primV(6586, 1, 16200)
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: | primV(6586, 1, 16200) |
|---|---|
| Verification status (*): | PRP |
| Official Comment (*): | Generalized Lucas primitive part |
| Unofficial Comments: | This prime has 1 user comment below. |
| Proof-code(s): (*): | x25 : Broadhurst, Water, OpenPFGW, Primo |
| Decimal Digits: | 32993 (log10 is 32992.89162938) |
| Rank (*): | 66449 (digit rank is 1) |
| Entrance Rank (*): | 46421 |
| Currently on list? (*): | short |
| Submitted: | 1/13/2013 11:19:48 UTC |
| Last modified: | 3/11/2023 15:54:10 UTC |
| Database id: | 110705 |
| Status Flags: | Verify |
| Score (*): | 36.1335 (normalized score 0.0001) |
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.
- Generalized Lucas primitive part (archivable *)
- Prime on list: yes, rank 8
Subcategory: "Generalized Lucas primitive part"
(archival tag id 214907, tag last modified 2023-03-11 15:53:59)
User comments about this prime (disclaimer):
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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.
field value prime_id 110705 person_id 9 machine Ditto P4 P4 what prp notes Command: /home/ditto/client/pfgw -tc -q"primV(6586,1,16200)" 2>&1 PFGW Version 3.4.5.32BIT.20110215.x86_Dev [GWNUM 26.5] Primality testing primV(6586,1,16200) [N-1/N+1, Brillhart-Lehmer-Selfridge] Running N-1 test using base 43 Running N+1 test using discriminant 67, base 14+sqrt(67) Calling N-1 BLS with factored part 1.60% and helper 0.04% (4.85% proof) primV(6586,1,16200) is Fermat and Lucas PRP! (514.7202s+0.2471s) [Elapsed time: 8.58 minutes] modified 2020-07-07 22:30:23 created 2013-01-13 11:27:29 id 151684
field value prime_id 110705 person_id 9 machine Ditto P4 P4 what trial_divided notes Command: /home/ditto/client/pfgw -o -f -q"primV(6586,1,16200)" 2>&1 PFGW Version 3.4.5.32BIT.20110215.x86_Dev [GWNUM 26.5] primV(6586,1,16200) 1/1 mro=0 trial factoring to 10395960 primV(6586,1,16200) has no small factor. [Elapsed time: 35.912 seconds] modified 2020-07-07 22:30:23 created 2013-01-13 11:35:02 id 151686
Query times: 0.0003 seconds to select prime, 0.0004 seconds to seek comments.
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