3510160221387831655 · (23363 - 21121) - 3 · 21122 - 7
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: | 3510160221387831655 · (23363 - 21121) - 3 · 21122 - 7 |
|---|---|
| Verification status (*): | Proven |
| Official Comment (*): | Quadruplet (1) |
| Proof-code(s): (*): | F : Forbes |
| Decimal Digits: | 1031 (log10 is 1030.9092023583) |
| Rank (*): | 128124 (digit rank is 5) |
| Entrance Rank (*): | 43281 |
| Currently on list? (*): | no |
| Submitted: | 2/21/2000 23:18:54 UTC |
| Last modified: | 11/20/2024 09:29:18 UTC |
| Database id: | 55883 |
| Status Flags: | none |
| Score (*): | 25.3672 (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 29
Subcategory: "Quadruplet (1)"
(archival tag id 177853, 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 55883 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 3510160221387831655*(2^3363-2^1121)-3*2^1122-7 [N-1/N+1, Brillhart-Lehmer-Selfridge]
Reading factors from helper file helper.php?id=1100000002650737449
trial
Running N-1 test using base 3
Generic modular reduction using generic reduction AVX-512 FFT length 1K on A 3427-bit number
Running N+1 test using discriminant 11, base 7+sqrt(11)
Generic modular reduction using generic reduction AVX-512 FFT length 1K on A 3427-bit number
Calling N+1 BLS with factored part 35.11% and helper 0.85% (106.16% proof)
3510160221387831655*(2^3363-2^1121)-3*2^1122-7 is prime! (0.3786s+0.0002s)
[Elapsed time: 5.00 seconds]
Helper File:
2
5
15677003
3
19
1493
2243
2833
37171
43759
174763
29771303
37133053
1824726041
6088599401
58142098448088409
359071640268582342735956401
99171623271154790413320826656970847...(258 digits)...56964108698561163783822705921475217modified 2024-11-20 09:29:18 created 2024-11-20 09:29:13 id 184588
field value prime_id 55883 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 3 Primality testing 3510160221387831655*(2^3363-2^1121)-3*2^1122-7 [N-1/N+1, Brillhart-Lehmer-Selfridge] Running N+1 test using discriminant 11, base 7+sqrt(11) Running N+1 test using discriminant 11, base 8+sqrt(11) Calling N+1 BLS with factored part 2.54% and helper 0.15% (7.86% proof) 3510160221387831655*(2^3363-2^1121)-3*2^1122-7 is Fermat and Lucas PRP! (16.040000 seconds) modified 2003-03-25 17:23:04 created 2003-01-04 05:33:06 id 60580
Query times: 0.0002 seconds to select prime, 0.0003 seconds to seek comments.
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