Phi(12345, 7176)/31531760245313526865033921
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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(12345, 7176)/31531760245313526865033921
Verification status (*):PRP
Official Comment:ECPP
Unofficial Comments:This prime has 1 user comment below.
Proof-code(s): (*):c54 : Wu_T, Primo
Decimal Digits:25331   (log10 is 25330.784111701)
Rank (*):61449 (digit rank is 1)
Entrance Rank (*):61090
Currently on list? (*):short
Submitted:6/4/2017 13:54:50 CDT
Last modified:6/4/2017 14:20:20 CDT
Database id:123455
Status Flags:Verify, TrialDiv
Score (*):35.3169 (normalized score 0.0002)

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.
Elliptic Curve Primality Proof (archivable *)
Prime on list: yes, rank 6
Subcategory: "ECPP"
(archival tag id 218758, tag last modified 2017-06-04 14:20:21)

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.

Tom Wu writes (6 Jun 2017): 
Certificate available on the Primo Top-20 page.

Direct links to certificate parts: part 1 part 2

If the above links don't work, use the alternate download link on Google Drive.

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_id123455
person_id9
machineUsing: Xeon (pool) 4c+4c 3.5GHz
whatprp
notesCommand: /home/caldwell/clientpool/1/pfgw64 -tc -q"Phi(12345,7176)/31531760245313526865033921" 2>&1
PFGW Version 3.7.7.64BIT.20130722.x86_Dev [GWNUM 27.11]
Primality testing Phi(12345,7176)/3153176024...6865033921 [N-1/N+1, Brillhart-Lehmer-Selfridge]
Running N-1 test using base 11
Running N-1 test using base 13
Running N-1 test using base 17
Running N+1 test using discriminant 23, base 1+sqrt(23)
Calling N+1 BLS with factored part 0.05% and helper 0.05% (0.20% proof)


Phi(12345,7176)/3153176024...6865033921 is Fermat and Lucas PRP! (61.9733s+0.0043s)
[Elapsed time: 62.00 seconds]
modified2017-08-07 13:02:22
created2017-06-04 14:13:01
id169107

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