p(82352631)
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(82352631) |
|---|---|
| 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: | 10101 (log10 is 10100.688234038) |
| Rank (*): | 82667 (digit rank is 11) |
| Entrance Rank (*): | 56405 |
| Currently on list? (*): | no |
| Submitted: | 1/17/2012 12:57:00 UTC |
| Last modified: | 3/11/2023 15:54:10 UTC |
| Database id: | 103950 |
| Blob database id: | 275 |
| Status Flags: | Verify |
| Score (*): | 32.4711 (normalized score 0) |
Description: (from blob table id=275)
[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 318
Subcategory: "ECPP"
(archival tag id 213784, tag last modified 2024-04-24 05:37:25)- Partitions (archivable *)
- Prime on list: no, rank 55
Subcategory: "Partitions"
(archival tag id 213785, 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 103950 person_id 9 machine RedHat Virtual STEM Server what prp notes PFGW Version 3.3.4.20100405.x86_Stable [GWNUM 25.14] Primality testing 4877674586...3388428219 [N-1/N+1, Brillhart-Lehmer-Selfridge] Running N-1 test using base 2 Running N+1 test using discriminant 7, base 2+sqrt(7) Calling N-1 BLS with factored part 0.08% and helper 0.08% (0.33% proof) 4877674586...3388428219 is Fermat and Lucas PRP! (20.5723s+0.0128s) [Elapsed time: 30.00 seconds] modified 2020-07-07 22:30:29 created 2012-01-17 13:00:12 id 137489
field value prime_id 103950 person_id 9 machine Ditto P4 P4 what trial_divided notes PFGW Version 3.4.5.32BIT.20110215.x86_Dev [GWNUM 26.5] 4877674586263320....8741253388428219 1/1 mro=0 trial factoring to 2904614 4877674586...3388428219 has no small factor. [Elapsed time: 11.776 seconds] modified 2020-07-07 22:30:29 created 2012-01-17 13:05:01 id 137490
Query times: 0.0002 seconds to select prime, 0.0003 seconds to seek comments.
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