4 · 311279466 + 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: | 4 · 311279466 + 1 |
|---|---|
| Verification status (*): | External |
| Official Comment (*): | Generalized Fermat |
| Unofficial Comments: | This prime has 1 user comment below. |
| Proof-code(s): (*): | A2 : Propper, Srsieve, PRST |
| Decimal Digits: | 5381674 (log10 is 5381673.5725478) |
| Rank (*): | 38 (digit rank is 1) |
| Entrance Rank (*): | 35 |
| Currently on list? (*): | yes |
| Submitted: | 9/10/2024 15:14:07 UTC |
| Last modified: | 9/23/2024 22:37:25 UTC |
| Database id: | 138515 |
| Status Flags: | none |
| Score (*): | 51.7907 (normalized score 783.2946) |
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 (archivable *)
- Prime on list: yes, rank 8
Subcategory: "Generalized Fermat"
(archival tag id 229656, tag last modified 2024-10-04 15:37:11)
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 138515 person_id 9 machine Using: Digital Ocean Droplet what composite notes Command: /var/www/clientpool/1/pfgw64 -V -f -t -q"4*3^11279466+1" >command_output 2>&1
PFGW Version 4.0.4.64BIT.20221214.x86_Dev [GWNUM 30.11]
Primality testing 4*3^11279466+1 [N-1, Brillhart-Lehmer-Selfridge]
trial
Running N-1 test using base 2
Special modular reduction using all-complex FMA3 FFT length 1M, Pass1=512, Pass2=2K, clm=2 on 4*3^11279466+1
Running N-1 test using base 5
Special modular reduction using all-complex FMA3 FFT length 1M, Pass1=512, Pass2=2K, clm=2 on 4*3^11279466+1
Running N-1 test using base 7
Special modular reduction using all-complex FMA3 FFT length 1M, Pass1=512, Pass2=2K, clm=2 on 4*3^11279466+1
Detected in MAXERR>0.45 (round off check) in Exponentiator::Iterate
Iteration: 17877532/17877534 ERROR: ROUND OFF 0.5>0.45
(Test aborted, try again using the -a1 switch)
Running N-1 test using base 11
Special modular reduction using all-complex FMA3 FFT length 1152K, Pass1=384, Pass2=3K, clm=2 on 4*3^11279466+1
4*3^11279466+1 is composite (785578.5584s+0.1089s)
[Elapsed time: 9.09 days]modified 2024-09-22 12:03:33 created 2024-09-13 09:50:34 id 184359
Query times: 0.0003 seconds to select prime, 0.0003 seconds to seek comments.
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