Conjecture no. 8 – Another conjecture relating to the Sophie Germain Primes

The equation P, P+2x=Ap +B where all constants are positive integers and all x values are also positive integers,the GCD of (a,b)=1 , b-a if b>a or a-b if a>b /= 2x so that when a prime is prime for both P, P+2x and where x is an even number or odd there also exists two primes of both P,P+2x for Ap+B ,there is infinitely many such primes. For example, take the equation 2p+1. We will explain below how this works. 2p+1=3,3+2(1) where p= (3,5) so 2(3)+1=7 and 2(5)+1=11 where both ( 7,11) are primes. As always, I welcome my readers to try and prove this fact. I will also link the wikipedia articles necessary to understand my conjecture. https://en.wikipedia.org/wiki/Dirichlet%27s_theorem_on_arithmetic_progressions https://en.wikipedia.org/wiki/Sophie_Germain_prime https://en.wikipedia.org/wiki/Polignac%27s_conjecture https://en.wikipedia.org/wiki/Cousin_prime Thank you Nunghead