64 (number) it is possible to find sequences of 64 consecutive integers 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 up to its own digits yields 64, hence it is a self number. 64 is a superperfect number—a number such that σ(σ("n")) = 2"n". 64 is the index of Graham's number in the rapidly growing sequence 3↑↑↑↑3, 3 ↑ 3,… Sixty-four is: 64 (number) 64 (sixty-four) is the natural number following 63 and preceding 65. Sixty-four is the square of 8, the cube
Proof that π is irrational recursive integration by parts allows us to deduce that, if "a" and "b" are natural number such that = "a"/"b" and "f" is the polynomial function from [0,] into R defined by then: This last integral is 0, since "f" is the null function (because "f" is a polynomial function of degree 2"n"). Since each function "f" (with ) takes integer values on 0 and on and since the same thing happens with the sine and the cosine functions, this proves that "A"("b") is an integer. Since it is also greater than 0, it must be a natural number. But