primA(123405)
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: | primA(123405) |
|---|---|
| Verification status (*): | PRP |
| Official Comment (*): | Lucas Aurifeuillian primitive part, ECPP |
| Unofficial Comments: | This prime has 1 user comment below. |
| Proof-code(s): (*): | c8 : Broadhurst, Water, Primo |
| Decimal Digits: | 6502 (log10 is 6501.0068695973) |
| Rank (*): | 88298 (digit rank is 2) |
| Entrance Rank (*): | 67996 |
| Currently on list? (*): | no |
| Submitted: | 4/10/2013 22:16:07 UTC |
| Last modified: | 3/11/2023 15:54:10 UTC |
| Database id: | 112357 |
| Status Flags: | Verify |
| Score (*): | 31.1044 (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.
- Lucas Aurifeuillian primitive part (archivable *)
- Prime on list: no, rank 33
Subcategory: "Lucas Aurifeuillian primitive part"
(archival tag id 215623, tag last modified 2024-03-24 06:37:15)- Elliptic Curve Primality Proof (archivable *)
- Prime on list: no, rank 463
Subcategory: "ECPP"
(archival tag id 215624, tag last modified 2024-04-24 05:37:25)
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 112357 person_id 9 machine RedHat P4 P4 what trial_divided notes PFGW Version 3.4.5.32BIT.20110215.x86_Dev [GWNUM 26.5] 1015943596487506....3561434741646401 1/1 mro=0 trial factoring to 1802825 1015943596...4741646401 has no small factor. [Elapsed time: 4.931 seconds] modified 2020-07-07 22:30:21 created 2013-04-10 22:18:01 id 155066
field value prime_id 112357 person_id 9 machine RedHat P4 P4 what prp notes PFGW Version 3.4.5.32BIT.20110215.x86_Dev [GWNUM 26.5] Primality testing 1015943596...4741646401 [N-1/N+1, Brillhart-Lehmer-Selfridge] Running N-1 test using base 29 Running N-1 test using base 31 Running N+1 test using discriminant 41, base 14+sqrt(41) Calling N-1 BLS with factored part 0.69% and helper 0.13% (2.18% proof) 1015943596...4741646401 is Fermat and Lucas PRP! (20.3381s+0.0020s) [Elapsed time: 20.00 seconds] modified 2020-07-07 22:30:21 created 2013-04-10 22:23:02 id 155068
Query times: 0.0002 seconds to select prime, 0.0003 seconds to seek comments.
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