34 (number)

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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
- 2.1 Astronomy
3 In other fields
4 Historical years

[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

The atomic number of selenium

[edit] Astronomy

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:

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
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.
A "rule" about the Internet that states: "If it exists, there is porn of it. No exceptions."
The jersey number of a number of popular and important sports stars. "34" is sometimes seen as a "lucky number" in sports:
- The jersey number of Calgary Flames' Miikka Kiprusoff
- The jersey number of former Houston Rockets legend Hakeem Olajuwon
- The jersey number of former Chicago Bears football player Walter Payton, former Buffalo Bills football player Thurman Thomas, and former Houston Oilers football player Earl Campbell
- The jersey number of Minnesota Twins legend Kirby Puckett
- The jersey number of former baseball pitcher Nolan Ryan
- The jersey number of former baseball pitcher Fernando Valenzuela
- The jersey number of NBA star Paul Pierce
Kevin Lepage's Nextel Cup number for Front Row Motorsports