Question 1074883
the discriminant is sqrt (144-4k), and this has to be a perfect square.
the root is 12+/- sqrt (144-4k) all divided by 2
prime numbers produced by 6+/- x occur when x is odd.  
they are limited to 5 and 7 as the roots, when the discriminant is 4, the sqrt of it= 2, and divided by 2 is 1.  For the discriminant to be 4, b^2-4ac has to be 4, and that occurs when k is  35.
other roots would be 4,8, neither prime
3 and 9, 2 and 10 don't work.
x^2-12x+35=0
{{{graph(300,300,-10,10,-10,10,x^2-12x+35)}}}