(362109319 - 1)/36209
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: | (362109319 - 1)/36209 |
|---|---|
| Verification status (*): | Proven |
| Official Comment (*): | Generalized repunit |
| Unofficial Comments: | This prime has 1 user comment below. |
| Proof-code(s): (*): | p170 : Wu_T, Primo, OpenPFGW |
| Decimal Digits: | 42480 (log10 is 42479.164206239) |
| Rank (*): | 64340 (digit rank is 1) |
| Entrance Rank (*): | 55393 |
| Currently on list? (*): | no |
| Submitted: | 3/31/2019 07:32:54 UTC |
| Last modified: | 11/22/2024 08:57:21 UTC |
| Database id: | 126349 |
| Status Flags: | none |
| Score (*): | 36.9139 (normalized score 0.0002) |
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.
- Generalized Repunit (archivable *)
- Prime on list: no, rank 24
Subcategory: "Generalized Repunit"
(archival tag id 220195, tag last modified 2024-09-26 03:37:11)
User comments about this prime (disclaimer):
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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 126349 person_id 9 machine Using: Digital Ocean Droplet what prime notes Command: /var/www/clientpool/1/pfgw64 -V -f -tc -hhelper.php?id=1100000002625632457 -q"(36210^9319-1)/36209" >command_output 2>&1
PFGW Version 4.0.4.64BIT.20221214.x86_Dev [GWNUM 30.11]
Primality testing (36210^9319-1)/36209 [N-1/N+1, Brillhart-Lehmer-Selfridge]
Reading factors from helper file helper.php?id=1100000002625632457
trial
Running N-1 test using base 3
Generic modular reduction using generic reduction AVX-512 FFT length 16K on A 141113-bit number
Running N-1 test using base 7
Generic modular reduction using generic reduction AVX-512 FFT length 16K on A 141113-bit number
Running N-1 test using base 13
Generic modular reduction using generic reduction AVX-512 FFT length 16K on A 141113-bit number
Running N+1 test using discriminant 23, base 1+sqrt(23)
Generic modular reduction using generic reduction AVX-512 FFT length 16K on A 141113-bit number
Calling N-1 BLS with factored part 33.57% and helper 0.04% (100.76% proof)
(36210^9319-1)/36209 is prime! (156.0094s+0.0003s)
[Elapsed time: 2.67 minutes]
Helper File:
2
3
5
7
17
67
71
103
313
607
739
9319
18637
37273
35911573
1311200311
24252955627
198009971972221
67770901181293339
91969861895144749
31640705868513151084394123
11714213685209663970470826487376356...(14130 digits)...01539769164696062603118891495550143
179
15971
47236266937modified 2024-11-22 08:57:21 created 2024-11-22 08:54:41 id 184628
field value prime_id 126349 person_id 9 machine Using: Xeon (pool) 4c+4c 3.5GHz what prp notes Command: /home/caldwell/clientpool/1/pfgw64 -tc -q"(36210^9319-1)/36209" 2>&1 PFGW Version 3.7.7.64BIT.20130722.x86_Dev [GWNUM 27.11] Primality testing (36210^9319-1)/36209 [N-1/N+1, Brillhart-Lehmer-Selfridge] Running N-1 test using base 3 Running N-1 test using base 7 Running N-1 test using base 13 Running N+1 test using discriminant 23, base 1+sqrt(23) Calling N-1 BLS with factored part 0.07% and helper 0.02% (0.24% proof) (36210^9319-1)/36209 is Fermat and Lucas PRP! (225.4790s+0.0010s) [Elapsed time: 3.77 minutes] modified 2020-07-07 22:30:13 created 2019-03-31 07:33:01 id 172030
Query times: 0.0002 seconds to select prime, 0.0003 seconds to seek comments.
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