Phi(3, 55599177147)

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.

This prime's information:

Description:Phi(3, 55599177147)
Verification status (*):Proven
Official Comment (*):Generalized unique
Unofficial Comments:This prime has 1 user comment below.
Proof-code(s): (*):p437 : Propper, Batalov, CycloSv, Cyclo, EMsieve, PIES, OpenPFGW
Decimal Digits:1681149   (log10 is 1681148.7607751)
Rank (*):383 (digit rank is 1)
Entrance Rank (*):378
Currently on list? (*):short
Submitted:11/18/2023 00:41:33 UTC
Last modified:11/19/2023 12:37:18 UTC
Database id:136668
Status Flags:none
Score (*):48.2263 (normalized score 30.1247)

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 12
Subcategory: "Generalized Unique"
(archival tag id 228967, tag last modified 2023-12-01 08:37:18)

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 (18 Nov 2023):  (report abuse)
This number is Phi(3^12, 55599) and extends OEIS A153438 past previous element Phi(3^11, 94259)

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_id136668
person_id9
machineUsing: Digital Ocean Droplet
whatprime
notesCommand: /var/www/clientpool/1/pfgw64 -V -f -t -q"Phi(3,55599^177147)" >command_output 2>&1
PFGW Version 4.0.4.64BIT.20221214.x86_Dev [GWNUM 30.11]
Primality testing Phi(3,55599^177147) [N-1, Brillhart-Lehmer-Selfridge]
trial


Running N-1 test using base 11
Generic modular reduction using generic reduction AVX-512 FFT length 576K, Pass1=1152, Pass2=512, clm=1 on A 5584656-bit number
Calling Brillhart-Lehmer-Selfridge with factored part 44.97%


Phi(3,55599^177147) is prime! (57293.1342s+0.1191s)
[Elapsed time: 15.92 hours]
modified2023-11-19 12:29:49
created2023-11-18 20:34:52
id182503

Query times: 0.0003 seconds to select prime, 0.0005 seconds to seek comments.
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