-8- 6CCM320A (CM320X) SECTION D – Distribution of Prime
... (i) First, the number we are after is 3, whence the triple is (3, 11, 19). If p 6= 3, then it is necessarily not divisible by 3, hence either p = 3k +1 or p = 3k + 2. In the former case p + 8 = 3(k + 3) cannot be prime and in the latter case p + 16 = 3(k + 6) cannot be prime. (ii) Arguing by contrad ...
... (i) First, the number we are after is 3, whence the triple is (3, 11, 19). If p 6= 3, then it is necessarily not divisible by 3, hence either p = 3k +1 or p = 3k + 2. In the former case p + 8 = 3(k + 3) cannot be prime and in the latter case p + 16 = 3(k + 6) cannot be prime. (ii) Arguing by contrad ...