(2216091 - 1) · (104950 - 15183422626) - 1
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: | (2216091 - 1) · (104950 - 15183422626) - 1 |
|---|---|
| Verification status (*): | Proven |
| Official Comment (*): | Twin (p) |
| Unofficial Comments: | This prime has 1 user comment below. |
| Proof-code(s): (*): | p449 : Rodriguez2, OpenPFGW |
| Decimal Digits: | 70000 (log10 is 69999.872793025) |
| Rank (*): | 57799 (digit rank is 2) |
| Entrance Rank (*): | 57789 |
| Currently on list? (*): | yes |
| Submitted: | 7/11/2025 06:17:47 UTC |
| Last modified: | 7/11/2025 12:37:13 UTC |
| Database id: | 140931 |
| Status Flags: | none |
| Score (*): | 38.4549 (normalized score 0.0008) |
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.
- Twin Primes (archivable *)
- Prime on list: yes, rank 20
Subcategory: "Twin (p)"
(archival tag id 239418, tag last modified 2025-07-11 12:37:13)
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 140931 person_id 9 machine Using: Digital Ocean Droplet what prime notes Command: /var/www/clientpool/1/pfgw64 -V -f -tp -hhelper_mersenne -q"(2^216091-1)*(10^4950-15183422626)-1" >command_output 2>&1
PFGW Version 4.0.4.64BIT.20221214.x86_Dev [GWNUM 30.11]
Primality testing (2^216091-1)*(10^4950-15183422626)-1 [N+1, Brillhart-Lehmer-Selfridge]
Reading factors from helper file helper_mersenne
trial
Running N+1 test using discriminant 3, base 3+sqrt(3)
Generic modular reduction using generic reduction AVX-512 FFT length 24K on A 232537-bit number
Calling Brillhart-Lehmer-Selfridge with factored part 92.93%
(2^216091-1)*(10^4950-15183422626)-1 is prime! (352.9324s+0.0013s)
[Elapsed time: 5.92 minutes]
Helper File:
2^216091-1modified 2025-07-11 11:51:07 created 2025-07-11 11:45:12 id 187017
Query times: 0.0003 seconds to select prime, 0.0005 seconds to seek comments.
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