34 (number)

From Wikipedia, the free encyclopedia

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

← 30 31 32 33 34 35 36 37 38 39 → List of numbers — Integers 0 10 20 30 40 50 60 70 80 90 →
Cardinal	34 thirty-four
Ordinal	34th thirty-fourth
Factorization	$2\cdot 17$
Divisors	1, 2, 17, 34
Roman numeral	XXXIV
Binary	100010
Hexadecimal	22

1 In mathematics
2 In science
3 In other fields
4 Historical years
5 References

[edit] In mathematics

34 is the ninth distinct biprime 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 biprimes 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.

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

The atomic number of selenium
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
The Saros number of the solar eclipse series which began on -1917 August 4 and ended on -384 February 9. The duration of Saros series 34 was 1532.5 years, and it contained 86 solar eclipses.
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:

Secret meaning in Sigma Phi Epsilon Fraternity
The traffic code of Istanbul, Turkey
Kevin Schwantz's race number
"#34," a song by Dave Matthews Band
The magic square puzzle in the 1970s 34 Skidoo
In the title of the 1947 movie Miracle on 34th Street, remade in 1994
The number of the French department Hérault
+34 is the code for international direct-dial phone calls to Spain
The lucky number of Victor Pelevin's protagonist Stepan Mikhailov in the novel "Numbers", published as part of DTT(NN) [Dialectics in Times of Transition (from Nowhere into Nothing)]
In the book The Count of Monte Cristo, 34 is Edmond Dantès prisoner number.
The number previously worn by NBA Hall of Famer Hakeem Olajuwon
The number retired by the Minnesota Twins of the late Kirby Puckett
The number worn by Shaquille O'Neal during his run with the Los Angeles Lakers
The number retired by the Chicago Bears of the late Walter Payton