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This is a list of articles about prime numbers. A prime number (or prime) is a natural number greater than 1 that has no positive divisors other than 1 and itself. By Euclid's theorem, there are an infinite number of prime numbers. Subsets of the prime numbers may be generated with various formulas for primes.
In arithmetic and algebra, the fourth power of a number n is the result of multiplying four instances of n together. So: n 4 = n × n × n × n. Fourth powers are also formed by multiplying a number by its cube.
A list of articles about numbers (not about numerals). Topics include powers of ten, notable integers, prime and cardinal numbers, and the myriad system.
A cube has all multiplicities divisible by 3 ... A factorial x! is the product of all numbers from 1 to x. The first: 1, 2, 6, 24, 120, 720, 5040, 40320, 362880, ...
He does not go further than this, but from this it follows that the sum of the first n cubes equals the sum of the first n(n + 1) / 2 odd numbers, that is, the odd numbers from 1 to n(n + 1) − 1. The average of these numbers is obviously n(n + 1) / 2 , and there are n(n + 1) / 2 of them, so their sum is ( n(n + 1 ...
The cube of a number or any other mathematical expression is denoted by a superscript 3, for example 2 3 = 8 or (x + 1) 3. The cube is also the number multiplied by its square: n 3 = n × n 2 = n × n × n. The cube function is the function x ↦ x 3 (often denoted y = x 3) that maps a number to its cube. It is an odd function, as
1728 is one less than the first taxicab or Hardy–Ramanujan number 1729, ... Where 1728 is the cube of 12, the sum 1 + 728 = 729 = 9 3. The digit sum of 1728 is 18.
Proof without words that the difference of two consecutive cubes is a centered hexagonal number by arranging n 3 semitransparent balls in a cube and viewing along a space diagonal – colour denotes cube layer and line style denotes hex number