Phi(3, - 192098131072)

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, - 192098131072)
Verification status (*):Proven
Official Comment (*):Generalized unique
Unofficial Comments:This prime has 1 user comment below.
Proof-code(s): (*):p379 : Batalov, CycloSv, Cyclo, EMsieve, PIES, OpenPFGW
Decimal Digits:1385044   (log10 is 1385043.812232)
Rank (*):415 (digit rank is 1)
Entrance Rank (*):52
Currently on list? (*):short
Submitted:2/8/2015 18:11:48 UTC
Last modified:3/11/2023 15:54:10 UTC
Database id:119266
Status Flags:TrialDiv
Score (*):47.6322 (normalized score 17.4815)

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 224088, tag last modified 2023-03-11 15:53:59)

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 (10 Feb 2015):  (report abuse)
This prime extends the OEIS sequence A246119 (final check that b=192098 is the least base that produces a prime is complete, with all candidates checked once; there will be a double-check in the near future within the PrimeGrid project).

The search for this prime was effected on a small EC2 cloud farm (40 GRID K520 GPUs), at a cost of approximately $1K over ~ three weeks.

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,-192098^131072)" 2>&1 PFGW Version [GWNUM 27.11] Primality testing Phi(3,-192098^131072) [N-1, Brillhart-Lehmer-Selfridge] Running N-1 test using base 7 Calling Brillhart-Lehmer-Selfridge with factored part 47.15% Phi(3,-192098^131072) is prime! (47535.0204s+0.3372s) [Elapsed time: 13.20 hours]
modified2020-07-07 22:30:17
created2015-02-08 18:21:01

Query times: 0.0003 seconds to select prime, 0.0004 seconds to seek comments.
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