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 be 0, because otherwise it would follow from claim 1 that each "f"("x") ("n" ∈ N) would be 0, which would contradict claim 2. Now, take a natural number "c" such that all three numbers "bc"/"k", "ck"/"x" and "c"/"x" are integers and consider the sequence Then On the other hand, it follows from claim 1 that which is a linear combination of "g" and "g" with integer coefficients. Therefore, each "g" is an integer multiple of "y". Besides, it follows from claim 2 that each "g" is greater than 0 (and therefore that "g" ≥ |"y"|) if "n" is large