331426625784936325 · (23363 - 21121) - 3 · 21122 - 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: | 331426625784936325 · (23363 - 21121) - 3 · 21122 - 5 |
|---|---|
| Verification status (*): | Proven |
| Official Comment (*): | Quadruplet (2) |
| Proof-code(s): (*): | F : Forbes |
| Decimal Digits: | 1030 (log10 is 1029.8842628133) |
| Rank (*): | 127623 (digit rank is 6) |
| Entrance Rank (*): | 36576 |
| Currently on list? (*): | no |
| Submitted: | 1998 |
| Last modified: | 11/20/2024 09:20:06 UTC |
| Database id: | 55981 |
| Status Flags: | none |
| Score (*): | 25.3641 (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 30
Subcategory: "Quadruplet (2)"
(archival tag id 177894, 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 55981 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 331426625784936325*(2^3363-2^1121)-3*2^1122-5 [N-1/N+1, Brillhart-Lehmer-Selfridge]
Reading factors from helper file helper.php?id=1100000002650728676
trial
Running N-1 test using base 2
Generic modular reduction using generic reduction AVX-512 FFT length 1K on A 3423-bit number
Running N+1 test using discriminant 5, base 1+sqrt(5)
Generic modular reduction using generic reduction AVX-512 FFT length 1K on A 3423-bit number
Calling N-1 BLS with factored part 33.56% and helper 0.76% (101.49% proof)
331426625784936325*(2^3363-2^1121)-3*2^1122-5 is prime! (0.3170s+0.0034s)
[Elapsed time: 5.00 seconds]
Helper File:
2
3
19
2243
2833
37171
174763
5010781
1824726041
6088599401
58142098448088409
359071640268582342735956401
99171623271154790413320826656970847...(258 digits)...56964108698561163783822705921475217
7
13
23
53
283modified 2024-11-20 09:20:06 created 2024-11-20 09:20:01 id 184585
field value prime_id 55981 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 331426625784936325*(2^3363-2^1121)-3*2^1122-5 [N-1/N+1, Brillhart-Lehmer-Selfridge] Running N+1 test using discriminant 5, base 1+sqrt(5) Running N+1 test using discriminant 5, base 2+sqrt(5) Running N+1 test using discriminant 5, base 5+sqrt(5) Running N+1 test using discriminant 5, base 9+sqrt(5) Calling N-1 BLS with factored part 1.81% and helper 0.76% (6.20% proof) 331426625784936325*(2^3363-2^1121)-3*2^1122-5 is Fermat and Lucas PRP! (27.790000 seconds) modified 2003-03-25 17:23:05 created 2003-01-04 05:24:27 id 60414
Query times: 0.0002 seconds to select prime, 0.0003 seconds to seek comments.
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