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

In mathematics

34 has four divisors. Its neighbors, 33 and 35 also have 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 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 magic square:

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

Thirty-four is a heptagonal number.

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.

In science

• The atomic number of selenium

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.

In other fields

• 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 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 lucky number of Victor Pelevin's protagonist Stepan Mikhailov in the novel "Numbers", published as part of DTT(NN) in Times of Transition (from Nowhere into Nothing)

Historical years

Integers

Treinta y cuatro | Tridek kvar | 34 (nombre) | 34 | 34 | Trentaquattro | 34 (skaičius) | 34 (getal) | 34 | Trentaquàtte | 34 (tall) | 34 (liczba) | Trinta e quatro | 34 (число) | 34 (število) | 34 (tal) | 34 | 34