# 3 number

This article discusses the number three. For the year AD 3, see 3. For other uses of 3, see 3 (disambiguation)
 0 10 20 30 40 50 60 70 80 90 >> Cardinal 3 three Ordinal 3rd third Numeral system ternary Factorization prime Divisors 1, 3 Roman numeral III Unicode representation of Roman numeral Ⅲ, ⅲ prefixes tri- (from Greek) tre-/ter- (from Latin) Binary 11 Octal 3 Duodecimal 3 Hexadecimal 3 Hebrew ג (Gimel)

3 (three) is a number, numeral, and glyph. It is the natural number following 2 and preceding 4.

## In mathematics

• Three is the first odd prime number, and the second smallest prime after two.
• Three is the first Fermat prime (220 + 1).
• Three is the first Mersenne prime (22 - 1).
• Three is the second Sophie Germain prime.
• Three is the second Mersenne prime exponent.
• Three is the first lucky prime.
• Three is the first Genocchi prime.
• Three is the second factorial prime (2! + 1).
• Three is the first unique prime due to the properties of its reciprocal.
• Three is the second triangular number.
• Three is the only prime which is one less than a perfect square. Any other number which is one less than a perfect square will be the product of the numbers one more than, and one less than, the square root of said square.
• Three points determine a plane (unless they are collinear).
• Three is the fourth Fibonacci number and the third that is unique. It is also the second Lucas prime and the second Stern prime.

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• Three is the fourth open meandric number.
• Vulgar fractions with 3 in the denominator have a single digit repeating sequences in their decimal expansions, (.000..., .333..., .666..., .999...)
• A natural number is divisible by three if the sum of its digits in base 10 is divisible by 3. For example, the number 21 is divisible by three (3 times 7) and the sum of its digits is 2 + 1 = 3. Because of this, the reverse of any number that is divisible by three (or indeed, any permutation of its digits) is also divisible by three. For instance, 1368 and its reverse 8631 are both divisible by three (and so are 1386, 3168, 3186, 3618, etc..).
• A triangle is the most durable shape possible, the only "perfect" figure which if all endpoints have hinges will never change its shape unless the sides themselves are bent.

## The Arabic glyph

Three is often the largest number written with as many lines as the number represents. The Romans tired of writing 4 as IIII, but to this day 3 is written as three lines in Roman and Chinese numerals. This was the way the Brahmin Indians wrote it, and the Gupta made the three lines more curved. The Nagari started rotating the lines clockwise and ending each line with a slight downward stroke on the right. Eventually they made these strokes connect with the lines below, and evolved it to a character that looks very much like a modern 3 with an extra stroke at the bottom. It was the Western Ghubar Arabs who finally eliminated the extra stroke and created our modern 3. (The "extra" stroke, however, was very important to the Eastern Arabs, and they made it much larger, while rotating the strokes above to lie along a horizontal axis, and to this day Eastern Arabs write a 3 that looks like a mirrored 7 with ridges on its top line).

In fonts with text figures, 3 usually has a descender, for example, File:TextFigs036.png, though in some Template:Ll fonts it has an ascender instead of a descender.

## In human culture

Many human cultures have given the concept of three-ness symbolic meanings.

The process of synthesis in Hegelian dialectic creates three-ness from two-ness.

Three (三, formal writing: 叁, pinyin san1) is considered a good number in Chinese culture because it sounds like the word "alive" (生 pinyin sheng1), compared to four that sounds like the word "death".

Counting to three is common in situations where a group of people wish to perform an action in synchrony: Now, on the count of three, everybody pull!  Assuming the counter is proceeding at a uniform rate, the first two counts are necessary to establish the rate, but then everyone can predict when "three" will come based on "one" and "two"; this is likely why three is used instead of some other number.

## In music

In music, the Roman numeral iii is the mediant scale degree, chord, or diatonic function, when distinguished III = major and iii = minor. Three is important to popular American rock group, The White Stripes, and has become one of the trademarks of their style. Their lead singer has changed his name to Three Quid. It is also is in the name of many music groups, including Three Dog Night, Three Days Grace, and 3 Inches of Blood. The band (3) featuring Joey Eppard uses the number alone as its moniker.