34 (number)
| ||||
|---|---|---|---|---|
| Cardinal | thirty-four | |||
| Ordinal | 34th (thirty-fourth) | |||
| Factorization | 2 × 17 | |||
| Divisors | 1, 2, 17, 34 | |||
| Greek numeral | ΛΔ´ | |||
| Roman numeral | XXXIV | |||
| Binary | 1000102 | |||
| Ternary | 10213 | |||
| Octal | 428 | |||
| Duodecimal | 2A12 | |||
| Hexadecimal | 2216 | |||
34 (thirty-four) is the natural number following 33 and preceding 35.
In mathematics[edit]
34 is the ninth distinct semiprime and has four divisors including one and itself. Its neighbors, 33 and 35, also are distinct semiprimes, having four divisors each, and 34 is the smallest number to be surrounded by numbers with the same number of divisors as it has.
It is the ninth Fibonacci number[1] and a companion Pell number.[2] Since it is an odd-indexed Fibonacci number, 34 is a Markov number,[3] appearing in solutions with other Fibonacci numbers, such as (1, 13, 34), (1, 34, 89), etc.
34 is the magic constant of a 4 by 4 normal magic square:[4]
This number is also the magic constant of n-Queens Problem for n = 4.[5]
34 is a heptagonal number.[6]
There are 34 topologically distinct convex heptahedra, excluding mirror images.[7]
There is no solution to the equation φ(x) = 34, making 34 a nontotient.[8] Nor is there a solution to the equation x − φ(x) = 34, making 34 a noncototient.[9]
It is a Erdős–Woods number.[10]
In science[edit]
- The atomic number of selenium
- Potentially one of the magic numbers in physics.[11][12]
- Messier object M34, a magnitude 6.0 open cluster in the constellation Perseus
- The New General Catalogue object NGC 34, a peculiar galaxy in the constellation Cetus
Literature[edit]
- In The Count of Monte Cristo, Number 34 is how Edmond Dantès is referred to during his imprisonment in the Château d'If.
Transportation[edit]
- 34th Street (Manhattan), a major cross-town street in New York City
- 34th Street (New York City Subway), multiple New York City subway stations
In other fields[edit]
34 is also:
- The traffic code of Istanbul, Turkey
- "#34", a song by the Dave Matthews Band
- The number of the French department Hérault
- +34 is the code for international direct-dial phone calls to Spain
See also[edit]
References[edit]
- ^ "Sloane's A000045 : Fibonacci numbers". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 2016-05-31.
- ^ "Sloane's A002203 : Companion Pell numbers". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 2016-05-31.
- ^ Weisstein, Eric W. "Markov Number". mathworld.wolfram.com. Retrieved 2020-08-21.
- ^ Higgins, Peter (2008). Number Story: From Counting to Cryptography. New York: Copernicus. p. 53. ISBN 978-1-84800-000-1.
- ^ Sloane, N. J. A. (ed.). "Sequence A006003". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
- ^ "Sloane's A000566 : Heptagonal numbers". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 2016-05-31.
- ^ "Counting polyhedra". Numericana. Retrieved 2022-04-20.
- ^ "Sloane's A005277 : Nontotients". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 2016-05-31.
- ^ "Sloane's A005278 : Noncototients". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 2016-05-31.
- ^ "Sloane's A059756 : Erdős–Woods numbers". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 2020-12-04.
- ^ "Evidence for a new nuclear 'magic number'" (Press release). Saitama, Japan: Riken. 2013-10-10. Retrieved 2013-10-14.
- ^ Steppenbeck, D.; Takeuchi, S.; Aoi, N.; et al. (2013-10-10). "Evidence for a new nuclear 'magic number' from the level structure of 54Ca". Nature. 502 (7470): 207–210. Bibcode:2013Natur.502..207S. doi:10.1038/nature12522. PMID 24108051. S2CID 205235415.
External links[edit]
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Wikimedia Commons has media related to 34 (number). |
- Prime Curios! 34 from the Prime Pages