27689 is a 4k+1 prime and so it can be expressed as a sum of two squares in one way only viz. 133^2 + 100^2.

27689 is a number n with no repeating digits, whose additive digital (5) and multiplicative digital (0) roots are different from any of their digits and also from each other.

27689 can be rendered as a digit equation as follows:

2 = 7 - 6 - 8 + 9