Question 432964
{{{x^4 + 4 = (x^4 + 4x^2 + 4) - 4x^2

=  (x^2 + 2)^2 - 4x^2 = (x^2 - 2x + 2)(x^2 + 2x + 2)

}}}

For all natural numbers {{{x >= 2}}}, each of the two factors above is a positive integer greater than 1, hence the number itself is composite.  If x = 1, the number itself is {{{1^4 + 4 = 5}}}, which is prime.  The solution is complete.