p(221444161)
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(221444161) |
|---|---|
| Verification status (*): | PRP |
| Official Comment (*): | Partitions, ECPP |
| Unofficial Comments: | This prime has 1 user comment below. |
| Proof-code(s): (*): | c77 : Batalov, Primo |
| Decimal Digits: | 16569 (log10 is 16568.376495635) |
| Rank (*): | 76814 (digit rank is 1) |
| Entrance Rank (*): | 65673 |
| Currently on list? (*): | yes |
| Submitted: | 4/18/2017 14:42:43 UTC |
| Last modified: | 5/20/2023 20:59:19 UTC |
| Database id: | 123290 |
| Blob database id: | 365 |
| Status Flags: | Verify |
| Score (*): | 34.0039 (normalized score 0) |
Description: (from blob table id=365)
The number of unrestricted integer partitions of 221444161 is p(221444161).
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 159
Subcategory: "ECPP"
(archival tag id 218706, tag last modified 2024-12-16 19:37:11)- Partitions (archivable *)
- Prime on list: yes, rank 7
Subcategory: "Partitions"
(archival tag id 218707, 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 123290 person_id 9 machine Using: Xeon (pool) 4c+4c 3.5GHz what prp notes PFGW Version 3.7.7.64BIT.20130722.x86_Dev [GWNUM 27.11] Primality testing 2379554384...4199797591 [N-1/N+1, Brillhart-Lehmer-Selfridge] Running N-1 test using base 3 Running N+1 test using discriminant 11, base 1+sqrt(11) Calling N-1 BLS with factored part 0.02% and helper 0.01% (0.07% proof) 2379554384...4199797591 is Fermat and Lucas PRP! (21.3673s+0.0056s) [Elapsed time: 21.00 seconds] modified 2020-07-07 22:30:16 created 2017-04-18 15:13:02 id 168940
Query times: 0.0002 seconds to select prime, 0.0003 seconds to seek comments.
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