6 · Bern(3458)/28329084584758278770932715893606309

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(3458)/28329084584758278770932715893606309
Verification status (*):PRP
Official Comment (*):Irregular, ECPP
Unofficial Comments:This prime has 1 user comment below.
Proof-code(s): (*):c8 : Broadhurst, Water, Primo
Decimal Digits:7945   (log10 is 7944.1559701429)
Rank (*):85294 (digit rank is 1)
Entrance Rank (*):64860
Currently on list? (*):short
Submitted:2/24/2013 22:27:39 UTC
Last modified:3/11/2023 15:54:10 UTC
Database id:111321
Status Flags:Verify
Score (*):31.7265 (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 11
Subcategory: "Irregular Primes"
(archival tag id 215095, tag last modified 2023-03-11 16:02:31)
Elliptic Curve Primality Proof (archivable *)
Prime on list: no, rank 406
Subcategory: "ECPP"
(archival tag id 215096, 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 Broadhurst writes (11 Sep 2014):  (report abuse)

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
notesPFGW Version [GWNUM 26.5] 1432089442117530....3131297651655891 1/1 mro=0 trial factoring to 2240077 1432089442...7651655891 has no small factor. [Elapsed time: 7.552 seconds]
modified2020-07-07 22:30:22
created2013-02-24 22:35:07

machineDitto P4 P4
notesPFGW Version [GWNUM 26.5] Primality testing 1432089442...7651655891 [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 7, base 1+sqrt(7) Calling N-1 BLS with factored part 0.13% and helper 0.08% (0.48% proof) 1432089442...7651655891 is Fermat and Lucas PRP! (36.1434s+0.0059s) [Elapsed time: 36.00 seconds]
modified2020-07-07 22:30:22
created2013-02-24 22:38:08

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