let l and m are positive integer solutions

then l+m=p and lm=q


therefore lm is a prime then l or m is a prime an d the other is 1

let l=1 then 1+ m=p

so m and p are 2 consecutive prime numbers

but we know that 2 and 3 are the only consecutive primes

then m=2 and l-1

so p=3 and q=2