# 2

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This article is about the number. For the years, see [2 BC](/source/2_BC) and [AD 2](/source/AD_2). For other uses, see [2 (disambiguation)](/source/2_(disambiguation)), [II (disambiguation)](/source/II_(disambiguation)), and [Number Two (disambiguation)](/source/Number_Two_(disambiguation)).

**2** (**two**) is a [number](/source/Number), [numeral](/source/Numeral_(linguistics)) and [digit](/source/Numerical_digit). It is the [natural number](/source/Natural_number) following [1](/source/1) and preceding [3](/source/3). It is the smallest and the only even [prime number](/source/Prime_number).

Because it forms the basis of a [duality](/source/Dualistic_cosmology), it has [religious](/source/Religion) and [spiritual](/source/Spirituality) significance in many [cultures](/source/Culture).

## Mathematics

The number 2 is the second natural number, after [1](/source/1). Each natural number, including 2, is constructed by succession, that is, by adding 1 to the previous natural number.[1] 2 is the smallest and the only even [prime number](/source/Prime_number), and the first [Ramanujan prime](/source/Ramanujan_prime).[2] It is also the first [superior highly composite number](/source/Superior_highly_composite_number),[3] and the first [colossally abundant number](/source/Colossally_abundant_number).[4]

An [integer](/source/Integer) is determined to be [even](/source/Parity_(mathematics)) if it is [divisible](/source/Division_(mathematics)) by two. When written in base 10, all [multiples](/source/Multiple_(mathematics)) of 2 will end in [0](/source/0), 2, 4, 6, or [8](/source/8);[5] more generally, in any even base, even numbers will end with an even digit.

[Binary](/source/Binary_number) is a number system with a [base](/source/Radix) of two, where each "[bit](/source/Bit)" (binary digit) is either 0 (off) or 1 (on). It is used extensively in [computing](/source/Computer), since simple on-off logic is relatively simple to keep track of with [electronics](/source/Electronics).[6]

A [digon](/source/Digon) is a polygon with two sides (or [edges](/source/Edge_(geometry))) and two [vertices](/source/Vertex_(geometry)).[7]: 52 In [Euclidean space](/source/Euclidean_space), digons are [degenerate](/source/Degeneracy_(mathematics)), collapsing to a line segment between the two vertices.[8] In [spherical geometry](/source/Spherical_geometry), however, non-degenerate digons can exist.[9]

Two distinct [points](/source/Point_(geometry)) in a [plane](/source/Plane_(geometry)) are always [sufficient](/source/Necessity_and_sufficiency) to define a unique [line](/source/Line_(geometry)) in a nontrivial Euclidean space.[10]

The integers modulo 2 form the [finite field](/source/Finite_field) \mathbb F_2, the smallest finite field. It has two elements, usually denoted 0 and 1, and addition in \mathbb F_2 corresponds to parity. Thus reduction modulo 2 records the [parity](/source/Parity_(mathematics)) of an integer: even integers are congruent to 0 modulo 2, and odd integers are congruent to 1 modulo 2. In algebra, structures of [characteristic](/source/Characteristic_(algebra)) 2 have special behavior because 1+1=0; in particular, every element satisfies x=-x. For this reason, many algebraic constructions have separate forms in characteristic 2.[11]

A symmetry of order two is called an [involution](/source/Involution_(mathematics)).

### List of basic calculations

Multiplication 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 20 25 50 100 1000 2 * x 2 4 6 8 10 12 14 16 18 20 22 24 26 28 30 32 40 50 100 200 2000

Division 1 2 3 4 5 6 7 8 9 10 11 12 2 ÷ x 2 1 0.6 0.5 0.4 0.3 0.285714 0.25 0.2 0.2 0.18 0.16 x ÷ 2 0.5 1 1.5 2 2.5 3 3.5 4 4.5 5 5.5 6

Division 13 14 15 16 17 18 19 20 2 ÷ x 0.153846 0.142857 0.13 0.125 0.1176470588235294 0.1 0.105263157894736842 0.1 x ÷ 2 6.5 7 7.5 8 8.5 9 9.5 10

Exponentiation 1 2 3 4 5 6 7 8 9 10 11 12 2x 2 4 8 16 32 64 128 256 512 1024 2048 4096 x2 1 4 9 16 25 36 49 64 81 100 121 144

Exponentiation 13 14 15 16 17 18 19 20 2x 8192 16384 32768 65536 131072 262144 524288 1048576 x2 169 196 225 256 289 324 361 400

## As a word

*Two* is most commonly a [determiner](/source/English_determiners) used with [plural](/source/Grammatical_number) countable nouns, as in *two days* or *I'll take these two*.[12] *Two* is a [noun](/source/English_nouns) when it refers to the number two as in *two plus two is four.*

The word *two* is derived from the [Old English](/source/Old_English) words *twā* ([feminine](/source/Grammatical_gender)), *tū* (neuter), and *twēġen* (masculine, which survives today in the form [twain](https://en.wiktionary.org/wiki/twain)).[13]

## Evolution of the Arabic digit

The digit used in the modern [Western world](/source/Western_world) to represent the number 2 traces its roots back to the Indic [Brahmic script](/source/Brahmic_script), where "2" was written as two horizontal lines. The modern [Chinese](/source/Chinese_written_language) and [Japanese](/source/Japanese_writing_system) languages (and Korean [Hanja](/source/Hanja)) still use this method. The [Gupta script](/source/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](/source/Devanagari) script, the top line was written more like a curve connecting to the bottom line. In the [Arabic](/source/Arabic) [Ghubar](/source/Ghub%C4%81r_numerals) writing, the bottom line was completely vertical, and the digit 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 digit.[14]

## In science

- The first [magic number](/source/Magic_number_(physics)) - number of electrons in the innermost electron shell of an atom.[15]
- The chemical element with atomic number 2 is [helium](/source/Helium).

## See also

- [Binary number](/source/Binary_number)
- [Square root of 2](/source/Square_root_of_2)
- [−2](/source/%E2%88%922)

## References

1. Colman, Samuel (1912). ['**Nature's Harmonic Unity: A Treatise on Its Relation to Proportional Form'**](https://archive.org/details/naturesharmonic00coangoog/page/n26/mode/2up). Coan, C. Arthur (ed.). New York and London: G.P. Putnam's Sons. p. 10.

1. ["Sloane's A104272 : Ramanujan primes"](https://web.archive.org/web/20110428165633/https://oeis.org/A104272). *The On-Line Encyclopedia of Integer Sequences*. OEIS Foundation. Archived from [the original](https://oeis.org/A104272) on 2011-04-28. Retrieved 2016-06-01.

1. ["A002201 - OEIS"](https://oeis.org/A002201). *oeis.org*. [Archived](https://web.archive.org/web/20101229032520/https://oeis.org/A002201) 2010-12-29 at the Wayback Machine. Retrieved 2024-11-28.

1. ["A004490 - OEIS"](https://oeis.org/A004490). *oeis.org*. [Archived](https://web.archive.org/web/20120525075430/https://oeis.org/A004490) 2012-05-25 at the Wayback Machine. Retrieved 2024-11-28.

1. Retrieved 2022-12-15.

1. ["How computers see the world - Binary - KS3 Computer Science Revision"](https://www.bbc.co.uk/bitesize/guides/z26rcdm/revision/1). *BBC Bitesize*. Retrieved 2024-06-05.

1. Wilson, Robin (2014). *Four Colors Suffice*. Revised color ed. Princeton University Press. ISBN 978-0-691-15822-8.

1. Weisstein, Eric W. "Digon." From MathWorld--A Wolfram Resource. [https://mathworld.wolfram.com/Digon.html](https://mathworld.wolfram.com/Digon.html)

1. ["Polygons on the Sphere"](https://sites.math.washington.edu/~king/coursedir/m445w04/class/snotes/02-09-moserNotes.html). *sites.math.washington.edu*. Notes from Math 445 for February 9, 2004. February 9, 2004. Retrieved 2026-02-15.

1. Carrell, Jim. ["Chapter 1 | Euclidean Spaces and Their Geometry"](https://personal.math.ubc.ca/~carrell/307_chap1.pdf). *MATH 307 Applied Linear Algebra*. [Archived](https://web.archive.org/web/20240605154649/https://personal.math.ubc.ca/~carrell/307_chap1.pdf) 2024-06-05 at the Wayback Machine. Retrieved 2024-06-05.

1. Knus, Max-Albert; Merkurjev, Alexander; Rost, Markus; Tignol, Jean-Pierre (1998). *The Book of Involutions*. Vol. 44. American Mathematical Society Colloquium Publications. Providence, Rhode Island: American Mathematical Society. ISBN 978-0-8218-0904-4.

1. Huddleston, Rodney D.; Pullum, Geoffrey K.; Reynolds, Brett (2022). *A student's introduction to English grammar*. 2nd ed. Cambridge, United Kingdom: [Cambridge University Press](/source/Cambridge_University_Press). p. 117. ISBN 978-1-316-51464-1. [OCLC 1255524478](https://www.worldcat.org/oclc/1255524478)

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

1. Watkins, Thayer. ["The Complete Explanation of the Nuclear Magic Numbers Which Indicate the Filling of Nucleonic Shells and the Revelation of Special Numbers Indicating the Filling of Subshells Within Those Shells"](https://web.archive.org/web/20191202130317/http://www.sjsu.edu/faculty/watkins/magicnumbers2.htm). San José State University. Archived from [the original](https://www.sjsu.edu/faculty/watkins/magicnumbers2.htm) on 2019-12-02. Retrieved 2019-12-22.

## External links

- [Prime curiosities: 2](http://primes.utm.edu/curios/page.php/2.html)

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Adapted from the Wikipedia article [2](https://en.wikipedia.org/wiki/2) by Wikipedia contributors ([contributor history](https://en.wikipedia.org/wiki/2?action=history)). Available under [Creative Commons Attribution-ShareAlike 4.0 International](https://creativecommons.org/licenses/by-sa/4.0/). Changes may have been made.