Show the (3^77-1)/2 is odd and composite.
(Hint: consider 3^77mod4 and the formula a^n-b^n=(a-b)(a^(n-1)+a^(n-2)*b+...+a*b^(n-2)+b^(n-1)) for any positive integers a, b, n).
I rewrote (3^77-1) as (3^77-1^77) and then in the form given in the hint, which when simplified turns the number into 3^76+3^75+...+3^1+3^0, but I'm not sure where to go from there, or how 3^77mod4 is useful.