In[1]:= HanteiQ[n_] :=
  Block[{m = n^2},
   PrimeQ[m + 1] && NextPrime[m + 1, 4] == m + 13 &&
    NextPrime[m + 13] == m + 27];
Total[Select[Range[10, 150000000, 10], HanteiQ]] // Timing

Out[1]= {515.804, 676333270}