27677 is a product of two 4k+1 primes and so it can be expressed as a sum of two squares in two different ways viz. 11^2 + 166^2 and 74^2 + 149^2.

27677 is a number n such that n + POD(n) and n - POD(n) are both prime, here POD = 4116 and the primes are 31793 and 23561. See Bespoken for Sequence entry.

27677 is a cyclic and Duffinian number.

27677 can be rendered as a digit equation as follows:

2 = 7 - 6 + 7 / 7