68 (number)

68 is a composite number; a square-prime, of the form (p2, q) where q is a higher prime.

[2] All higher even numbers that have been checked are the sum of three or more pairs of primes; the conjecture that 68 is the largest number with this property is closely related to the Goldbach conjecture and, like it, remains unproven.

[3] Because of the factorization of 68 as 22 × (222 + 1), a 68-sided regular polygon may be constructed with compass and straightedge.

[4] There are exactly 68 10-bit binary numbers in which each bit has an adjacent bit with the same value,[5] exactly 68 combinatorially distinct triangulations of a given triangle with four points interior to it,[6] and exactly 68 intervals in the Tamari lattice describing the ways of parenthesizing five items.

[14] It is a happy number, meaning that repeatedly summing the squares of its digits eventually leads to 1:[15]