64 (number)

64 (sixty-four) is the natural number following 63 and preceding 65.

Mathematics

Sixty-four is the square of

• the smallest number with exactly seven divisors,
• the first whole number (greater than one) that is both a perfect square, and a perfect cube.
• the lowest positive
  Fermat prime
  .

64 is the fourth superperfect number — a number such that σ(σ(n)) = 2n.^[3]

64 is the sum of Euler's totient function for the first fourteen integers.^[4]

The number of graphs on four labeled nodes is 64.^[5]

It is also the fourth dodecagonal number,^[6] and seventh centered triangular number.^[7]

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 the seventh Erdős–Woods number.^[8]

In decimal, no integer added to the sum of its own digits yields 64; hence, 64 is the tenth self number.^[9]

64 is the index of Graham's number in the rapidly growing sequence 3↑↑↑↑3, 3 ↑^{3↑↑↑↑3} 3, …

There are 64 total vertices in a 6-cube.

In the fourth dimension, there are 64 uniform polychora aside from two infinite families of duoprisms and antiprismatic prisms, and 64 Bravais lattices.^[10]

In other fields

Science

64 is the atomic number of gadolinium, a lanthanide.

64 is the number of

64 is the size in bits of certain data types in some computer programming languages, where a 64-bit integer can represent values up to 2⁶⁴ = 18,446,744,073,709,551,616.

• Base64 encoding
  , and other data compression formats.

Gaming

64 is the number of squares in a regular eight by eight chessboard.

64 is the maximum item stack size in Minecraft, where the number is called a 'stack'.

I Ching

The number of

See also

• Other powers of two: 4, 8, 16, 32, 64, 128, ...
• 64-bit computing

References