Concept
64 (sixty-four) is the natural number following 63 and preceding 65. Sixty-four is the square of 8, the cube of 4, and the sixth-power of 2. It is the smallest number with exactly seven divisors. 64 is the first non-unitary sixth-power prime of the form p6 where p is a prime number. The aliquot sum of a 2-power (2n) is always one less than the 2-power itself therefore the aliquot sum of 64 is 63, within an aliquot sequence of two composite members ( 64,63,41,1,0) to the prime 41 in the 41-aliquot tree. It is the lowest positive power of two that is adjacent to neither a Mersenne prime nor a Fermat prime. 64 is the sum of Euler's totient function for the first fourteen integers. It is also a dodecagonal number and a centered triangular number. 64 is also the first whole number (greater than 1) that is both a perfect square and a perfect cube. Since it is possible to find sequences of 65 consecutive integers (intervals of length 64) such that each inner member shares a factor with either the first or the last member, 64 is an Erdős–Woods number. In base 10, no integer added to the sum of its own digits yields 64; hence 64 is a self number. 64 is a superperfect number—a number such that σ(σ(n)) = 2n. 64 is the index of Graham's number in the rapidly growing sequence 3↑↑↑↑3, 3 ↑^3↑↑↑↑3 3,... In the fourth dimension, there are 64 uniform polychora aside from two infinite families of duoprisms and antiprismatic prisms, and 64 Bravais lattices. The atomic number of gadolinium, a lanthanide Messier object M64, a magnitude 9.0 galaxy in the constellation Coma Berenices, also known as the Black Eye Galaxy. The New General Catalogue object NGC 64, a barred spiral galaxy in the constellation Cetus. In some computer programming languages, the size in bits of certain data types 64-bit computing A 64-bit integer can represent up to 18,446,744,073,709,551,616 values. Base 64 is used in with Base64 encoding and other data compression formats. In 8-bit home computers, a common shorthand for the Commodore 64 The ASCII code 64 is for the @ symbol The Nintendo 64 video game console and (historically) the Commodore 64.