Pythagoras Triplet

From a^2 + b^2 = c^2
If a = prime, then c = b+1, or p^2 + b^2 = (b+1)^2
If a not prime, b & c shall be prime except: 3 set of triplet (for first 100 number)
i.e. 56, 33, 65
      63, 16, 65
      77, 36, 85

The plot of p & a is highly correlation.
But the plot of a & b for non-prime quite scatter.