Phi(3, - 9687365536)

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Description:Phi(3, - 9687365536)
Verification status (*):Proven
Official Comment (*):Generalized unique
Unofficial Comments:This prime has 1 user comment below.
Proof-code(s): (*):L4026 : Batalov, Cyclo, EMsieve, PIES, LLR
Decimal Digits:653552   (log10 is 653551.56676178)
Rank (*):2401 (digit rank is 1)
Entrance Rank (*):371
Currently on list? (*):yes
Submitted:12/30/2014 12:17:42 CDT
Last modified:12/30/2014 15:20:15 CDT
Database id:119031
Status Flags:TrialDiv
Score (*):45.3275 (normalized score 2.4486)

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 45
Subcategory: "Generalized Unique"
(archival tag id 224121, tag last modified 2020-08-04 13:50:04)

User comments about this prime (disclaimer):

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Serge Batalov writes (1 Jan 2015):  (report abuse)
Extends the OEIS sequence A246119 (i.e. b=96873 is the least base that produces a prime).

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_id119031
person_id9
machineUsing: Xeon 4c+4c 3.5GHz
whatprime
notesCommand: /home/caldwell/client/pfgw/pfgw64 -t -q"Phi(3,-96873^65536)" 2>&1 PFGW Version 3.7.7.64BIT.20130722.x86_Dev [GWNUM 27.11] Primality testing Phi(3,-96873^65536) [N-1, Brillhart-Lehmer-Selfridge] Running N-1 test using base 11 Calling Brillhart-Lehmer-Selfridge with factored part 45.22% Phi(3,-96873^65536) is prime! (9207.5759s+0.1433s) [Elapsed time: 2.56 hours]
modified2020-07-07 17:30:17
created2014-12-30 12:21:01
id164635

Query times: 0.0006 seconds to select prime, 0.0011 seconds to seek comments.
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