732050 · 64392301 + 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: | 732050 · 64392301 + 1 |
|---|---|
| Verification status (*): | Proven |
| Official Comment (*): | Generalized Cullen |
| Unofficial Comments: | This prime has 1 user comment below. |
| Proof-code(s): (*): | L5765 : Propper, Gcwsieve, LLR |
| Decimal Digits: | 3417881 (log10 is 3417880.3797521) |
| Rank (*): | 104 (digit rank is 1) |
| Entrance Rank (*): | 89 |
| Currently on list? (*): | short |
| Submitted: | 9/9/2023 13:11:39 UTC |
| Last modified: | 9/14/2023 05:37:17 UTC |
| Database id: | 136426 |
| Status Flags: | none |
| Score (*): | 50.4006 (normalized score 224.7982) |
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 Cullen (archivable *)
- Prime on list: yes, rank 7
Subcategory: "Generalized Cullen"
(archival tag id 228813, tag last modified 2023-12-29 19:37:13)
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 136426 person_id 9 machine Using: Digital Ocean Droplet what prime notes Command: /var/www/clientpool/1/pfgw64 -V -f -t -q"732050*6^4392301+1" >command_output 2>&1
PFGW Version 4.0.4.64BIT.20221214.x86_Dev [GWNUM 30.11]
Primality testing 732050*6^4392301+1 [N-1, Brillhart-Lehmer-Selfridge]
trial
Running N-1 test using base 17
Special modular reduction using zero-padded AVX-512 FFT length 1280K, Pass1=128, Pass2=10K, clm=2 on 732050*6^4392301+1
Detected in MAXERR>0.45 (round off check) in Exponentiator::Iterate
Iteration: 11353952/11353954 ERROR: ROUND OFF 0.49748>0.45
(Test aborted, try again using the -a1 switch)
Running N-1 test using base 23
Special modular reduction using zero-padded AVX-512 FFT length 1344K, Pass1=192, Pass2=7K, clm=4 on 732050*6^4392301+1
Running N-1 test using base 37
Special modular reduction using zero-padded AVX-512 FFT length 1280K, Pass1=128, Pass2=10K, clm=2 on 732050*6^4392301+1
Running N-1 test using base 71
Special modular reduction using zero-padded AVX-512 FFT length 1280K, Pass1=128, Pass2=10K, clm=2 on 732050*6^4392301+1
Detected in MAXERR>0.45 (round off check) in Exponentiator::Iterate
Iteration: 11353952/11353954 ERROR: ROUND OFF 0.49748>0.45
(Test aborted, try again using the -a1 switch)
Running N-1 test using base 79
Special modular reduction using zero-padded AVX-512 FFT length 1344K, Pass1=192, Pass2=7K, clm=4 on 732050*6^4392301+1
Calling Brillhart-Lehmer-Selfridge with factored part 61.31%
732050*6^4392301+1 is prime! (401675.6935s+0.0287s)
[Elapsed time: 4.65 days]modified 2023-09-14 04:46:40 created 2023-09-09 13:12:01 id 182258
Query times: 0.0003 seconds to select prime, 0.0004 seconds to seek comments.
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