(78866031017 · (2166678 - 1) - 4) · 283339 - 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: | (78866031017 · (2166678 - 1) - 4) · 283339 - 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: | 75274 (log10 is 75273.513315907) |
| Rank (*): | 54995 (digit rank is 2) |
| Entrance Rank (*): | 54977 |
| Currently on list? (*): | yes |
| Submitted: | 11/25/2024 06:25:14 UTC |
| Last modified: | 11/25/2024 07:48:24 UTC |
| Database id: | 138735 |
| Status Flags: | none |
| Score (*): | 38.6788 (normalized score 0.0015) |
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: "Consecutive primes in arithmetic progression (1,d=*)"
(archival tag id 229765, tag last modified 2024-11-25 06:37:12)
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 138735 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 (78866031017*(2^166678-1)-4)*2^83339-3 [N-1/N+1, Brillhart-Lehmer-Selfridge]
Reading factors from helper file helper_file_id_138735
trial
Running N-1 test using base 2
Generic modular reduction using generic reduction AVX-512 FFT length 24K on A 250055-bit number
Running N-1 test using base 5
Generic modular reduction using generic reduction AVX-512 FFT length 24K on A 250055-bit number
Running N-1 test using base 11
Generic modular reduction using generic reduction AVX-512 FFT length 24K on A 250055-bit number
Running N+1 test using discriminant 23, base 3+sqrt(23)
Generic modular reduction using generic reduction AVX-512 FFT length 24K on A 250055-bit number
Detected in MAXERR>0.45 (round off check) in Exponentiator::Iterate
Iteration: 60/250073 ERROR: ROUND OFF 0.45173>0.45
(Test aborted, try again using the -a1 switch)
Running N+1 test using discriminant 23, base 3+sqrt(23)
Generic modular reduction using generic reduction AVX-512 FFT length 25K on A 250055-bit number
Calling N-1 BLS with factored part 33.33% and helper 0.00% (100.01% proof)
(78866031017*(2^166678-1)-4)*2^83339-3 is prime! (420.9678s+0.0009s)
[Elapsed time: 7.08 minutes]
Helper file contains: "(2^83339 + 1)/3"modified 2024-11-25 07:48:24 created 2024-11-25 07:41:19 id 184771
field value prime_id 138735 person_id 9 machine Using: Digital Ocean Droplet what prp notes Command: /var/www/clientpool/1/pfgw64 -V -f -tc -q"(78866031017*(2^166678-1)-4)*2^83339-3" >command_output 2>&1
PFGW Version 4.0.4.64BIT.20221214.x86_Dev [GWNUM 30.11]
Primality testing (78866031017*(2^166678-1)-4)*2^83339-3 [N-1/N+1, Brillhart-Lehmer-Selfridge]
trial
Running N-1 test using base 2
Generic modular reduction using generic reduction AVX-512 FFT length 24K on A 250055-bit number
Running N-1 test using base 5
Generic modular reduction using generic reduction AVX-512 FFT length 24K on A 250055-bit number
Running N-1 test using base 11
Generic modular reduction using generic reduction AVX-512 FFT length 24K on A 250055-bit number
Running N+1 test using discriminant 23, base 3+sqrt(23)
Generic modular reduction using generic reduction AVX-512 FFT length 24K on A 250055-bit number
Detected in MAXERR>0.45 (round off check) in Exponentiator::Iterate
Iteration: 60/250073 ERROR: ROUND OFF 0.45173>0.45
(Test aborted, try again using the -a1 switch)
Running N+1 test using discriminant 23, base 3+sqrt(23)
Generic modular reduction using generic reduction AVX-512 FFT length 25K on A 250055-bit number
Calling N-1 BLS with factored part 0.01% and helper 0.00% (0.02% proof)
(78866031017*(2^166678-1)-4)*2^83339-3 is Fermat and Lucas PRP! (408.1396s+0.0018s)
[Elapsed time: 6.85 minutes]modified 2024-11-25 06:34:12 created 2024-11-25 06:27:21 id 184762
Query times: 0.0002 seconds to select prime, 0.0036 seconds to seek comments.
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