15 · 21276177 + 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: | 15 · 21276177 + 1 |
|---|---|
| Verification status (*): | Proven |
| Official Comment (*): | Divides GF(1276174,3), GF(1276174,10) |
| Unofficial Comments: | This prime has 1 user comment below. |
| Proof-code(s): (*): | g279 : Cooper, NewPGen, PRP, Proth.exe |
| Decimal Digits: | 384169 (log10 is 384168.73286773) |
| Rank (*): | 18647 (digit rank is 1) |
| Entrance Rank (*): | 71 |
| Currently on list? (*): | yes |
| Submitted: | 2/15/2006 09:28:29 UTC |
| Last modified: | 3/11/2023 15:54:10 UTC |
| Database id: | 77070 |
| Status Flags: | none |
| Score (*): | 43.6954 (normalized score 0.2388) |
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 Fermat Divisors (bases 3,5,6,10,12) (archivable *)
- Prime on list: yes, rank 19, weight 46.403534196924
Subcategory: "Divides GF(*,10)"
(archival tag id 187081, tag last modified 2023-07-02 21:37:20)- Generalized Fermat Divisors (bases 3,5,6,10,12) (archivable *)
- Prime on list: no, rank 26, weight 46.403534196924
Subcategory: "Divides GF(*,3)"
(archival tag id 187080, tag last modified 2024-03-22 08:37:11)
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 77070 person_id 9 machine Linux P4 2.8GHz what trial_divided notes Command: /home/caldwell/client/TrialDiv/TrialDiv -q 15 2 1276177 1 2>&1 [Elapsed time: 13.880 seconds] modified 2020-07-07 22:30:42 created 2006-02-15 09:52:00 id 83132
field value prime_id 77070 person_id 9 machine Linux P4 2.8GHz what prime notes Command: /home/caldwell/client/pfgw -t -q"15*2^1276177+1" 2>&1 PFGW Version 20031027.x86_Dev (Beta 'caveat utilitor') [FFT v22.13 w/P4] Primality testing 15*2^1276177+1 [N-1, Brillhart-Lehmer-Selfridge] Running N-1 test using base 7 Using SSE2 FFT Adjusting authentication level by 1 for PRIMALITY PROOF Reduced from FFT(163840,20) to FFT(163840,19) Reduced from FFT(163840,19) to FFT(163840,18) Reduced from FFT(163840,18) to FFT(163840,17) Reduced from FFT(163840,17) to FFT(163840,16) 2552370 bit request FFT size=(163840,16) Calling Brillhart-Lehmer-Selfridge with factored part 100.00% 15*2^1276177+1 is prime! (27312.9832s+0.0352s) [Elapsed time: 27313 seconds] modified 2020-07-07 22:30:42 created 2006-02-15 09:53:01 id 83133
Query times: 0.0002 seconds to select prime, 0.0003 seconds to seek comments.
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