve, PIES, LLR
Decimal Digits:527312   (log10 is 527311.614587094)
Rank (*):2740 (digit rank is 1)
Entrance Rank (*):1437
Currently on list? (*):yes
Submitted:12/19/2016 21:07:29 CDT
Last modified:12/20/2016 00:50:28 CDT
Database id:122622
Status Flags:TrialDiv
Score (*):44.6684 (normalized score 1.5312)

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: no, rank 68
Subcategory: "Generalized Unique"
(archival tag id 224144, 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.
fieldvalue
prime_id122622
person_id9
machineUsing: Xeon 4c+4c 3.5GHz
whatprime
notesCommand: /home/caldwell/client/pfgw/pfgw64 -t -q"Phi(3,-231255^49152)" 2>&1 PFGW Version 3.7.7.64BIT.20130722.x86_Dev [GWNUM 27.11] Primality testing Phi(3,-231255^49152) [N-1, Brillhart-Lehmer-Selfridge] Running N-1 test using base 11 Running N-1 test using base 29 Calling Brillhart-Lehmer-Selfridge with factored part 43.48% Phi(3,-231255^49152) is prime! (11824.1034s+0.1116s) [Elapsed time: 3.28 hours]
modified2020-07-07 17:30:16
created2016-12-19 21:11:01
id168264

Query times: 0.0017 seconds to select prime, 0.0006 seconds to seek comments.
Printed from the PrimePages <primes.utm.edu> © Chris Caldwell.