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

In mathematics

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 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. 34 is the

magic constant The magic constant or magic sum of a magic square is the sum of numbers in any row, column, or diagonal of the magic square. For example, the magic square shown below has a magic constant of 15. For a normal magic square of order ''n'' – that is ...

of a 4 by 4 normal

magic square In recreational mathematics, a square array of numbers, usually positive integers, is called a magic square if the sums of the numbers in each row, each column, and both main diagonals are the same. The 'order' of the magic square is the number ...

: This number is also the

n-Queens Problem The eight queens puzzle is the problem of placing eight chess queens on an 8×8 chessboard so that no two queens threaten each other; thus, a solution requires that no two queens share the same row, column, or diagonal. There are 92 solutions. ...

for n = 4. 34 is a heptagonal number. There are 34 topologically distinct convex heptahedra, excluding mirror images. 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. It is an Erdős–Woods number.

In science

*The atomic number of selenium *Potentially one of the magic numbers in physics. * Messier object M34, a magnitude 6.0 open cluster in the

constellation A constellation is an area on the celestial sphere in which a group of visible stars forms Asterism (astronomy), a perceived pattern or outline, typically representing an animal, mythological subject, or inanimate object. The origins of the e ...

Perseus In Greek mythology, Perseus (Help:IPA/English, /ˈpɜːrsiəs, -sjuːs/; Greek language, Greek: Περσεύς, Romanization of Greek, translit. Perseús) is the legendary founder of Mycenae and of the Perseid dynasty. He was, alongside Cadmus ...

*The

New General Catalogue The ''New General Catalogue of Nebulae and Clusters of Stars'' (abbreviated NGC) is an astronomical catalogue of deep-sky objects compiled by John Louis Emil Dreyer in 1888. The NGC contains 7,840 objects, including galaxies, star clusters and ...

br>object

NGC 34 NGC 17, also known as NGC 34, is a spiral galaxy in the constellation Cetus. It is the result of a merger between two disk galaxies, resulting in a recent starburst in the central regions and continuing starforming activity. The galaxy is sti ...

, a peculiar galaxy in the constellation Cetus *The vertebral column is made up of up to 34 vertebrae.

Literature

* In ''

The Count of Monte Cristo ''The Count of Monte Cristo'' (french: Le Comte de Monte-Cristo) is an adventure novel written by French author Alexandre Dumas (''père'') completed in 1844. It is one of the author's more popular works, along with ''The Three Musketeers''. Li ...

'', Number 34 is how

Edmond Dantès Edmond Dantès () is a title character and the protagonist of Alexandre Dumas's 1844 adventure novel ''The Count of Monte Cristo''. Within the story's narrative, Dantès is an intelligent, honest and loving man who turns bitter and vengeful after ...

is referred to during his imprisonment in the

Château d'If The Château d'If () is a fortress located on the Île d'If, the smallest island in the Frioul archipelago, situated about offshore from Marseille in southeastern France. Built in the 16th century, it later served as a prison until the end o ...

Transportation

34th Street (Manhattan) 34th Street is a major crosstown street in the New York City borough of Manhattan. It runs the width of Manhattan Island from West Side Highway on the West Side to the FDR Drive on the East Side. 34th Street is used as a crosstown artery betwee ...

, a major cross-town street in New York City * 34th Street (New York City Subway), multiple New York City subway stations

In other fields

34 is also: *The traffic code of Istanbul, Turkey * " #34", a song by the Dave Matthews Band *The number of the French department Hérault * +34 is the code for international direct-dial phone calls to Spain

References

External links

Prime Curios! 34
from the Prime Pages {{Integers, zero Integers