Quadratics with primes!

If the zeroes of the quadratic polynomial $f(x)=x^{2}+bx+c$ are prime numbers such that the $x$ -coordinate of vertex of curve of $y=x^2+bx+c$ is not an integer. And if $f(7)>0$ and $4(5+b)+c<4$ , then find the values of $b$ and $c$ .