U(8454, - 1, 5039)
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: | U(8454, - 1, 5039) |
|---|---|
| Verification status (*): | PRP |
| Official Comment (*): | Generalized Lucas number |
| Unofficial Comments: | This prime has 1 user comment below. |
| Proof-code(s): (*): | x25 : Broadhurst, Water, OpenPFGW, Primo |
| Decimal Digits: | 19785 (log10 is 19784.539613326) |
| Rank (*): | 74071 (digit rank is 1) |
| Entrance Rank (*): | 53189 |
| Currently on list? (*): | short |
| Submitted: | 1/10/2013 10:06:43 UTC |
| Last modified: | 3/11/2023 15:54:10 UTC |
| Database id: | 110680 |
| Status Flags: | Verify |
| Score (*): | 34.5527 (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.
- Generalized Lucas Number (archivable *)
- Prime on list: yes, rank 19
Subcategory: "Generalized Lucas Number"
(archival tag id 214904, tag last modified 2023-10-24 02:37:13)
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 110680 person_id 9 machine RedHat P4 P4 what trial_divided notes Command: /home/caldwell/client/pfgw -o -f -q"lucasU(8454,-1,5039)" 2>&1 PFGW Version 3.4.5.32BIT.20110215.x86_Dev [GWNUM 26.5] lucasU(8454,-1,5039) 1/1 mro=0 trial factoring to 5998703 lucasU(8454,-1,5039) has no small factor. [Elapsed time: 13.728 seconds] modified 2020-07-07 22:30:23 created 2013-01-10 10:18:02 id 151634
field value prime_id 110680 person_id 9 machine Ditto P4 P4 what prp notes Command: /home/ditto/client/pfgw -tc -q"lucasU(8454,-1,5039)" 2>&1 PFGW Version 3.4.5.32BIT.20110215.x86_Dev [GWNUM 26.5] Primality testing lucasU(8454,-1,5039) [N-1/N+1, Brillhart-Lehmer-Selfridge] Running N-1 test using base 47 Running N-1 test using base 59 Running N-1 test using base 79 Running N+1 test using discriminant 127, base 3+sqrt(127) Calling N-1 BLS with factored part 1.15% and helper 0.38% (3.85% proof) lucasU(8454,-1,5039) is Fermat and Lucas PRP! (245.1395s+0.0037s) [Elapsed time: 4.08 minutes] modified 2020-07-07 22:30:23 created 2013-01-10 11:36:50 id 151635
Query times: 0.0002 seconds to select prime, 0.0003 seconds to seek comments.
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