p(60016427)
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(60016427) |
|---|---|
| Verification status (*): | PRP |
| Official Comment (*): | Partitions, ECPP |
| Proof-code(s): (*): | c46 : Boncompagni, Primo |
| Decimal Digits: | 8622 (log10 is 8621.6360043206) |
| Rank (*): | 84273 (digit rank is 3) |
| Entrance Rank (*): | 56407 |
| Currently on list? (*): | no |
| Submitted: | 9/29/2011 16:08:32 UTC |
| Last modified: | 3/11/2023 15:54:10 UTC |
| Database id: | 102255 |
| Blob database id: | 270 |
| Status Flags: | Verify |
| Score (*): | 31.9803 (normalized score 0) |
Description: (from blob table id=270)
p(60016427) is the number of partitions of the number\r\n60016427. For the primality proof, see the PRIMO certificate.
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 369
Subcategory: "ECPP"
(archival tag id 213503, tag last modified 2024-04-24 05:37:25)- Partitions (archivable *)
- Prime on list: no, rank 58
Subcategory: "Partitions"
(archival tag id 213504, tag last modified 2023-03-11 15:53:59)
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 102255 person_id 9 machine RedHat P4 P4 what trial_divided notes PFGW Version 3.4.5.32BIT.20110215.x86_Dev [GWNUM 26.5] 4324933855469276....2166572439671883 1/1 mro=0 trial factoring to 2447567 4324933855...2439671883 has no small factor. [Elapsed time: 8.072 seconds] modified 2020-07-07 22:30:30 created 2011-09-29 16:18:02 id 134101
field value prime_id 102255 person_id 9 machine RedHat P4 P4 what prp notes PFGW Version 3.4.5.32BIT.20110215.x86_Dev [GWNUM 26.5] Primality testing 4324933855...2439671883 [N-1/N+1, Brillhart-Lehmer-Selfridge] Running N-1 test using base 2 Running N+1 test using discriminant 5, base 1+sqrt(5) Calling N-1 BLS with factored part 0.04% and helper 0.03% (0.15% proof) 4324933855...2439671883 is Fermat and Lucas PRP! (29.0339s+0.0157s) [Elapsed time: 29.00 seconds] modified 2020-07-07 22:30:30 created 2011-09-29 16:23:01 id 134102
Query times: 0.0002 seconds to select prime, 0.0003 seconds to seek comments.
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