34 (number)

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33 34 35
Cardinal thirty-four
Ordinal 34th
(thirty-fourth)
Factorization 2 · 17
Divisors 1, 2, 17, 34
Roman numeral XXXIV
Binary 1000102
Ternary 10213
Quaternary 2024
Quinary 1145
Senary 546
Octal 428
Duodecimal 2A12
Hexadecimal 2216
Vigesimal 1E20
Base 36 Y36

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 also in the first cluster of three distinct semiprimes, being within 33, 34, 35; the next such cluster of semiprimes is 85, 86, 87.

It is the ninth Fibonacci number and a companion Pell number. Since it is an odd-indexed Fibonacci number, 34 is a Markov number, appearing in solutions with other Fibonacci numbers, such as (1, 13, 34), (1, 34, 89), etc.

This number is the magic constant of a 4 by 4 normal magic square:[1]

MagicSquare-AlbrechtDürer.png

Thirty-four is a heptagonal number.

It has the aliquot sum, 20, in the following descending sequence 34,20,22,14,10,8,7,1. and it is the 6th composite member of the 7-aliquot tree.

There is no solution to the equation φ(x) = 34, making 34 a nontotient. Nor is there a solution to the equation x - φ(x) = 34, making 34 a noncototient.

In science[edit]

In sports[edit]

Transportation[edit]

In other fields[edit]

34 is also:

See also[edit]

Rule 34 (Internet meme)

References[edit]

  1. ^ Higgins, Peter (2008). Number Story: From Counting to Cryptography. New York: Copernicus. p. 53. ISBN 978-1-84800-000-1. 
  2. ^ "Evidence for a new nuclear ‘magic number’" (Press release). Saitama, Japan: Riken. 2013-10-10. Retrieved 2013-10-14. 
  3. ^ 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: 207–210. doi:10.1038/nature12522. Retrieved 2013-10-14. 

External links[edit]