Phi(3, - 40651598304)
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At this site we maintain a list of the 5000 Largest Known Primes which is updated hourly. This list is the most important databases at The Prime Pages: 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:

field (help)value
Description:Phi(3, - 40651598304)
Verification status (*):Proven
Official Comment:Generalized unique
Proof-code(s): (*):L4506 : Propper, Batalov, CycloSv, EMsieve, PIES, Prime95, LLR
Decimal Digits:1102790   (log10 is 1102789.32730893)
Rank (*):189 (digit rank is 1)
Entrance Rank (*):121
Currently on list? (*):short
Submitted:12/24/2016 10:45:04 CDT
Last modified:12/24/2016 19:20:23 CDT
Database id:122645
Status Flags:TrialDiv
Score (*):46.9332 (normalized score 20.6845)

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 16
Subcategory: "Generalized Unique"
(archival tag id 218555, tag last modified 2017-03-06 16:20:05)

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 (pool) 4c+4c 3.5GHz
notesCommand: /home/caldwell/clientpool/1/pfgw64 -t -q"Phi(3,-406515^98304)" 2>&1
PFGW Version [GWNUM 27.11]
Primality testing Phi(3,-406515^98304) [N-1, Brillhart-Lehmer-Selfridge]
Running N-1 test using base 29
Calling Brillhart-Lehmer-Selfridge with factored part 39.52%

Phi(3,-406515^98304) is prime! (29033.5702s+0.2931s)
[Elapsed time: 8.06 hours]
modified2017-01-27 05:57:10
created2016-12-24 10:53:01

Query times: 0.0005 seconds to select prime, 0.0006 seconds to seek comments.