# 2

 ← 1 2 3 →
Cardinaltwo
Ordinal2nd (second / twoth)
Numeral systembinary
Factorizationprime
Gaussian integer factorization${\displaystyle (1+i)(1-i)}$
Prime1st
Divisors1, 2
Greek numeralΒ´
Roman numeralII
Roman numeral (unicode)Ⅱ, ⅱ
Greek prefixdi-
Latin prefixduo- bi-
Old English prefixtwi-
Binary102
Ternary23
Quaternary24
Quinary25
Senary26
Octal28
Duodecimal212
Vigesimal220
Base 36236
Greek numeralβ'
Arabic & Kurdish٢
Urdu
Ge'ez
Bengali
Chinese numeral二，弍，貳
Devanāgarī
Telugu
Tamil
Hebrewב
Japanese numeral二/弐
Khmer
Korean이，둘
Thai

2 (two) is a number, numeral, and glyph. It is the natural number following 1 and preceding 3.

## 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").[1] 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.[2]

Two is the third (or fourth) Fibonacci number.

Two is the base of the binary system, the numeral system with the least number of 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

${\displaystyle \sum _{k=0}^{\infty }{\frac {1}{2^{k}}}=1+{\frac {1}{2}}+{\frac {1}{4}}+{\frac {1}{8}}+{\frac {1}{16}}+\cdots =2.}$

This comes from the fact that:

${\displaystyle \sum _{k=0}^{\infty }{\frac {1}{n^{k}}}=1+{\frac {1}{n-1}}\quad {\mbox{for all}}\quad n\in \mathbb {R} >1.}$

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

${\displaystyle \sum _{k=0}^{n-1}2^{k}=2^{n}-1}$

and also

${\displaystyle \sum _{k=a}^{n-1}2^{k}=2^{n}-\sum _{k=0}^{a-1}2^{k}-1}$

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 = VE + F = 2, where V is the number of vertices, E is the number of edges, and F is the number of faces.

### List of basic calculations

Multiplication 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 50 100 1000
2 × x 2 4 6 8 10 12 14 16 18 20 22 24 26 28 30 32 34 36 38 40 42 44 46 48 50 100 200 2000
Division 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15
2 ÷ x 2 1 0.6 0.5 0.4 0.3 0.285714 0.25 0.2 0.2 0.18 0.16 0.153846 0.142857 0.13
x ÷ 2 0.5 1 1.5 2 2.5 3 3.5 4 4.5 5 5.5 6 6.5 7 7.5
Exponentiation 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20
2x 2 4 8 16 32 64 128 256 512 1024 2048 4096 8192 16384 32768 65536 131072 262144 524288 1048576
x2 1 4 9 16 25 36 49 64 81 100 121 144 169 196 225 256 289 324 361 400

Other Languages
አማርኛ: ሁለት
Ænglisc: 2 (getæl)
العربية: 2 (عدد)
ܐܪܡܝܐ: 2 (ܡܢܝܢܐ)
অসমীয়া: ২ (সংখ্যা)
asturianu: Dos
Avañe'ẽ: Mokõi
авар: КӀиго
Aymar aru: Paya
azərbaycanca: 2 (ədəd)
تۆرکجه: ۲ (سایی)
Bân-lâm-gú: 2
башҡортса: 2 (һан)
беларуская: 2 (лік)
Bislama: Tu
български: 2 (число)
བོད་ཡིག: ༢ (གྲངས་ཀ།)
bosanski: 2 (broj)
brezhoneg: Daou
català: Dos
Чӑвашла: 2 (хисеп)
Cebuano: 2 (numero)
čeština: 2 (číslo)
chiShona: Piri
chiTumbuka: Vibili
Cymraeg: Dau
dansk: 2 (tal)
Deitsch: Zwee
Deutsch: Zwei
eesti: Kaks
Ελληνικά: 2 (αριθμός)
emiliàn e rumagnòl: 2 (nùmer)
español: Dos
Esperanto: 2 (nombro)
estremeñu: Dos
euskara: Bi
فارسی: ۲ (عدد)
føroyskt: 2 (tal)
français: 2 (nombre)
Fulfulde: Ɗiɗi
furlan: 2 (numar)
Gaeilge: 2 (uimhir)
galego: Dous
ГӀалгӀай: 2 (таьрахь)

ગુજરાતી: ૨ (બે)

хальмг: 2
한국어: 2
Hausa: 2
հայերեն: 2 (թիվ)
हिन्दी:
hrvatski: Dva
Bahasa Hulontalo: 2
Igbo: Abụo
Bahasa Indonesia: 2 (angka)
interlingua: 2 (numero)
Iñupiak: Malġuk
isiXhosa: Zimbini
íslenska: Tveir
italiano: 2 (numero)
עברית: 2 (מספר)
ಕನ್ನಡ: ಎರಡು
ქართული: 2 (რიცხვი)
қазақша: 2 (сан)
Kinyarwanda: Kabiri
Kirundi: Kabiri
Kiswahili: Mbili
коми: 2 (кык)
Kreyòl ayisyen: 2 (nonm)
kurdî: Du
лакку: КӀива
Latina: Duo
latviešu: 2 (skaitlis)
Lëtzebuergesch: Zwee
lietuvių: 2 (skaičius)
Limburgs: Twieë
lingála: Míbalé
Luganda: Bbiri
lumbaart: Nümar 2
magyar: 2 (szám)
македонски: 2 (број)
മലയാളം: 2 (അക്കം)
მარგალური: ჟირი
Bahasa Melayu: 2 (nombor)
Mìng-dĕ̤ng-ngṳ̄: 2
монгол: Хоёр
မြန်မာဘာသာ:
Nāhuatl: Ōme
Na Vosa Vakaviti: Rua
Nederlands: 2 (getal)
Nedersaksies: 2 (getal)

Napulitano: Ddoje
нохчийн: Шиъ
Nordfriisk: Tau
norsk: 2 (tall)
norsk nynorsk: Talet 2
ଓଡ଼ିଆ: ୨ (ସଂଖ୍ୟା)
oʻzbekcha/ўзбекча: 2 (son)
پنجابی: 2
پښتو: ۲
Перем Коми: 2 (кык)
ភាសាខ្មែរ: ២ (លេខ)
polski: 2 (liczba)
português: Dois
română: 2 (cifră)
Runa Simi: Iskay
русский: 2 (число)
саха тыла: Икки (ахсаан)
ᱥᱟᱱᱛᱟᱲᱤ: ᱒ (ᱵᱟᱨ)
Gagana Samoa: Lua (numera)
Scots: 2 (nummer)
Sesotho sa Leboa: 2 (nomoro)
shqip: 2 (numër)
sicilianu: 2 (nùmmuru)
සිංහල: දෙක
Simple English: 2 (number)
slovenčina: 2 (číslo)
slovenščina: 2 (število)
ślůnski: 2 (nůmera)
Soomaaliga: 2 (tiro)
کوردی: ٢ (ژمارە)
Sranantongo: Numro 2
српски / srpski: 2 (број)
srpskohrvatski / српскохрватски: 2 (broj)
suomi: 2 (luku)
svenska: 2 (tal)
Tagalog: 2 (bilang)
தமிழ்: 2 (எண்)
татарча/tatarça: 2 (сан)
తెలుగు: రెండు
ไทย: 2
ትግርኛ: ክልተ
тоҷикӣ: 2 (адад)
Tshivenda: Mbili
Türkçe: 2 (sayı)
Türkmençe: 2 (san)
тыва дыл: 2
ᨅᨔ ᨕᨘᨁᨗ: 2 (nomoro)
українська: 2 (число)
اردو: 2 (عدد)
Vahcuengh: 2
vepsän kel’: 2 (lugu)
Tiếng Việt: 2 (số)

West-Vlams: 2 (getal)
Winaray: 2 (ihap)
Wolof: Ñaar

Xitsonga: Mbirhi
ייִדיש: 2 (נומער)
Yorùbá: 2 (nọ́mbà)