Tale of Two Towers

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

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In mathematics

Two has many properties 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 and hexadecimal, divisibility by 2 is easily tested by merely looking at the one's place digit. If it's 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 and the first prime number, and the only even one (for this reason it is sometimes humorously called "the oddest prime"). The next prime is three. 2 is the first Sophie Germain prime, the first factorial prime, the first Lucas prime, and the first Smarandache-Wellin prime. It is an Eisenstein prime with no imaginary part and real part of the form 3n − 1. It is also a Stern prime, a Pell number, and a Markov number, appearing in infinitely many solutions to the Markov Diophantine equation involving odd-indexed Pell numbers.

It is the third Fibonacci number, and the third and fifth Perrin numbers.

Despite being a prime, two is also a highly composite number, because it has more divisors than the number one. The next highly composite number is four.

Vulgar fractions with 2 or 5 in the denominator do not yield infinite decimal expansions, as is the case with most primes, because they are prime factors of ten, the base.

Two is the base of the simplest numeral system in which natural numbers can be written concisely, being the length of the number a logarithm of the value of the number (whereas in base 1 the length of the number is the value of the number itself); the binary system is used in computers.

For any number x:

x+x = 2·x addition to multiplication

x·x = x² multiplication to exponentiation

x^x = x↑↑2 exponentiation to tetration

Two also has the unique property that 2+2 = 2·2 = 2²=2↑↑2=2↑↑↑2, and so on, no matter how high the operation is.

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:

Read more at Wikipedia.org