13 · 2684560 + 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: | 13 · 2684560 + 1 |
|---|---|
| Verification status (*): | Proven |
| Official Comment (*): | Divides GF(684557,10), GF(684559,6) |
| Proof-code(s): (*): | g267 : Grobstich, NewPGen, PRP, Proth.exe |
| Decimal Digits: | 206075 (log10 is 206074.20777509) |
| Rank (*): | 33043 (digit rank is 1) |
| Entrance Rank (*): | 58 |
| Currently on list? (*): | no |
| Submitted: | 7/1/2003 07:18:49 UTC |
| Last modified: | 3/11/2023 15:54:10 UTC |
| Database id: | 65345 |
| Status Flags: | none |
| Score (*): | 41.7803 (normalized score 0.0256) |
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 Divisors (bases 3,5,6,10,12) (archivable *)
- Prime on list: no, rank 30, weight 44.345342906167
Subcategory: "Divides GF(*,6)"
(archival tag id 187172, tag last modified 2025-04-06 04:37:11)- Generalized Fermat Divisors (bases 3,5,6,10,12) (archivable *)
- Prime on list: no, rank 26, weight 44.345342906167
Subcategory: "Divides GF(*,10)"
(archival tag id 187171, tag last modified 2025-02-15 09:37:29)
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 65345 person_id 9 machine Linux P4 2.8GHz what prime notes PFGW Version 20020311.x86_Dev (Alpha software, 'caveat utilitor') Running N-1 test using base 3 Primality testing 13*2^684560+1 [N-1, Brillhart-Lehmer-Selfridge] Calling Brillhart-Lehmer-Selfridge with factored part 100.00% 13*2^684560+1 is prime! (-731.244592 seconds) modified 2020-07-07 22:30:47 created 2003-07-01 20:33:13 id 70183
Query times: 0.0002 seconds to select prime, 0.0004 seconds to seek comments.
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