Phi(285, - 2637124)/13082397832081

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(285, - 2637124)/13082397832081
Verification status (*):PRP
Official Comment (*):ECPP
Unofficial Comments:This prime has 1 user comment below.
Proof-code(s): (*):c54 : Wu_T, Primo
Decimal Digits:15267   (log10 is 15266.29683791)
Rank (*):76974 (digit rank is 1)
Entrance Rank (*):51165
Currently on list? (*):no
Submitted:2/16/2012 07:33:34 UTC
Last modified:3/11/2023 15:54:10 UTC
Database id:104671
Status Flags:Verify
Score (*):33.7505 (normalized score 0)

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: no, rank 164
Subcategory: "ECPP"
(archival tag id 214044, tag last modified 2024-07-11 00:37:12)

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 (12 May 2021):  (report abuse)
This prime is a helper for the N-1 primality proof of the GRU prime N=Phi(13681,26371).

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.
machineDitto P4 P4
notesCommand: /home/ditto/client/pfgw -o -f -q"Phi(285,-26371^24)/13082397832081" 2>&1 PFGW Version [GWNUM 26.5] Phi(285,-26371^24)/13082397832081 1/1 mro=0 trial factoring to 4536744 Phi(285,-26371^24)/13082397832081 has no small factor. [Elapsed time: 6.045 seconds]
modified2020-07-07 22:30:28
created2012-02-16 07:35:01

machineDitto P4 P4
notesCommand: /home/ditto/client/pfgw -tc -q"Phi(285,-26371^24)/13082397832081" 2>&1 PFGW Version [GWNUM 26.5] Primality testing Phi(285,-26371^24)/13082397832081 [N-1/N+1, Brillhart-Lehmer-Selfridge] Running N-1 test using base 11 Running N+1 test using discriminant 17, base 2+sqrt(17) Calling N+1 BLS with factored part 0.05% and helper 0.05% (0.21% proof) Phi(285,-26371^24)/13082397832081 is Fermat and Lucas PRP! (91.3547s+0.0294s) [Elapsed time: 1.53 minutes]
modified2020-07-07 22:30:28
created2012-02-16 07:38:01

Query times: 0.0002 seconds to select prime, 0.0003 seconds to seek comments.
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