primB(219165)
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: | primB(219165) |
|---|---|
| Verification status (*): | PRP |
| Official Comment (*): | Lucas Aurifeuillian primitive part, ECPP |
| Unofficial Comments: | This prime has 1 user comment below. |
| Proof-code(s): (*): | c77 : Batalov, Primo |
| Decimal Digits: | 11557 (log10 is 11556.835862525) |
| Rank (*): | 83944 (digit rank is 1) |
| Entrance Rank (*): | 68031 |
| Currently on list? (*): | yes |
| Submitted: | 5/18/2015 06:26:13 UTC |
| Last modified: | 5/20/2023 20:59:19 UTC |
| Database id: | 119926 |
| Status Flags: | Verify |
| Score (*): | 32.8885 (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.
- Elliptic Curve Primality Proof (archivable *)
- Prime on list: no, rank 278
Subcategory: "ECPP"
(archival tag id 218046, tag last modified 2025-01-20 23:37:20)- Lucas Aurifeuillian primitive part (archivable *)
- Prime on list: yes, rank 20
Subcategory: "Lucas Aurifeuillian primitive part"
(archival tag id 218045, tag last modified 2024-03-24 06:37:15)
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 119926 person_id 9 machine Using: Xeon 4c+4c 3.5GHz what prp notes PFGW Version 3.7.7.64BIT.20130722.x86_Dev [GWNUM 27.11] Primality testing 6852712706...3159577601 [N-1/N+1, Brillhart-Lehmer-Selfridge] Running N-1 test using base 13 Running N-1 test using base 17 Running N+1 test using discriminant 37, base 21+sqrt(37) Calling N-1 BLS with factored part 0.53% and helper 0.00% (1.59% proof) 6852712706...3159577601 is Fermat and Lucas PRP! (10.9467s+0.0764s) [Elapsed time: 11.00 seconds] modified 2020-07-07 22:30:17 created 2015-05-18 06:31:02 id 165550
Query times: 0.0003 seconds to select prime, 0.0003 seconds to seek comments.
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