6 · Bern(5462)/23238026668982614152809832227

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:6 · Bern(5462)/23238026668982614152809832227
Verification status (*):PRP
Official Comment (*):Irregular, ECPP
Unofficial Comments:This prime has 1 user comment below.
Proof-code(s): (*):c64 : Metcalfe, Minovic, Ritschel, TOPS, Primo
Decimal Digits:13657   (log10 is 13656.620815761)
Rank (*):78844 (digit rank is 1)
Entrance Rank (*):59565
Currently on list? (*):short
Submitted:5/14/2013 05:18:03 UTC
Last modified:3/11/2023 15:54:10 UTC
Database id:114142
Status Flags:Verify
Score (*):33.4056 (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.
Irregular Primes (archivable *)
Prime on list: yes, rank 7
Subcategory: "Irregular Primes"
(archival tag id 217151, tag last modified 2023-03-11 16:02:31)
Elliptic Curve Primality Proof (archivable *)
Prime on list: no, rank 195
Subcategory: "ECPP"
(archival tag id 217152, 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.

David Metcalfe writes (11 Sep 2014):  (report abuse)
Certificate available from here.

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.
machineRedHat P4 P4
notesPFGW Version [GWNUM 26.5] Primality testing 4176531494...8889381213 [N-1/N+1, Brillhart-Lehmer-Selfridge] Running N-1 test using base 2 Running N-1 test using base 3 Running N+1 test using discriminant 11, base 3+sqrt(11) Calling N-1 BLS with factored part 0.09% and helper 0.06% (0.33% proof) 4176531494...8889381213 is Fermat and Lucas PRP! (104.7961s+0.0050s) [Elapsed time: 1.73 minutes]
modified2020-07-07 22:30:19
created2013-05-14 05:23:24

machineDitto P4 P4
notesPFGW Version [GWNUM 26.5] 4176531494031264....7529128889381213 1/1 mro=0 trial factoring to 4023025 4176531494...8889381213 has no small factor. [Elapsed time: 21.963 seconds]
modified2020-07-07 22:30:19
created2013-05-14 05:35:24

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