64 (number) 64 (number) 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. 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 that is both a perfect square and a perfect cube. Since
Magic cube classes Perfect magic cube. Nasik; A. H. Frost (1866) referred to all but the simple magic cube as Nasik!<br> C. Planck (1905) redefined "Nasik" to mean magic hypercubes of any order or dimension in which all possible lines summed correctly.<br> i.e. Nasik is a preferred alternate, and less ambiguous term for the "perfect" class.<br>Minimum correct summations required = 13"m". All pan-"r"-agonals sum correctly for "r" = 1, 2 and 3. Alternate Perfect Note that the above is a relatively new definition of "perfect". Until about 1995 there was much confusion about what constituted a "perfect" magic cube (see the discussion under