natural number
In mathematics, the natural numbers are those numbers used for counting (as in "there are ''six'' coins on the table") and ordering (as in "this is the ''third'' largest city in the country").
Numbers used for counting are called ''Cardinal n ...
semiprime
In mathematics, a semiprime is a natural number that is the product of exactly two prime numbers. The two primes in the product may equal each other, so the semiprimes include the squares of prime numbers.
Because there are infinitely many prime nu ...
and has four
divisor
In mathematics, a divisor of an integer n, also called a factor of n, is an integer m that may be multiplied by some integer to produce n. In this case, one also says that n is a multiple of m. An integer n is divisible or evenly divisible by ...
s 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
In mathematics, the Fibonacci numbers, commonly denoted , form a sequence, the Fibonacci sequence, in which each number is the sum of the two preceding ones. The sequence commonly starts from 0 and 1, although some authors start the sequence from ...
and a companion
Pell number
In mathematics, the Pell numbers are an infinite sequence of integers, known since ancient times, that comprise the denominators of the closest rational approximations to the square root of 2. This sequence of approximations begins , , , , an ...
. Since it is an odd-indexed Fibonacci number, 34 is a
Markov number
A Markov number or Markoff number is a positive integer ''x'', ''y'' or ''z'' that is part of a solution to the Markov Diophantine equation
:x^2 + y^2 + z^2 = 3xyz,\,
studied by .
The first few Markov numbers are
: 1, 2, 5, 13, 29, 34, 89 ...
, 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
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
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 A heptagonal number is a figurate number that is constructed by combining heptagons with ascending size. The ''n''-th heptagonal number is given by the formula
:H_n=\frac.
The first few heptagonal numbers are:
: 0, 1, 7, 18, 34, 55, 81, 112 ...
nontotient
In number theory, a nontotient is a positive integer ''n'' which is not a totient number: it is not in the range of Euler's totient function φ, that is, the equation φ(''x'') = ''n'' has no solution ''x''. In other words, ''n'' is a nontotient ...
. Nor is there a solution to the equation ''x'' − φ(''x'') = 34, making 34 a
noncototient In mathematics, a noncototient is a positive integer ''n'' that cannot be expressed as the difference between a positive integer ''m'' and the number of coprime integers below it. That is, ''m'' − φ(''m'') = ''n'', where ...
.
It is an
Erdős–Woods number In number theory, a positive integer is said to be an Erdős–Woods number if it has the following property:
there exists a positive integer such that in the sequence of consecutive integers, each of the elements has a non-trivial common factor ...
.
In science
*The
atomic number
The atomic number or nuclear charge number (symbol ''Z'') of a chemical element is the charge number of an atomic nucleus. For ordinary nuclei, this is equal to the proton number (''n''p) or the number of protons found in the nucleus of every ...
of
selenium
Selenium is a chemical element with the symbol Se and atomic number 34. It is a nonmetal (more rarely considered a metalloid) with properties that are intermediate between the elements above and below in the periodic table, sulfur and tellurium, ...
Messier object
The Messier objects are a set of 110 astronomical objects catalogued by the French astronomer Charles Messier in his ''Catalogue des Nébuleuses et des Amas d'Étoiles'' (''Catalogue of Nebulae and Star Clusters'').
Because Messier was only int ...
magnitude
Magnitude may refer to:
Mathematics
*Euclidean vector, a quantity defined by both its magnitude and its direction
*Magnitude (mathematics), the relative size of an object
*Norm (mathematics), a term for the size or length of a vector
*Order of ...
6.0
open cluster
An open cluster is a type of star cluster made of up to a few thousand stars that were formed from the same giant molecular cloud and have roughly the same age. More than 1,100 open clusters have been discovered within the Milky Way galaxy, and ...
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 ...
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
A peculiar galaxy is a galaxy of unusual size, shape, or composition. Between five and ten percent of known galaxies are categorized as peculiar. Astronomers have identified two types of peculiar galaxies: ''interacting galaxies'' and ''active ga ...
in the constellation
Cetus
Cetus () is a constellation, sometimes called 'the whale' in English. The Cetus (mythology), Cetus was a sea monster in Greek mythology which both Perseus and Heracles needed to slay. Cetus is in the region of the sky that contains other water- ...
*The
vertebral column
The vertebral column, also known as the backbone or spine, is part of the axial skeleton. The vertebral column is the defining characteristic of a vertebrate in which the notochord (a flexible rod of uniform composition) found in all chordata, ...
is made up of up to 34
vertebrae
The spinal column, a defining synapomorphy shared by nearly all vertebrates,Hagfish are believed to have secondarily lost their spinal column is a moderately flexible series of vertebrae (singular vertebra), each constituting a characteristic i ...
.
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 ...
.
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 ...
Istanbul
Istanbul ( , ; tr, İstanbul ), formerly known as Constantinople ( grc-gre, Κωνσταντινούπολις; la, Constantinopolis), is the List of largest cities and towns in Turkey, largest city in Turkey, serving as the country's economic, ...
,
Turkey
Turkey ( tr, Türkiye ), officially the Republic of Türkiye ( tr, Türkiye Cumhuriyeti, links=no ), is a list of transcontinental countries, transcontinental country located mainly on the Anatolia, Anatolian Peninsula in Western Asia, with ...
Dave Matthews Band
Dave Matthews Band (also known by the initials DMB) is an American rock band formed in Charlottesville, Virginia, in 1991. The band's founding members were singer-songwriter and guitarist Dave Matthews, bassist Stefan Lessard, drummer and bac ...
*The number of the French department
Hérault
Hérault (; oc, Erau, ) is a department of the region of Occitania, Southern France. Named after the Hérault River, its prefecture is Montpellier. It had a population of 1,175,623 in 2019.+34 is the code for international direct-dial phone calls to
Spain
, image_flag = Bandera de España.svg
, image_coat = Escudo de España (mazonado).svg
, national_motto = ''Plus ultra'' (Latin)(English: "Further Beyond")
, national_anthem = (English: "Royal March")
, i ...
See also
*
Rule 34
Rule 34 is an Internet meme which claims that Internet pornography exists concerning every conceivable topic. The concept is commonly depicted as fan art of normally non-erotic subjects engaging in sexual behavior. It can also include writing ...
Prime Pages The PrimePages is a website about prime numbers maintained by Chris Caldwell at the University of Tennessee at Martin.
The site maintains the list of the "5,000 largest known primes", selected smaller primes of special forms, and many "top twenty" ...