Q13/093) Find twin primes p and q(=p + 2) such that pq-2 is also a prime

P q are twin primes so they are 3 and 5 or p = 6n+ 1 and q = 6n – 1

If p = 6n- 1 and q = 6n + 1 then pq - 2 = 6n^2 – 1 – 2 = 36n^2 – 3 = 3(12n^2-1)

it is > 3 (minimum value = 33)  and 3 is a factor so cannot be prime

That leaves us with p = 3 , q = 5 and pq-2 = 13 meeting the condition