U(2449, - 1, 12671)
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(2449, - 1, 12671) |
|---|---|
| Verification status (*): | PRP |
| Official Comment (*): | Generalized Lucas number, cyclotomy |
| Unofficial Comments: | This prime has 1 user comment below. |
| Proof-code(s): (*): | x45 : Batalov, OpenPFGW, Primo, Unknown |
| Decimal Digits: | 42939 (log10 is 42938.48882491) |
| Rank (*): | 63431 (digit rank is 1) |
| Entrance Rank (*): | 54827 |
| Currently on list? (*): | short |
| Submitted: | 11/22/2018 00:31:58 UTC |
| Last modified: | 5/20/2023 20:59:19 UTC |
| Database id: | 125807 |
| Status Flags: | Verify |
| Score (*): | 36.9471 (normalized score 0.0003) |
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 3
Subcategory: "Generalized Lucas Number"
(archival tag id 219987, tag last modified 2023-03-11 15:53:59)- Cyclotomy Proof (tolerated *)
- Prime on list: no, rank 1
Subcategory: "Cyclotomy Proof"
(archival tag id 219988, 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 125807 person_id 9 machine Using: Xeon (pool) 4c+4c 3.5GHz what prp notes Command: /home/caldwell/clientpool/1/pfgw64 -tc -q"lucasU(2449,-1,12671)" 2>&1 PFGW Version 3.7.7.64BIT.20130722.x86_Dev [GWNUM 27.11] Primality testing lucasU(2449,-1,12671) [N-1/N+1, Brillhart-Lehmer-Selfridge] Running N-1 test using base 59 Running N-1 test using base 83 Running N-1 test using base 107 Running N+1 test using discriminant 113, base 2+sqrt(113) Calling N-1 BLS with factored part 0.64% and helper 0.17% (2.09% proof) lucasU(2449,-1,12671) is Fermat and Lucas PRP! (232.4249s+0.0037s) [Elapsed time: 3.88 minutes] modified 2020-07-07 22:30:14 created 2018-11-22 00:33:01 id 171484
Query times: 0.0002 seconds to select prime, 0.0003 seconds to seek comments.
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