612497 · 18612497 + 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: | 612497 · 18612497 + 1 |
|---|---|
| Verification status (*): | Proven |
| Official Comment (*): | Generalized Cullen |
| Proof-code(s): (*): | L5765 : Propper, Gcwsieve, LLR |
| Decimal Digits: | 768857 (log10 is 768856.43066223) |
| Rank (*): | 3669 (digit rank is 1) |
| Entrance Rank (*): | 3051 |
| Currently on list? (*): | yes |
| Submitted: | 5/20/2023 02:31:07 UTC |
| Last modified: | 5/20/2023 20:59:19 UTC |
| Database id: | 136064 |
| Status Flags: | none |
| Score (*): | 45.8263 (normalized score 2.3297) |
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 Cullen (archivable *)
- Prime on list: no, rank 28
Subcategory: "Generalized Cullen"
(archival tag id 228575, tag last modified 2023-12-29 19:37:13)
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 136064 person_id 9 machine Using: Digital Ocean Droplet what prime notes Command: /var/www/clientpool/1/pfgw64 -V -t -q"612497*18^612497+1" 2>&1
PFGW Version 4.0.4.64BIT.20221214.x86_Dev [GWNUM 30.11]
Primality testing 612497*18^612497+1 [N-1, Brillhart-Lehmer-Selfridge]
Running N-1 test using base 5
Special modular reduction using zero-padded AVX-512 FFT length 300K, Pass1=960, Pass2=320, clm=1 on 612497*18^612497+1
Running N-1 test using base 13
Special modular reduction using zero-padded AVX-512 FFT length 300K, Pass1=960, Pass2=320, clm=1 on 612497*18^612497+1
Calling Brillhart-Lehmer-Selfridge with factored part 76.02%
612497*18^612497+1 is prime! (6407.0629s+0.0066s)
[Elapsed time: 1.78 hours]modified 2023-05-20 06:11:17 created 2023-05-20 04:24:30 id 181894
Query times: 0.0003 seconds to select prime, 0.0004 seconds to seek comments.
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