p(51831641)
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: | p(51831641) |
|---|---|
| Verification status (*): | PRP |
| Official Comment (*): | Partitions, ECPP |
| Unofficial Comments: | This prime has 1 user comment below. |
| Proof-code(s): (*): | c56 : Soule, Minovic, OpenPFGW, Primo |
| Decimal Digits: | 8012 (log10 is 8011.6602134916) |
| Rank (*): | 84927 (digit rank is 1) |
| Entrance Rank (*): | 56839 |
| Currently on list? (*): | no |
| Submitted: | 9/16/2011 06:32:54 UTC |
| Last modified: | 3/11/2023 15:54:10 UTC |
| Database id: | 101998 |
| Blob database id: | 268 |
| Status Flags: | Verify |
| Score (*): | 31.7527 (normalized score 0) |
Description: (from blob table id=268)
[This prime has a pre-calculated decimal expansion (linked blob)]
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 397
Subcategory: "ECPP"
(archival tag id 213457, tag last modified 2024-04-19 02:37:11)- Partitions (archivable *)
- Prime on list: no, rank 68
Subcategory: "Partitions"
(archival tag id 213458, tag last modified 2023-03-11 15:53:59)
User comments about this prime (disclaimer):
User comments are allowed to convey mathematical information about this number, how it was proven prime.... See our guidelines and restrictions.
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 101998 person_id 9 machine Ditto P4 P4 what trial_divided notes PFGW Version 3.4.5.32BIT.20110215.x86_Dev [GWNUM 26.5] 4572847839645468....7197973601139073 1/1 mro=0 trial factoring to 2260758 4572847839...3601139073 has no small factor. [Elapsed time: 7.084 seconds] modified 2020-07-07 22:30:30 created 2011-09-16 06:35:02 id 133562
field value prime_id 101998 person_id 9 machine Ditto P4 P4 what prp notes PFGW Version 3.4.5.32BIT.20110215.x86_Dev [GWNUM 26.5] Primality testing 4572847839...3601139073 [N-1/N+1, Brillhart-Lehmer-Selfridge] Running N-1 test using base 5 Running N+1 test using discriminant 13, base 6+sqrt(13) Calling N-1 BLS with factored part 0.13% and helper 0.02% (0.42% proof) 4572847839...3601139073 is Fermat and Lucas PRP! (22.6380s+0.0025s) [Elapsed time: 23.00 seconds] modified 2020-07-07 22:30:30 created 2011-09-16 06:38:01 id 133563
Query times: 0.0002 seconds to select prime, 0.0003 seconds to seek comments.
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