4 (four) is a
number
A number is a mathematical object used to count, measure, and label. The original examples are the natural numbers 1, 2, 3, 4, and so forth. Numbers can be represented in language with number words. More universally, individual numbers ...
,
numeral
A numeral is a figure, symbol, or group of figures or symbols denoting a number. It may refer to:
* Numeral system used in mathematics
* Numeral (linguistics), a part of speech denoting numbers (e.g. ''one'' and ''first'' in English)
* Numerical d ...
and
digit
Digit may refer to:
Mathematics and science
* Numerical digit, as used in mathematics or computer science
** Hindu-Arabic numerals, the most common modern representation of numerical digits
* Digit (anatomy), the most distal part of a limb, such ...
. It is the
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 ...
following
3 and preceding
5. It is the smallest
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 ...
and
composite number
A composite number is a positive integer that can be formed by multiplying two smaller positive integers. Equivalently, it is a positive integer that has at least one divisor other than 1 and itself. Every positive integer is composite, prime, ...
, and is
considered unlucky in many East Asian cultures.
In mathematics
Four is the smallest
composite number
A composite number is a positive integer that can be formed by multiplying two smaller positive integers. Equivalently, it is a positive integer that has at least one divisor other than 1 and itself. Every positive integer is composite, prime, ...
, its proper
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 being and . Four is the sum and product of
two
2 (two) is a number, numeral and digit. It is the natural number following 1 and preceding 3. It is the smallest and only even prime number. Because it forms the basis of a duality, it has religious and spiritual significance in many culture ...
with itself:
+
=
=
x
, the only number
such that
+
=
=
x
, which also makes four the smallest squared
prime number
A prime number (or a prime) is a natural number greater than 1 that is not a product of two smaller natural numbers. A natural number greater than 1 that is not prime is called a composite number. For example, 5 is prime because the only way ...
. In
Knuth's up-arrow notation
In mathematics, Knuth's up-arrow notation is a method of notation for very large integers, introduced by Donald Knuth in 1976.
In his 1947 paper, R. L. Goodstein introduced the specific sequence of operations that are now called ''hyperoperat ...
, , and so forth, for any number of up arrows. By consequence, four is the only square one more than a prime number, specifically
three
3 is a number, numeral, and glyph.
3, three, or III may also refer to:
* AD 3, the third year of the AD era
* 3 BC, the third year before the AD era
* March, the third month
Books
* ''Three of Them'' (Russian: ', literally, "three"), a 1901 ...
. The sum of the first four prime numbers
two
2 (two) is a number, numeral and digit. It is the natural number following 1 and preceding 3. It is the smallest and only even prime number. Because it forms the basis of a duality, it has religious and spiritual significance in many culture ...
+
three
3 is a number, numeral, and glyph.
3, three, or III may also refer to:
* AD 3, the third year of the AD era
* 3 BC, the third year before the AD era
* March, the third month
Books
* ''Three of Them'' (Russian: ', literally, "three"), a 1901 ...
+
five
5 is a number, numeral, and glyph.
5, five or number 5 may also refer to:
* AD 5, the fifth year of the AD era
* 5 BC, the fifth year before the AD era
Literature
* ''5'' (visual novel), a 2008 visual novel by Ram
* ''5'' (comics), an awar ...
+
seven
7 is a number, numeral, and glyph.
7 or seven may also refer to:
* AD 7, the seventh year of the AD era
* 7 BC, the seventh year before the AD era
* The month of
July
Music Artists
* Seven (Swiss singer) (born 1978), a Swiss recording artist ...
is the only sum of four consecutive prime numbers that yields an
odd
Odd means unpaired, occasional, strange or unusual, or a person who is viewed as eccentric.
Odd may also refer to:
Acronym
* ODD (Text Encoding Initiative) ("One Document Does it all"), an abstracted literate-programming format for describing X ...
prime number,
seventeen
Seventeen or 17 may refer to:
*17 (number), the natural number following 16 and preceding 18
* one of the years 17 BC, AD 17, 1917, 2017
Literature
Magazines
* ''Seventeen'' (American magazine), an American magazine
* ''Seventeen'' (Japanese ...
, which is the fourth
super-prime. Four lies between the first proper pair of
twin primes
A twin prime is a prime number that is either 2 less or 2 more than another prime number—for example, either member of the twin prime pair (41, 43). In other words, a twin prime is a prime that has a prime gap of two. Sometimes the term ''twin pr ...
,
three
3 is a number, numeral, and glyph.
3, three, or III may also refer to:
* AD 3, the third year of the AD era
* 3 BC, the third year before the AD era
* March, the third month
Books
* ''Three of Them'' (Russian: ', literally, "three"), a 1901 ...
and
five
5 is a number, numeral, and glyph.
5, five or number 5 may also refer to:
* AD 5, the fifth year of the AD era
* 5 BC, the fifth year before the AD era
Literature
* ''5'' (visual novel), a 2008 visual novel by Ram
* ''5'' (comics), an awar ...
, which are the first two
Fermat prime
In mathematics, a Fermat number, named after Pierre de Fermat, who first studied them, is a positive integer of the form
:F_ = 2^ + 1,
where ''n'' is a non-negative integer. The first few Fermat numbers are:
: 3, 5, 17, 257, 65537, 4294967 ...
s, like
seventeen
Seventeen or 17 may refer to:
*17 (number), the natural number following 16 and preceding 18
* one of the years 17 BC, AD 17, 1917, 2017
Literature
Magazines
* ''Seventeen'' (American magazine), an American magazine
* ''Seventeen'' (Japanese ...
, which is the third. On the other hand, the
square
In Euclidean geometry, a square is a regular quadrilateral, which means that it has four equal sides and four equal angles (90-degree angles, π/2 radian angles, or right angles). It can also be defined as a rectangle with two equal-length a ...
of four 4
2, equivalently the
fourth power
In arithmetic and algebra, the fourth power of a number ''n'' is the result of multiplying four instances of ''n'' together. So:
:''n''4 = ''n'' × ''n'' × ''n'' × ''n''
Fourth powers are also formed by multiplying a number by its cube. Furthe ...
of two 2
4, is
sixteen; the only number that has
=
as a form of
factorization
In mathematics, factorization (or factorisation, see English spelling differences) or factoring consists of writing a number or another mathematical object as a product of several ''factors'', usually smaller or simpler objects of the same kind ...
. Holistically, there are four elementary arithmetic
operations
Operation or Operations may refer to:
Arts, entertainment and media
* ''Operation'' (game), a battery-operated board game that challenges dexterity
* Operation (music), a term used in musical set theory
* ''Operations'' (magazine), Multi-Man ...
in mathematics:
addition
Addition (usually signified by the plus symbol ) is one of the four basic operations of arithmetic, the other three being subtraction, multiplication and division. The addition of two whole numbers results in the total amount or ''sum'' of ...
(+),
subtraction
Subtraction is an arithmetic operation that represents the operation of removing objects from a collection. Subtraction is signified by the minus sign, . For example, in the adjacent picture, there are peaches—meaning 5 peaches with 2 taken ...
(−),
multiplication
Multiplication (often denoted by the cross symbol , by the mid-line dot operator , by juxtaposition, or, on computers, by an asterisk ) is one of the four elementary mathematical operations of arithmetic, with the other ones being ad ...
(×), and
division
Division or divider may refer to:
Mathematics
*Division (mathematics), the inverse of multiplication
*Division algorithm, a method for computing the result of mathematical division
Military
* Division (military), a formation typically consisting ...
(÷); and four basic
number system
A number is a mathematical object used to count, measure, and label. The original examples are the natural numbers 1, 2, 3, 4, and so forth. Numbers can be represented in language with number words. More universally, individual numbers ca ...
s, the
real number
In mathematics, a real number is a number that can be used to measurement, measure a ''continuous'' one-dimensional quantity such as a distance, time, duration or temperature. Here, ''continuous'' means that values can have arbitrarily small var ...
s
,
rational number
In mathematics, a rational number is a number that can be expressed as the quotient or fraction of two integers, a numerator and a non-zero denominator . For example, is a rational number, as is every integer (e.g. ). The set of all ra ...
s
,
integer
An integer is the number zero (), a positive natural number (, , , etc.) or a negative integer with a minus sign ( −1, −2, −3, etc.). The negative numbers are the additive inverses of the corresponding positive numbers. In the language ...
s
, and
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 ...
s
.
Each natural number divisible by 4 is a difference of squares of two natural numbers, i.e.
=
−
. A number is a multiple of 4 if its last two digits are a multiple of 4. For example, 1092 is a multiple of 4 because .
Lagrange's four-square theorem
Lagrange's four-square theorem, also known as Bachet's conjecture, states that every natural number can be represented as the sum of four integer squares. That is, the squares form an additive basis of order four.
p = a_0^2 + a_1^2 + a_2^2 + a_3 ...
states that every positive integer can be written as the sum of at most four
square number
In mathematics, a square number or perfect square is an integer that is the square of an integer; in other words, it is the product of some integer with itself. For example, 9 is a square number, since it equals and can be written as .
The u ...
s. Three are not always sufficient; for instance cannot be written as the sum of three squares.
There are four
all-Harshad number
In mathematics, a harshad number (or Niven number) in a given number base is an integer that is divisible by the sum of its digits when written in that base.
Harshad numbers in base are also known as -harshad (or -Niven) numbers.
Harshad numbe ...
s:
1,
2, ''4'', and
6.
12, which is divisible by four thrice over, is a Harshad number in all bases except
octal
The octal numeral system, or oct for short, is the radix, base-8 number system, and uses the Numerical digit, digits 0 to 7. This is to say that 10octal represents eight and 100octal represents sixty-four. However, English, like most languages, ...
.
A four-sided plane figure is a
quadrilateral
In geometry a quadrilateral is a four-sided polygon, having four edges (sides) and four corners (vertices). The word is derived from the Latin words ''quadri'', a variant of four, and ''latus'', meaning "side". It is also called a tetragon, ...
or quadrangle, sometimes also called a ''tetragon''. It can be further classified as a
rectangle or ''oblong'',