3 · 2213321 + 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.
| Description: | 3 · 2213321 + 1 |
|---|---|
| Verification status (*): | Proven |
| Official Comment (*): | Divides Fermat F(213319); GF(213319,3), GF(213319,5), GF(213316,6), GF(213319,12) [g0] |
| Proof-code(s): (*): | Y : Young |
| Decimal Digits: | 64217 (log10 is 64216.496826291) |
| Rank (*): | 52492 (digit rank is 1) |
| Entrance Rank (*): | 7 |
| Currently on list? (*): | no |
| Submitted: | 5/1997 |
| Last modified: | 2/3/2014 21:20:04 CDT |
| Database id: | 401 |
| Status Flags: | none |
| Score (*): | 38.189 (normalized score 0.0016) |
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 43, weight 39.287634372887
Subcategory: "Divides GF(*,6)"
(archival tag id 217609, tag last modified 2022-05-12 21:37:21)- Generalized Fermat Divisors (bases 3,5,6,10,12) (archivable *)
- Prime on list: no, rank 44, weight 39.287634372887
Subcategory: "Divides GF(*,5)"
(archival tag id 217608, tag last modified 2020-10-29 19:20:16)- Generalized Fermat Divisors (bases 3,5,6,10,12) (archivable *)
- Prime on list: no, rank 47, weight 39.287634372887
Subcategory: "Divides GF(*,3)"
(archival tag id 217607, tag last modified 2021-02-26 11:20:20)- Fermat Divisors (archivable *)
- Prime on list: no, rank 34, weight 39.287634372887
Subcategory: "Divides Fermat"
(archival tag id 217606, tag last modified 2021-01-16 15:20:20)- Generalized Fermat Divisors (bases 3,5,6,10,12) (archivable *)
- Prime on list: no, rank 43, weight 39.287634372887
Subcategory: "Divides GF(*,12)"
(archival tag id 217610, tag last modified 2022-04-12 17:37:10)
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 401 person_id 9 machine WinXP P4 1.8GHz what prime notes PFGW Version 20021217.Win_Dev (Beta 'caveat utilitor') [FFT v22.7 w/P4] Running N-1 test using base 5 Primality testing 3*2^213321+1 [N-1, Brillhart-Lehmer-Selfridge] Calling Brillhart-Lehmer-Selfridge with factored part 100.00% 3*2^213321+1 is prime! (362.352000 seconds) modified 2003-03-25 11:21:49 created 2003-01-21 15:08:28 id 67161
Query times: 0.0003 seconds to select prime, 0.0004 seconds to seek comments.
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