193 · 23329782 + 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: | 193 · 23329782 + 1 |
|---|---|
| Verification status (*): | Proven |
| Official Comment (*): | Divides Fermat F(3329780) |
| Unofficial Comments: | This prime has 1 user comment below. |
| Proof-code(s): (*): | L3460 : Ottusch, PSieve, Srsieve, PrimeGrid, LLR |
| Decimal Digits: | 1002367 (log10 is 1002366.5465793) |
| Rank (*): | 2768 (digit rank is 1) |
| Entrance Rank (*): | 98 |
| Currently on list? (*): | yes |
| Submitted: | 7/25/2014 22:58:37 UTC |
| Last modified: | 5/20/2023 20:59:19 UTC |
| Database id: | 118254 |
| Status Flags: | none |
| Score (*): | 46.6402 (normalized score 4.5403) |
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.
- Fermat Divisors (archivable *)
- Prime on list: yes, rank 5, weight 51.902980931542
Subcategory: "Divides Fermat"
(archival tag id 217768, tag last modified 2023-07-18 02:37:34)
User comments about this prime (disclaimer):
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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 118254 person_id 9 machine Xeon 4c+4c 3.5GHz what prime notes Command: /home/caldwell/client/pfgw/pfgw64 -t -q"193*2^3329782+1" 2>&1 PFGW Version 3.7.7.64BIT.20130722.x86_Dev [GWNUM 27.11] Primality testing 193*2^3329782+1 [N-1, Brillhart-Lehmer-Selfridge] Running N-1 test using base 3 Calling Brillhart-Lehmer-Selfridge with factored part 100.00% 193*2^3329782+1 is prime! (4842.2594s+0.0013s) [Elapsed time: 80.70 minutes] modified 2020-07-07 22:30:17 created 2014-07-25 23:01:01 id 163820
Query times: 0.0002 seconds to select prime, 0.0004 seconds to seek comments.
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