#### Answer

$x^{2}+3x+1$
(sample answer)

#### Work Step by Step

If the trinomial $x^{2}+bx+c$ can be factored, it will be in the form $(x+n)(x+m)$, where
the product of integers n and m is $c$
their sum is $b.$
"Prime" means it has no factorization using integer coefficients.
Let c=1.
It can be factored if the sum, b, equals 2 or -2.
So, select any other integer for b, say 3:
$x^{2}+3x+1$
(sample answer)