31 · 213514933 - 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: | 31 · 213514933 - 1 |
|---|---|
| Verification status (*): | Proven |
| Official Comment (*): | [none] |
| Proof-code(s): (*): | A2 : Propper, Srsieve, PRST |
| Decimal Digits: | 4068402 (log10 is 4068401.7137507) |
| Rank (*): | 80 (digit rank is 1) |
| Entrance Rank (*): | 79 |
| Currently on list? (*): | yes |
| Submitted: | 2/9/2025 13:50:00 UTC |
| Last modified: | 2/17/2025 06:37:28 UTC |
| Database id: | 139614 |
| Status Flags: | none |
| Score (*): | 50.9342 (normalized score 248.5965) |
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 139614 person_id 9 machine Using: Digital Ocean Droplet what prime notes Command: /var/www/clientpool/1/pfgw64 -V -f -tp -q"31*2^13514933-1" >command_output 2>&1
PFGW Version 4.0.4.64BIT.20221214.x86_Dev [GWNUM 30.11]
Primality testing 31*2^13514933-1 [N+1, Brillhart-Lehmer-Selfridge]
trial
Running N+1 test using discriminant 3, base 1+sqrt(3)
Special modular reduction using AVX-512 FFT length 800K, Pass1=128, Pass2=6400, clm=2 on 31*2^13514933-1
Detected in MAXERR>0.45 (round off check) in Exponentiator::Iterate
Iteration: 2363/13514939 ERROR: ROUND OFF 0.45594>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 AVX-512 FFT length 840K, Pass1=1344, Pass2=640, clm=1 on 31*2^13514933-1
Calling Brillhart-Lehmer-Selfridge with factored part 100.00%
31*2^13514933-1 is prime! (628543.7506s+0.0047s)
[Elapsed time: 7.27 days]modified 2025-02-17 06:23:25 created 2025-02-09 23:47:39 id 185707
Query times: 0.0002 seconds to select prime, 0.0003 seconds to seek comments.
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