(21666 + 2834 - 1)2 + 12769 · 21668
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: | (21666 + 2834 - 1)2 + 12769 · 21668 |
|---|---|
| Verification status (*): | Proven |
| Official Comment (*): | [none] |
| Proof-code(s): (*): | SU : Suyama |
| Decimal Digits: | 1004 (log10 is 1003.0319455524) |
| Rank (*): | 133182 (digit rank is 195) |
| Entrance Rank (*): | 900 |
| Currently on list? (*): | no |
| Submitted: | 1989 |
| Last modified: | 11/19/2024 13:39:17 UTC |
| Removed (*): | 1993 |
| Database id: | 58682 |
| Status Flags: | none |
| Score (*): | 25.2814 (normalized score 0) |
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 58682 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 (2^1666+2^834-1)^2+12769*2^1668 [N-1/N+1, Brillhart-Lehmer-Selfridge]
Reading factors from helper file helper.php?id=1100000007609479626
trial
Running N-1 test using base 3
Generic modular reduction using generic reduction AVX-512 FFT length 1K on A 3334-bit number
Running N-1 test using base 5
Generic modular reduction using generic reduction AVX-512 FFT length 1K on A 3334-bit number
Running N+1 test using discriminant 13, base 1+sqrt(13)
Generic modular reduction using generic reduction AVX-512 FFT length 1K on A 3334-bit number
Calling N-1 BLS with factored part 100.00% and helper 0.54% (300.54% proof)
(2^1666+2^834-1)^2+12769*2^1668 is prime! (0.1403s+0.0007s)
[Elapsed time: 5.00 seconds]
Helper File:
2
2176639
21583047502066328160260062588030588...(746 digits)...64403049439524523894062530065823361
3
68053modified 2024-11-19 13:39:17 created 2024-11-19 13:39:12 id 184580
field value prime_id 58682 person_id 9 machine Linux PII 200 what prp notes PFGW Version 20020311.x86_Dev (Alpha software, 'caveat utilitor') Running N-1 test using base 3 Primality testing (2^1666+2^834-1)^2+12769*2^1668 [N-1/N+1, Brillhart-Lehmer-Selfridge] Running N+1 test using discriminant 7, base 1+sqrt(7) Running N+1 test using discriminant 7, base 2+sqrt(7) Calling N-1 BLS with factored part 25.06% and helper 0.54% (75.72% proof) (2^1666+2^834-1)^2+12769*2^1668 is Fermat and Lucas PRP! (14.220000 seconds) modified 2003-03-25 17:23:05 created 2003-01-04 05:22:33 id 60379
Query times: 0.0002 seconds to select prime, 0.0003 seconds to seek comments.
Printed from the PrimePages <t5k.org> © Reginald McLean.