primA(219135)

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:primA(219135)
Verification status (*):PRP
Official Comment (*):Lucas Aurifeuillian primitive part, ECPP
Proof-code(s): (*):c8 : Broadhurst, Water, Primo
Decimal Digits:10462   (log10 is 10461.888055308)
Rank (*):82270 (digit rank is 1)
Entrance Rank (*):67366
Currently on list? (*):no
Submitted:9/11/2014 18:10:04 UTC
Last modified:5/20/2023 20:59:19 UTC
Database id:118484
Status Flags:Verify
Score (*):32.58 (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.
Lucas Aurifeuillian primitive part (archivable *)
Prime on list: no, rank 21
Subcategory: "Lucas Aurifeuillian primitive part"
(archival tag id 217815, tag last modified 2024-03-24 06:37:15)
Elliptic Curve Primality Proof (archivable *)
Prime on list: no, rank 299
Subcategory: "ECPP"
(archival tag id 217816, tag last modified 2024-03-24 06:37:14)

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_id118484
person_id9
machineUsing: Xeon 4c+4c 3.5GHz
whatprp
notesPFGW Version 3.7.7.64BIT.20130722.x86_Dev [GWNUM 27.11] Primality testing 7727789930...4210081121 [N-1/N+1, Brillhart-Lehmer-Selfridge] Running N-1 test using base 29 Running N-1 test using base 37 Running N-1 test using base 41 Running N+1 test using discriminant 47, base 2+sqrt(47) Calling N-1 BLS with factored part 0.42% and helper 0.07% (1.35% proof) 7727789930...4210081121 is Fermat and Lucas PRP! (11.8673s+0.0032s) [Elapsed time: 12.00 seconds]
modified2020-07-07 22:30:17
created2014-09-11 18:11:02
id164063

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