2 (two) is a number, numeral, and glyph. 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 cultures.

Contents

 1Evolution of the glyph

Evolution of the glyph

The glyph used in the modern Western world to represent the number 2 traces its roots back to the
Indic Brahmic script, where "2" was written as two horizontal lines. The
modern Chinese and Japanese languages still use this method. The Gupta script rotated the two
lines 45 degrees, making them diagonal. The top line was sometimes also shortened and had its
bottom end curve towards the center of the bottom line. In the Nagari script, the top line was written
more like a curve connecting to the bottom line. In the Arabic Ghubar writing, the bottom line was
completely vertical, and the glyph looked like a dotless closing question mark. Restoring the bottom
line to its original horizontal position, but keeping the top line as a curve that connects to the bottom
line leads to our modern glyph.[1]

In fonts with text figures, 2 usually is of x-height, for example,  .

In mathematics
An integer is called even if it is divisible by 2. For integers written in a numeral system based on an
even number, such as decimal, hexadecimal, or in any other base that is even, divisibility by 2 is
easily tested by merely looking at the last digit. If it is even, then the whole number is even. In
particular, when written in the decimal system, all multiples of 2 will end in 0, 2, 4, 6, or 8.
Two is the smallest prime number, and the only even prime number (for this reason it is sometimes
called "the oddest prime").[2] The next prime is three. Two and three are the only two consecutive
prime numbers. 2 is the first Sophie Germain prime, the first factorial prime, the first Lucas prime,
and the first Ramanujan prime.[3]
Two is the third (or fourth) Fibonacci number.
Two is the base of the binary system, the numeral system with the fewest tokens allowing to denote
a natural number n substantially more concise (log2 n tokens), compared to a direct representation
by the corresponding count of a single token (n tokens). This binary number system is used
extensively in computing.
For any number x:
x + x = 2 · x addition to multiplication
x · x = x2 multiplication to exponentiation
xx = x↑↑2 exponentiation to tetration
Extending this sequence of operations by introducing the notion of hyperoperations,
here denoted by "hyper(a,b,c)" with a and c being the first and second operand,
and b being the level in the above sketched sequence of operations, the following holds
in general:
hyper(x,n,x) = hyper(x,(n + 1),2).
Two has therefore the unique property that 2 + 2 = 2 · 2 = 22 = 2↑↑2 = 2↑↑↑2 = ...,
disregarding the level of the hyperoperation, here denoted by Knuth's up-arrow
notation. The number of up-arrows refers to the level of the hyperoperation.
Two is the only number x such that the sum of the reciprocals of the powers
of x equals itself. In symbols
This comes from the fact that:
Powers of two are central to the concept of Mersenne primes, and
important to computer science. Two is the first Mersenne prime exponent.
Taking the square root of a number is such a common mathematical
operation, that the spot on the root sign where the exponent would normally
be written for cubic and other roots, may simply be left blank for square
roots, as it is tacitly understood.
The square root of 2 was the first known irrational number.
The smallest field has two elements.
In a set-theoretical construction of the natural numbers, 2 is identified with
the set {{∅},∅}. This latter set is important in category theory: it is
a subobject classifier in the category of sets.
Two also has the unique property such that
and also
for a not equal to zero
In any n-dimensional, euclidean space two distinct points determine
a line.
For any polyhedron homeomorphic to a sphere, the Euler
characteristic is χ = V − E + F = 2, where V is the number
of vertices, E is the number of edges, and F is the number of faces.

Other

International maritime pennant for 2

In pre-1972 Indonesian and Malay orthography, 2 was shorthand
for the reduplication that forms plurals: orang "person", orang-
orang or orang2 "people".[citation needed]

References
1. ^ Georges Ifrah, The Universal History of Numbers: From
Prehistory to the Invention of the Computer transl. David Bellos et
al. London: The Harvill Press (1998): 393, Fig. 24.62
2. ^ John Horton Conway & Richard K. Guy, The Book of Numbers.
New York: Springer (1996): 25. ISBN 0-387-97993-X. "Two is
celebrated as the only even prime, which in some sense makes it
the oddest prime of all."
3. ^ "Sloane's A104272  : Ramanujan primes".  The On-Line
Encyclopedia of Integer Sequences. OEIS Foundation.
Retrieved 2016-06-01.

External links

 Mathematics portal

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 Prime curiosities: 2

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