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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 primitive part, ECPP|
|Proof-code(s): (*):||c74 : Lasher, Dubner, Primo|
|Decimal Digits:||14847 (log10 is 14846.422817996)|
|Rank (*):||75581 (digit rank is 1)|
|Entrance Rank (*):||65477|
|Currently on list? (*):||short|
|Submitted:||2/23/2016 16:43:23 UTC|
|Last modified:||3/11/2023 15:54:10 UTC|
|Status Flags:||Verify, TrialDiv|
|Score (*):||33.6642 (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 primitive part (archivable *)
- Prime on list: yes, rank 16
Subcategory: "Lucas primitive part"
(archival tag id 218223, tag last modified 2023-03-11 15:53:59)
- Elliptic Curve Primality Proof (archivable *)
- Prime on list: no, rank 144
(archival tag id 218224, tag last modified 2023-03-11 16:02:30)
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 121262 person_id 9 machine Using: Xeon 4c+4c 3.5GHz what prp notes PFGW Version 18.104.22.168BIT.20130722.x86_Dev [GWNUM 27.11] Primality testing 2647390436...6669204801 [N-1/N+1, Brillhart-Lehmer-Selfridge] Running N-1 test using base 29 Running N+1 test using discriminant 37, base 27+sqrt(37) Calling N-1 BLS with factored part 0.60% and helper 0.01% (1.83% proof) 2647390436...6669204801 is Fermat and Lucas PRP! (15.4695s+0.0049s) [Elapsed time: 15.00 seconds] modified 2020-07-07 22:30:16 created 2016-02-23 16:51:02 id 166897
Query times: 0.0002 seconds to select prime, 0.0004 seconds to seek comments.
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