827 · 22156678 - 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: | 827 · 22156678 - 1 |
|---|---|
| Verification status (*): | Proven |
| Official Comment (*): | [none] |
| Proof-code(s): (*): | L5819 : Schmidt2, LLR2, PSieve, Srsieve, NPLB, LLR |
| Decimal Digits: | 649228 (log10 is 649227.68649411) |
| Rank (*): | 4701 (digit rank is 1) |
| Entrance Rank (*): | 4112 |
| Currently on list? (*): | yes |
| Submitted: | 2/6/2024 08:02:54 UTC |
| Last modified: | 2/6/2024 16:37:17 UTC |
| Database id: | 137197 |
| Status Flags: | none |
| Score (*): | 45.3071 (normalized score 1.1963) |
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 137197 person_id 9 machine Using: Digital Ocean Droplet what prime notes Command: /var/www/clientpool/1/pfgw64 -V -f -tp -q"827*2^2156678-1" >command_output 2>&1
PFGW Version 4.0.4.64BIT.20221214.x86_Dev [GWNUM 30.11]
Primality testing 827*2^2156678-1 [N+1, Brillhart-Lehmer-Selfridge]
trial
Running N+1 test using discriminant 3, base 1+sqrt(3)
Special modular reduction using FMA3 FFT length 140K, Pass1=448, Pass2=320, clm=4 on 827*2^2156678-1
Detected in MAXERR>0.45 (round off check) in Exponentiator::Iterate
Iteration: 47/2156689 ERROR: ROUND OFF 0.48438>0.45
(Test aborted, try again using the -a1 switch)
Running N+1 test using discriminant 3, base 1+sqrt(3)
Special modular reduction using FMA3 FFT length 144K, Pass1=768, Pass2=192, clm=2 on 827*2^2156678-1
Calling Brillhart-Lehmer-Selfridge with factored part 100.00%
827*2^2156678-1 is prime! (6680.0528s+0.0011s)
[Elapsed time: 1.86 hours]modified 2024-02-06 16:22:55 created 2024-02-06 14:31:30 id 183036
Query times: 0.0002 seconds to select prime, 0.0003 seconds to seek comments.
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