8954571083387140525 · (23423 - 21141) - 3 · 21142 - 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: | 8954571083387140525 · (23423 - 21141) - 3 · 21142 - 1 |
|---|---|
| Verification status (*): | Proven |
| Official Comment (*): | Quadruplet (3) |
| Proof-code(s): (*): | F : Forbes |
| Decimal Digits: | 1050 (log10 is 1049.3777199461) |
| Rank (*): | 126712 (digit rank is 31) |
| Entrance Rank (*): | 42550 |
| Currently on list? (*): | no |
| Submitted: | 2/21/2000 23:18:54 UTC |
| Last modified: | 11/20/2024 13:27:56 UTC |
| Database id: | 55086 |
| Status Flags: | none |
| Score (*): | 25.4227 (normalized score 0) |
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.
- Quadruplet (archivable class *)
- Prime on list: no, rank 25
Subcategory: "Quadruplet (3)"
(archival tag id 177737, tag last modified 2023-07-22 12:37:40)
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 55086 person_id 9 machine Using: Digital Ocean Droplet what prime notes PFGW Version 4.0.4.64BIT.20221214.x86_Dev [GWNUM 30.11]
Primality testing 8954571083387140525*(2^3423-2^1141)-3*2^1142-1 [N-1/N+1, Brillhart-Lehmer-Selfridge]
Reading factors from helper file helper.php?id=1100000002650655876
trial
Running N-1 test using base 5
Generic modular reduction using generic reduction AVX-512 FFT length 1K on A 3488-bit number
Running N-1 test using base 7
Generic modular reduction using generic reduction AVX-512 FFT length 1K on A 3488-bit number
Running N+1 test using discriminant 19, base 1+sqrt(19)
Generic modular reduction using generic reduction AVX-512 FFT length 1K on A 3488-bit number
Calling N+1 BLS with factored part 33.08% and helper 4.22% (103.53% proof)
8954571083387140525*(2^3423-2^1141)-3*2^1142-1 is prime! (0.2676s+0.0001s)
[Elapsed time: 6.00 seconds]
Helper File:
2
11
751
1873
16267
11414025586151
32415737118607804769
3
13
179modified 2024-11-20 13:27:56 created 2024-11-20 13:27:50 id 184609
field value prime_id 55086 person_id 9 machine Windows XP P4 1.8GHz what prp notes Primality testing 8954571083387140525*(2^3423-2^1141)-3*2^1142-1 [N+1, Brillhart-Lehmer-Selfridge] Calling Brillhart-Lehmer-Selfridge with factored part 33.08% Proof incomplete rerun with -x52640724 8954571083387140525*(2^3423-2^1141)-3*2^1142-1 is Lucas PRP! (0.922000 seconds) PFGW Version 20021217.Win_Dev (Beta 'caveat utilitor') [FFT v22.7 w/P4] Running N+1 test using discriminant 5, base 1+sqrt(5) modified 2003-03-25 17:23:16 created 2002-12-31 16:20:28 id 58626
Query times: 0.0002 seconds to select prime, 0.0003 seconds to seek comments.
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