3 (three) 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 c ...

, numeral and digit. 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 n ...

following 2 and preceding 4, and is the smallest odd

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 ways ...

and the only prime preceding a

square number In mathematics, a square number or perfect square is an integer that is the square (algebra), square of an integer; in other words, it is the multiplication, product of some integer with itself. For example, 9 is a square number, since it equals ...

. It has religious or cultural significance in many societies.

Evolution of the Arabic digit

The use of three lines to denote the number 3 occurred in many writing systems, including some (like Roman and

Chinese numerals Chinese numerals are words and characters used to denote numbers in Chinese. Today, speakers of Chinese use three written numeral systems: the system of Arabic numerals used worldwide, and two indigenous systems. The more familiar indigenous sy ...

) that are still in use. That was also the original representation of 3 in the

Brahmic The Brahmic scripts, also known as Indic scripts, are a family of abugida writing systems. They are used throughout the Indian subcontinent, Southeast Asia and parts of East Asia. They are descended from the Brahmi script of ancient India ...

(Indian) numerical notation, its earliest forms aligned vertically. However, during the

Gupta Empire The Gupta Empire was an ancient Indian empire which existed from the early 4th century CE to late 6th century CE. At its zenith, from approximately 319 to 467 CE, it covered much of the Indian subcontinent. This period is considered as the Gol ...

the sign was modified by the addition of a curve on each line. The

Nāgarī script The Nāgarī script or Northern Nagari of Kashi is the ancestor of Devanagari, Nandinagari and other variants, and was first used to write Prakrit and Sanskrit. The term is sometimes used as a synonym for Devanagari script.Kathleen Kuiper (2010) ...

rotated the lines clockwise, so they appeared horizontally, and ended each line with a short downward stroke on the right. In cursive script, the three strokes were eventually connected to form a glyph resembling a with an additional stroke at the bottom: ३. The Indian digits spread to the

Caliphate A caliphate or khilāfah ( ar, خِلَافَة, ) is an institution or public office under the leadership of an Islamic steward with the title of caliph (; ar, خَلِيفَة , ), a person considered a political-religious successor to th ...

in the 9th century. The bottom stroke was dropped around the 10th century in the western parts of the Caliphate, such as the

Maghreb The Maghreb (; ar, الْمَغْرِب, al-Maghrib, lit=the west), also known as the Arab Maghreb ( ar, المغرب العربي) and Northwest Africa, is the western part of North Africa and the Arab world. The region includes Algeria, ...

and

Al-Andalus Al-Andalus DIN 31635, translit. ; an, al-Andalus; ast, al-Ándalus; eu, al-Andalus; ber, ⴰⵏⴷⴰⵍⵓⵙ, label=Berber languages, Berber, translit=Andalus; ca, al-Àndalus; gl, al-Andalus; oc, Al Andalús; pt, al-Ândalus; es, ...

, when a distinct variant ("Western Arabic") of the digit symbols developed, including modern Western 3. In contrast, the Eastern Arabs retained and enlarged that stroke, rotating the digit once more to yield the modern ("Eastern")

Arabic Arabic (, ' ; , ' or ) is a Semitic languages, Semitic language spoken primarily across the Arab world.Semitic languages: an international handbook / edited by Stefan Weninger; in collaboration with Geoffrey Khan, Michael P. Streck, Janet C ...

digit "٣". In most modern Western

typeface A typeface (or font family) is the design of lettering that can include variations in size, weight (e.g. bold), slope (e.g. italic), width (e.g. condensed), and so on. Each of these variations of the typeface is a font. There are list of type ...

s, the digit 3, like the other

decimal digit A numerical digit (often shortened to just digit) is a single symbol used alone (such as "2") or in combinations (such as "25"), to represent numbers in a positional numeral system. The name "digit" comes from the fact that the ten digits (Latin ...

s, has the height of a

capital letter Letter case is the distinction between the letters that are in larger uppercase or capitals (or more formally ''majuscule'') and smaller lowercase (or more formally ''minuscule'') in the written representation of certain languages. The writing ...

, and sits on the baseline. In typefaces with

text figures Text figures (also known as non-lining, lowercase, old style, ranging, hanging, medieval, billing, or antique figures or numerals) are numerals designed with varying heights in a fashion that resembles a typical line of running text, hence the ...

, on the other hand, the glyph usually has the height of a

lowercase letter Letter case is the distinction between the letters that are in larger uppercase or capitals (or more formally ''majuscule'') and smaller lowercase (or more formally ''minuscule'') in the written representation of certain languages. The writing ...

"x" and a

descender In typography and handwriting, a descender is the portion of a letter that extends below the baseline of a font. For example, in the letter ''y'', the descender is the "tail", or that portion of the diagonal line which lies below the ''v'' c ...

: "

". In some

French French (french: français(e), link=no) may refer to: * Something of, from, or related to France ** French language, which originated in France, and its various dialects and accents ** French people, a nation and ethnic group identified with Franc ...

text-figure typefaces, though, it has an ascender instead of a descender. A common graphic variant of the digit three has a flat top, similar to the letter Ʒ (ezh). This form is sometimes used to prevent falsifying a 3 as an 8. It is found on

UPC-A The Universal Product Code (UPC or UPC code) is a barcode symbology that is widely used worldwide for tracking trade items in stores. UPC (technically refers to UPC-A) consists of 12 digits that are uniquely assigned to each trade item. Along w ...

barcodes and

standard 52-card deck The standard 52-card deck of French-suited playing cards is the most common pack of playing cards used today. In English-speaking countries it is the only traditional pack used for playing cards; in many countries of the world, however, it is used ...

Mathematics

3 is the second smallest

and the first

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. It is the first

unique prime The reciprocals of prime numbers have been of interest to mathematicians for various reasons. They do not have a finite sum, as Leonhard Euler proved in 1737. Like all rational numbers, the reciprocals of primes have repeating decimal represen ...

, such that the

period length A periodic function is a Function (mathematics), function that repeats its values at regular intervals. For example, the trigonometric functions, which repeat at intervals of 2\pi radians, are periodic functions. Periodic functions are used th ...

value of 1 of the

decimal expansion A decimal representation of a non-negative real number is its expression as a sequence of symbols consisting of decimal digits traditionally written with a single separator: r = b_k b_\ldots b_0.a_1a_2\ldots Here is the decimal separator, is ...

of its

reciprocal Reciprocal may refer to: In mathematics * Multiplicative inverse, in mathematics, the number 1/''x'', which multiplied by ''x'' gives the product 1, also known as a ''reciprocal'' * Reciprocal polynomial, a polynomial obtained from another pol ...

, 0.333..., is unique. 3 is a

twin prime 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 ...

with 5, and a

cousin prime In number theory, cousin primes are prime numbers that differ by four. Compare this with twin primes, pairs of prime numbers that differ by two, and sexy primes, pairs of prime numbers that differ by six. The cousin primes (sequences and in OE ...

with 7, and the only known number

n

such that

n

! - 1 and

n

! + 1 are prime, as well as the only prime number

p

such that

p

- 1 yields another prime number, 2. A

triangle A triangle is a polygon with three Edge (geometry), edges and three Vertex (geometry), vertices. It is one of the basic shapes in geometry. A triangle with vertices ''A'', ''B'', and ''C'' is denoted \triangle ABC. In Euclidean geometry, an ...

is made of three sides. It is the smallest non-self-intersecting

polygon In geometry, a polygon () is a plane figure that is described by a finite number of straight line segments connected to form a closed ''polygonal chain'' (or ''polygonal circuit''). The bounded plane region, the bounding circuit, or the two toge ...

and the only polygon not to have proper

diagonals In geometry, a diagonal is a line segment joining two vertices of a polygon or polyhedron, when those vertices are not on the same edge. Informally, any sloping line is called diagonal. The word ''diagonal'' derives from the ancient Greek δ� ...

. When doing quick estimates, 3 is a rough approximation of , 3.1415..., and a very rough approximation of ''e'', 2.71828... 3 is the first

Mersenne prime In mathematics, a Mersenne prime is a prime number that is one less than a power of two. That is, it is a prime number of the form for some integer . They are named after Marin Mersenne, a French Minim friar, who studied them in the early 17t ...

, as well as the second Mersenne prime exponent and the second double Mersenne prime exponent, for 7 and 127, respectively. 3 is also the first of five known

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, which include 5, 17,

257 __NOTOC__ Year 257 ( CCLVII) was a common year starting on Thursday (link will display the full calendar) of the Julian calendar. At the time, it was known as the Year of the Consulship of Valerianus and Gallienus (or, less frequently, year 10 ...

, and

65537 65