@ErickWong I see that my question is not valid G(p) is must be less than $\frac{1}{3}$ I would be double counting a ton if it were greater. But if there exist a function G(p) that does removes all of the multiples it will need to be greater than or equal to $\frac{const}{\frac{(p+2)^2-1}{2}}$ as 'p' heads towards infinity. If G(p) is equal to that barrier there are a set of twin primes capped at 'const'. Thank you for the constructive feedback

So basically you’re getting into the rudiments of sieve theory, which was first developed by Brun a century ago to study twin primes, and remains an active area of research (recent breakthroughs by Zhang and Maynard have come closer to proving twin primes than I’d dreamed of). The basic idea follows the same pattern of inclusion-exclusion, with alternating adding and subtracting diffrernt