47356235323005 · 2333443 - 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: | 47356235323005 · 2333443 - 1 |
|---|---|
| Verification status (*): | Proven |
| Official Comment (*): | Sophie Germain (p) |
| Proof-code(s): (*): | L6077 : Vink, Schmidt2, Kwok, TwinGen, NewPGen, TPS, LLR |
| Decimal Digits: | 100391 (log10 is 100390.02022135) |
| Rank (*): | 49001 (digit rank is 2) |
| Entrance Rank (*): | 48962 |
| Currently on list? (*): | short |
| Submitted: | 10/4/2024 19:39:46 UTC |
| Last modified: | 10/4/2024 21:17:00 UTC |
| Database id: | 138611 |
| Status Flags: | none |
| Score (*): | 39.5662 (normalized score 0.0039) |
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.
- Sophie Germain (p) (archivable *)
- Prime on list: yes, rank 3
Subcategory: "Sophie Germain (p)"
(archival tag id 229675, tag last modified 2024-10-04 20:37:13)
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 138611 person_id 9 machine Using: Digital Ocean Droplet what prime notes Command: /var/www/clientpool/1/pfgw64 -V -f -tp -q"47356235323005*2^333443-1" >command_output 2>&1
PFGW Version 4.0.4.64BIT.20221214.x86_Dev [GWNUM 30.11]
Primality testing 47356235323005*2^333443-1 [N+1, Brillhart-Lehmer-Selfridge]
trial
Running N+1 test using discriminant 11, base 1+sqrt(11)
Special modular reduction using generic reduction FMA3 FFT length 32K, Pass1=512, Pass2=64, clm=2 on 47356235323005*2^333443-1
Detected in MAXERR>0.45 (round off check) in Exponentiator::Iterate
Iteration: 38/333490 ERROR: ROUND OFF 0.5>0.45
(Test aborted, try again using the -a1 switch)
Running N+1 test using discriminant 11, base 1+sqrt(11)
Special modular reduction using generic reduction FMA3 FFT length 36K, Pass1=768, Pass2=48, clm=2 on 47356235323005*2^333443-1
Calling Brillhart-Lehmer-Selfridge with factored part 99.99%
47356235323005*2^333443-1 is prime! (611.5775s+0.0005s)
[Elapsed time: 10.25 minutes]modified 2024-10-04 19:50:17 created 2024-10-04 19:40:01 id 184455
Query times: 0.0002 seconds to select prime, 0.0002 seconds to seek comments.
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