8954571083387140525 · (23423 - 21141) - 3 · 21142 - 5
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 - 5 |
|---|---|
| Verification status (*): | Proven |
| Official Comment (*): | Quadruplet (2) |
| Proof-code(s): (*): | F : Forbes |
| Decimal Digits: | 1050 (log10 is 1049.3777199461) |
| Rank (*): | 126713 (digit rank is 32) |
| Entrance Rank (*): | 42551 |
| Currently on list? (*): | no |
| Submitted: | 2/21/2000 23:18:54 UTC |
| Last modified: | 11/20/2024 13:28:32 UTC |
| Database id: | 55087 |
| 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 (2)"
(archival tag id 177738, 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 55087 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*2^1142-5 [N-1/N+1, Brillhart-Lehmer-Selfridge]
Reading factors from helper file helper.php?id=1100000002650655851
trial
Running N-1 test using base 2
Generic modular reduction using generic reduction AVX-512 FFT length 1K on A 3488-bit number
Running N-1 test using base 3
Generic modular reduction using generic reduction AVX-512 FFT length 1K on A 3488-bit number
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 discriminant 13, base 2+sqrt(13)
Generic modular reduction using generic reduction AVX-512 FFT length 1K on A 3488-bit number
Calling N-1 BLS with factored part 100.00% and helper 0.40% (300.49% proof)
8954571083387140525*(2^3423-2^1141)-3*2^1142-5 is prime! (0.3901s+0.0001s)
[Elapsed time: 5.00 seconds]
Helper File:
2
3
19
43
18257
448373
7664653
11281292593
184816459337
301870128784337
1023398150341859
1200893348906161
722526146028558523
337570547050390415041769
17060613539298460913312913761
72822418109085987998790016581598007...(213 digits)...15114941165614771538410126704161577
33100816037999877673791230453689391...(681 digits)...74979229402481384305736442192168871
4621modified 2024-11-20 13:28:32 created 2024-11-20 13:28:26 id 184610
field value prime_id 55087 person_id 9 machine Linux PII 200 what prp notes PFGW Version 20020311.x86_Dev (Alpha software, 'caveat utilitor') Running N-1 test using base 2 Primality testing 8954571083387140525*(2^3423-2^1141)-3*2^1142-5 [N-1/N+1, Brillhart-Lehmer-Selfridge] Running N+1 test using discriminant 5, base 1+sqrt(5) Calling N-1 BLS with factored part 0.75% and helper 0.40% (2.67% proof) 8954571083387140525*(2^3423-2^1141)-3*2^1142-5 is Fermat and Lucas PRP! (10.680000 seconds) modified 2003-03-25 17:23:04 created 2003-01-04 05:42:31 id 60742
Query times: 0.0002 seconds to select prime, 0.0003 seconds to seek comments.
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