9 · 23354 + 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: | 9 · 23354 + 1 |
|---|---|
| Verification status (*): | Proven |
| Official Comment (*): | Divides GF(3353,10) [D], generalized Fermat |
| Proof-code(s): (*): | CW : Cormack |
| Decimal Digits: | 1011 (log10 is 1010.6088479664) |
| Rank (*): | 132791 (digit rank is 8) |
| Entrance Rank (*): | 11 |
| Currently on list? (*): | no |
| Submitted: | 1979 |
| Last modified: | 3/11/2023 15:54:10 UTC |
| Database id: | 56509 |
| Status Flags: | none |
| Score (*): | 25.305 (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.
- Generalized Fermat Divisors (bases 3,5,6,10,12) (archivable *)
- Prime on list: no, rank 81, weight 27.502241479721
Subcategory: "Divides GF(*,10)"
(archival tag id 177985, tag last modified 2025-02-15 09:37:30)- Generalized Fermat (archivable *)
- Prime on list: no, rank 9185
Subcategory: "Generalized Fermat"
(archival tag id 208904, tag last modified 2025-03-29 19:37:17)
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 56509 person_id 9 machine Linux PII 200 what prime notes PFGW Version 1.1 for Pentium and compatibles Running N-1 test using base 5 Primality testing 9*2^3354+1 [N-1, Brillhart-Lehmer-Selfridge] Calling Brillhart-Lehmer-Selfridge with factored part 99.91% 9*2^3354+1 is prime! (0.990000 seconds) modified 2020-07-07 22:30:56 created 2002-12-04 15:40:02 id 5089
Query times: 0.0002 seconds to select prime, 0.0003 seconds to seek comments.
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