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:
|Verification status (*):||PRP|
|Official Comment (*):||Lucas Aurifeuillian primitive part, ECPP|
|Proof-code(s): (*):||c8 : Broadhurst, Water, Primo|
|Decimal Digits:||8282 (log10 is 8281.7622078261)|
|Rank (*):||83236 (digit rank is 1)|
|Entrance Rank (*):||67112|
|Currently on list? (*):||no|
|Submitted:||10/9/2013 22:18:22 UTC|
|Last modified:||5/20/2023 20:59:19 UTC|
|Score (*):||31.8555 (normalized score 0)|
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 22
Subcategory: "Lucas Aurifeuillian primitive part"
(archival tag id 217263, tag last modified 2023-10-03 00:37:15)
- Elliptic Curve Primality Proof (archivable *)
- Prime on list: no, rank 355
(archival tag id 217264, tag last modified 2023-10-03 00:37:15)
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.
field value prime_id 115859 person_id 9 machine Ditto P4 P4 what prp notes PFGW Version 188.8.131.52BIT.20110215.x86_Dev [GWNUM 26.5] Primality testing 5783727541...1794420131 [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 0.39% and helper 0.06% (1.23% proof) 5783727541...1794420131 is Fermat and Lucas PRP! (40.6168s+0.0063s) [Elapsed time: 40.00 seconds] modified 2020-07-07 22:30:18 created 2013-10-09 22:38:35 id 161360