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34 (number)

From Wikipedia, the free encyclopedia

34 (thirty-four) is the natural number following 33 and preceding 35.


Cardinal 34
thirty-four
Ordinal 34th
thirty-fourth
Factorization 2\cdot 17
Divisors 1, 2, 17, 34
Roman numeral XXXIV
Binary 100010
Hexadecimal 22

Contents

[edit] In mathematics

34 is a distinct biprime , the ninth in fact, and has four divisors including unity and itself. Its neighbors, 33 and 35 also are distinct biprimes 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 biprime , being within; 33,34,35, the next such cluster of Bi-Primes 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:

This number is also the magic constant of n-Queens Problem for n = 4.

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.

It is the sum of the first five factorials.

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

[edit] In science

[edit] Astronomy

  • The Saros number of the lunar eclipse series which began on -1633 May 2 and ended on -335 June 19. The duration of Saros series 34 was 1298.1 years, and it contained 73 lunar eclipses.

[edit] In other fields

34 is also:

[edit] Historical years

34 A.D., 34 B.C., 1934, 2034, etc. number 34 haunts little kids

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