3214654524288 + 1
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: | 3214654524288 + 1 |
|---|---|
| Verification status (*): | Proven |
| Official Comment (*): | Generalized Fermat |
| Unofficial Comments: | This prime has 1 user comment below. |
| Proof-code(s): (*): | L4309 : Kecic, GFNSvCUDA, GeneFer, AthGFNSieve, PrimeGrid, LLR |
| Decimal Digits: | 3411613 (log10 is 3411612.3941893) |
| Rank (*): | 126 (digit rank is 1) |
| Entrance Rank (*): | 30 |
| Currently on list? (*): | yes |
| Submitted: | 12/25/2019 12:02:28 UTC |
| Last modified: | 5/20/2023 20:59:19 UTC |
| Database id: | 130199 |
| Status Flags: | none |
| Score (*): | 50.395 (normalized score 191.16) |
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.
- Generalized Fermat (archivable *)
- Prime on list: no, rank 23
Subcategory: "Generalized Fermat"
(archival tag id 223655, tag last modified 2024-10-11 22:37:10)
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 130199 person_id 9 machine Using: Xeon 4c+4c 3.5GHz what prime notes Command: /home/caldwell/client/pfgw/pfgw64 -t -q"3214654^524288+1" 2>&1 PFGW Version 4.0.1.64BIT.20191203.x86_Dev [GWNUM 29.8] Primality testing 3214654^524288+1 [N-1, Brillhart-Lehmer-Selfridge] F: 3214654^524288+1 16384/36012170 (trial factor to 1442980243) F: 3214654^524288+1 34816/36012170 (trial factor to 1442980243) F: 3214654^524288+1 53248/36012170 (trial factor to 1442980243) Running N-1 test using base 3 Calling Brillhart-Lehmer-Selfridge with factored part 95.37% 3214654^524288+1 is prime! (364920.2327s+0.1426s) [Elapsed time: 4.22 days] modified 2020-07-07 22:30:10 created 2019-12-25 12:11:02 id 175885
Query times: 0.0002 seconds to select prime, 0.0018 seconds to seek comments.
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