One can get every prime which is NOT a Sophie Germain prime; that is to say, such that (p+1)/2 is not prime. Proof: if (p+1)/2 is not prime, then we can factor p+1 = xy. If p+1 is not prime, we can impose that x and y are greater than 2 and, since p is prime, it is not of the form x^2-1 (except for p=3). So we can take 2 < x < y.
Then take (a,b,c) = (1,x-1,y-1).
13 and 37 cannot be achieved.