274386 · Bern(2622)/8518594882415401157891061256276973722693

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:274386 · Bern(2622)/8518594882415401157891061256276973722693
Verification status (*):PRP
Official Comment (*):Irregular, ECPP
Proof-code(s): (*):c8 : Broadhurst, Water, Primo
Decimal Digits:5701   (log10 is 5700.024603917)
Rank (*):89876 (digit rank is 3)
Entrance Rank (*):68728
Currently on list? (*):short
Submitted:2/28/2013 20:32:27 UTC
Last modified:3/11/2023 15:54:10 UTC
Database id:111388
Status Flags:Verify
Score (*):30.6961 (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 15
Subcategory: "Irregular Primes"
(archival tag id 215140, tag last modified 2023-03-11 16:02:31)
Elliptic Curve Primality Proof (archivable *)
Prime on list: no, rank 522
Subcategory: "ECPP"
(archival tag id 215141, tag last modified 2024-07-11 00:37:12)

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] 1058288110507284....3651313712976977 1/1 mro=0 trial factoring to 1563338 1058288110...3712976977 has no small factor. [Elapsed time: 3.695 seconds]
modified2020-07-07 22:30:22
created2013-02-28 20:35:05

machineDitto P4 P4
notesPFGW Version [GWNUM 26.5] Primality testing 1058288110...3712976977 [N-1/N+1, Brillhart-Lehmer-Selfridge] Running N-1 test using base 3 Running N+1 test using discriminant 11, base 1+sqrt(11) Calling N+1 BLS with factored part 0.16% and helper 0.12% (0.60% proof) 1058288110...3712976977 is Fermat and Lucas PRP! (13.1163s+0.0017s) [Elapsed time: 13.00 seconds]
modified2020-07-07 22:30:22
created2013-02-28 20:38:04

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