Sorry, I missed out 1 more consideration. Upon finding the 4 possible x values, you need to substitute inside x^2 - 32x - 273 to see if it gives you a negative integer. If it does, you have to reject that x value because negative integers cannot be prime. x=-6 and x=38 will give a negative integer, thus you have to reject them. Possible values of x is therefore -8 or 40.