214923707595 · 249073 + 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: | 214923707595 · 249073 + 1 |
|---|---|
| Verification status (*): | Proven |
| Official Comment (*): | Cunningham chain 2nd kind (4p-3) |
| Proof-code(s): (*): | p364 : Batalov, NewPGen, OpenPFGW |
| Decimal Digits: | 14784 (log10 is 14783.777261542) |
| Rank (*): | 79907 (digit rank is 1) |
| Entrance Rank (*): | 78531 |
| Currently on list? (*): | yes |
| Submitted: | 1/2/2025 08:07:00 UTC |
| Last modified: | 1/2/2025 09:37:31 UTC |
| Database id: | 138816 |
| Status Flags: | none |
| Score (*): | 33.6511 (normalized score 0) |
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.
- Cunningham Chains (2nd kind) (archivable class *)
- Prime on list: yes, rank 1, weight 43.036259662692
Subcategory: "Cunningham chain 2nd kind (4p-3)"
(archival tag id 229811, tag last modified 2025-01-02 09:37:40)
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 138816 person_id 9 machine Using: Digital Ocean Droplet what prime notes Command: /var/www/clientpool/1/pfgw64 -V -f -t -q"214923707595*2^49073+1" >command_output 2>&1
PFGW Version 4.0.4.64BIT.20221214.x86_Dev [GWNUM 30.11]
Primality testing 214923707595*2^49073+1 [N-1, Brillhart-Lehmer-Selfridge]
trial
Running N-1 test using base 13
Special modular reduction using zero-padded FMA3 FFT length 5K on 214923707595*2^49073+1
Calling Brillhart-Lehmer-Selfridge with factored part 99.92%
214923707595*2^49073+1 is prime! (2.4486s+0.0061s)
[Elapsed time: 5.00 seconds]modified 2025-01-02 08:49:09 created 2025-01-02 08:49:04 id 184907
Query times: 0.0002 seconds to select prime, 0.0002 seconds to seek comments.
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