The number two has many properties in mathematics.[1] 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 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. In numeral systems based on an odd number, divisibility by 2 can be tested by having a digital root that is even.
Two is the smallest and first prime number, and the only even prime number[2] (for this reason it is sometimes called "the oddest prime").[3] 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, the first Ramanujan prime,[4] 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,[5] a Pell number,[6] the first Fibonacci prime, 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 second and fourth Perrin numbers.[7]
Despite being prime, two is also a superior highly composite number, because it is a natural number which has more divisors than any other number scaled relative to the number itself.[8] The next superior highly composite number is six.
Vulgar fractions with only 2 or 5 in the denominator do not yield infinite decimal expansions, as is the case with all other primes, because 2 and 5 are factors of ten, the decimal 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
xx = x↑↑2 exponentiation to tetration
In general:
hyper(x,n,x) = hyper(x,(n + 1),2)
Two also has the unique property that 2 + 2 = 2 · 2 = 22 = 2↑↑2 = 2↑↑↑2, and so on, no matter how high the level of the hyperoperation is.

- home
- math
- welcome to the number forum
- Viewing single post