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.
|Verification status (*):||PRP|
|Official Comment (*):||Fibonacci primitive part, ECPP|
|Proof-code(s): (*):||c8 : Broadhurst, Water, Primo|
|Decimal Digits:||6822 (log10 is 6821.4735104781)|
|Rank (*):||84059 (digit rank is 1)|
|Entrance Rank (*):||67798|
|Currently on list? (*):||short|
|Submitted:||4/30/2013 16:39:05 CDT|
|Last modified:||4/30/2013 16:50:31 CDT|
|Score (*):||31.2537 (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.
- Elliptic Curve Primality Proof (archivable *)
- Prime on list: no, rank 383
(archival tag id 217115, tag last modified 2022-06-26 16:37:20)
- Fibonacci Primitive Part (archivable *)
- Prime on list: yes, rank 18
Subcategory: "Fibonacci Primitive Part"
(archival tag id 217116, tag last modified 2022-06-05 01:50:18)
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 114023 person_id 9 machine Ditto P4 P4 what prp notes PFGW Version 18.104.22.168BIT.20110215.x86_Dev [GWNUM 26.5] Primality testing 2975161039...2382939201 [N-1/N+1, Brillhart-Lehmer-Selfridge] Running N-1 test using base 19 Running N-1 test using base 37 Running N+1 test using discriminant 43, base 9+sqrt(43) Calling N-1 BLS with factored part 0.94% and helper 0.05% (2.86% proof) 2975161039...2382939201 is Fermat and Lucas PRP! (23.2051s+0.0020s) [Elapsed time: 23.00 seconds] modified 2020-07-07 17:30:19 created 2013-04-30 16:39:16 id 158410
field value prime_id 114023 person_id 9 machine RedHat P4 P4 what trial_divided notes PFGW Version 22.214.171.124BIT.20110215.x86_Dev [GWNUM 26.5] 2975161039118578....6625072382939201 1/1 mro=0 trial factoring to 1899371 2975161039...2382939201 has no small factor. [Elapsed time: 5.099 seconds] modified 2020-07-07 17:30:19 created 2013-04-30 16:48:08 id 158415