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.
This prime's information:
| Description: | 3 · 2213321 + 1 |
|---|---|
| Verification status (*): | Proven |
| Official Comment (*): | Divides Fermat F(213319), GF(213319,3), GF(213316,6), GF(213319,12) [g0] |
| Proof-code(s): (*): | Y : Young |
| Decimal Digits: | 64217 (log10 is 64216.496826291) |
| Rank (*): | 58556 (digit rank is 1) |
| Entrance Rank (*): | 7 |
| Currently on list? (*): | no |
| Submitted: | 5/1997 |
| Last modified: | 6/2/2024 15:37:03 UTC |
| Database id: | 401 |
| Status Flags: | none |
| Score (*): | 38.189 (normalized score 0.0007) |
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 49, weight 39.287634372887
Subcategory: "Divides GF(*,12)"
(archival tag id 229545, tag last modified 2025-02-16 07:37:30)- Generalized Fermat Divisors (bases 3,5,6,10,12) (archivable *)
- Prime on list: no, rank 47, weight 39.287634372887
Subcategory: "Divides GF(*,6)"
(archival tag id 229544, tag last modified 2024-06-02 15:37:07)- Generalized Fermat Divisors (bases 3,5,6,10,12) (archivable *)
- Prime on list: no, rank 50, weight 39.287634372887
Subcategory: "Divides GF(*,3)"
(archival tag id 229543, tag last modified 2024-06-02 15:37:07)- Fermat Divisors (archivable *)
- Prime on list: no, rank 37, weight 39.287634372887
Subcategory: "Divides Fermat"
(archival tag id 229542, tag last modified 2025-01-14 07:37:11)
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 17:21:49 created 2003-01-21 21:08:28 id 67161
Query times: 0.0002 seconds to select prime, 0.0002 seconds to seek comments.
Printed from the PrimePages <t5k.org> © Reginald McLean.