954589277 · (2332267 - 2110758) + 2221511 - 3
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: | 954589277 · (2332267 - 2110758) + 2221511 - 3 |
|---|---|
| Verification status (*): | Proven |
| Official Comment (*): | Consecutive primes arithmetic progression (1,d=4) |
| Unofficial Comments: | This prime has 1 user comment below. |
| Proof-code(s): (*): | p408 : Batalov, PolySieve, OpenPFGW |
| Decimal Digits: | 100032 (log10 is 100031.31338584) |
| Rank (*): | 54110 (digit rank is 2) |
| Entrance Rank (*): | 54090 |
| Currently on list? (*): | yes |
| Submitted: | 4/21/2025 01:48:28 UTC |
| Last modified: | 4/21/2025 03:37:10 UTC |
| Database id: | 140616 |
| Status Flags: | none |
| Score (*): | 39.5552 (normalized score 0.0027) |
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: yes, rank 1
Subcategory: "1/2"
(archival tag id 239277, tag last modified 2025-04-21 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 140616 person_id 9 machine Using: Digital Ocean Droplet what prime notes Command: /var/www/clientpool/1/pfgw64 -V -f -t -hhelper140614.txt -q"954589277*(2^332267-2^110758)+2^221511-3" >command_output 2>&1
PFGW Version 4.0.4.64BIT.20221214.x86_Dev [GWNUM 30.11]
Primality testing 954589277*(2^332267-2^110758)+2^221511-3 [N-1, Brillhart-Lehmer-Selfridge]
Reading factors from helper file helper140614.txt
trial
Running N-1 test using base 2
Generic modular reduction using generic reduction AVX-512 FFT length 32K on A 332299-bit number
Calling Brillhart-Lehmer-Selfridge with factored part 66.65%
954589277*(2^332267-2^110758)+2^221511-3 is prime! (151.4487s+0.0004s)
[Elapsed time: 2.58 minutes]
Helper File:
(2^221509-1)/292391881modified 2025-04-21 03:14:37 created 2025-04-21 03:12:02 id 186707
field value prime_id 140616 person_id 9 machine Using: Digital Ocean Droplet what prp notes Command: /var/www/clientpool/1/pfgw64 -V -f -tc -q"954589277*(2^332267-2^110758)+2^221511-3" >command_output 2>&1
PFGW Version 4.0.4.64BIT.20221214.x86_Dev [GWNUM 30.11]
Primality testing 954589277*(2^332267-2^110758)+2^221511-3 [N-1/N+1, Brillhart-Lehmer-Selfridge]
trial
Running N-1 test using base 2
Generic modular reduction using generic reduction FMA3 FFT length 32K, Pass1=512, Pass2=64, clm=2 on A 332299-bit number
Running N+1 test using discriminant 5, base 5+sqrt(5)
Generic modular reduction using generic reduction FMA3 FFT length 32K, Pass1=512, Pass2=64, clm=2 on A 332299-bit number
Detected in MAXERR>0.45 (round off check) in Exponentiator::Iterate
Iteration: 1072/332298 ERROR: ROUND OFF 0.5>0.45
(Test aborted, try again using the -a1 switch)
Running N+1 test using discriminant 5, base 5+sqrt(5)
Generic modular reduction using generic reduction FMA3 FFT length 36K, Pass1=768, Pass2=48, clm=2 on A 332299-bit number
Calling N-1 BLS with factored part 0.01% and helper 0.00% (0.03% proof)
954589277*(2^332267-2^110758)+2^221511-3 is Fermat and Lucas PRP! (561.1339s+0.0006s)
[Elapsed time: 9.42 minutes]modified 2025-04-21 03:01:54 created 2025-04-21 02:52:29 id 186706
Query times: 0.0002 seconds to select prime, 0.0003 seconds to seek comments.
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