11922002779 · (2172486 - 286243) + 286245 - 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: | 11922002779 · (2172486 - 286243) + 286245 - 5 |
|---|---|
| Verification status (*): | Proven |
| Official Comment (*): | Consecutive primes arithmetic progression (1,d=6) |
| Unofficial Comments: | This prime has 1 user comment below. |
| Proof-code(s): (*): | p408 : Batalov, PolySieve, OpenPFGW |
| Decimal Digits: | 51934 (log10 is 51933.536181316) |
| Rank (*): | 63146 (digit rank is 4) |
| Entrance Rank (*): | 56531 |
| Currently on list? (*): | no |
| Submitted: | 5/3/2022 23:51:31 UTC |
| Last modified: | 11/5/2024 08:14:19 UTC |
| Database id: | 133896 |
| Status Flags: | none |
| Score (*): | 37.5341 (normalized score 0.0003) |
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.
- Consecutive Primes in Arithmetic Progression (archivable class *)
- Prime on list: no, rank 13
Subcategory: "1/2"
(archival tag id 238569, tag last modified 2025-05-13 18:37:10)
User comments about this prime (disclaimer):
User comments are allowed to convey mathematical information about this number, how it was proven prime.... See our guidelines and restrictions.
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 133896 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 11922002779*(2^172486-2^86243)+2^86245-5 [N-1/N+1, Brillhart-Lehmer-Selfridge]
Reading factors from helper file helper_file_id_133896
trial
Running N-1 test using base 2
Generic modular reduction using generic reduction AVX-512 FFT length 18K on A 172522-bit number
Running N-1 test using base 7
Generic modular reduction using generic reduction AVX-512 FFT length 18K on A 172522-bit number
Running N+1 test using discriminant 17, base 1+sqrt(17)
Generic modular reduction using generic reduction AVX-512 FFT length 18K on A 172522-bit number
Running N+1 test using discriminant 17, base 2+sqrt(17)
Generic modular reduction using generic reduction AVX-512 FFT length 18K on A 172522-bit number
Calling N+1 BLS with factored part 50.01% and helper 0.02% (150.06% proof)
11922002779*(2^172486-2^86243)+2^86245-5 is prime! (724.1745s+0.0060s)
[Elapsed time: 12.10 minutes]
Helper file contains: "2^86243-1"modified 2024-11-05 08:14:19 created 2024-11-05 08:02:13 id 184539
field value prime_id 133896 person_id 9 machine Using: Dual Intel Xeon Gold 5222 CPUs 3.8GHz what prp notes Command: /home/caldwell/clientpool/1/pfgw64 -tc -q"11922002779*(2^172486-2^86243)+2^86245-5" 2>&1 PFGW Version 4.0.1.64BIT.20191203.x86_Dev [GWNUM 29.8] Primality testing 11922002779*(2^172486-2^86243)+2^86245-5 [N-1/N+1, Brillhart-Lehmer-Selfridge] Running N-1 test using base 2 Running N-1 test using base 7 Running N+1 test using discriminant 17, base 1+sqrt(17) Calling N+1 BLS with factored part 0.02% and helper 0.02% (0.09% proof) 11922002779*(2^172486-2^86243)+2^86245-5 is Fermat and Lucas PRP! (91.8216s+0.0001s) [Elapsed time: 1.53 minutes] modified 2022-07-11 18:21:44 created 2022-05-03 23:56:01 id 179618
Query times: 0.0002 seconds to select prime, 0.0004 seconds to seek comments.
Printed from the PrimePages <t5k.org> © Reginald McLean.