Primes and the function $\displaystyle\prod_{\substack{p \in \mathbb{P}}} \Big( {\normalsize 1-\left(\frac{z-1}{p-1}\right)^2}\Big)$

Question

I wrote 3 articles about prime numbers construction, and i found a relation between gaps of $d$ consecutif primes and those functions $F(z) = \displaystyle\prod_{\substack{p \in \mathbb{P}}} \Big( {\normalsize 1-\frac{z^2}{p^2}} \Big)$ and $C(z) = \displaystyle\prod_{\substack{p \in \mathbb{P}}} \Big( {\normalsize 1-\left(\frac{z-1}{p-1}\right)^2}\Big)$.

I like to know if those functions are studied before ..

http://lagrida.com/prime_numbers_construction.html

http://lagrida.com/Fondamentale_Conjonctures_Prime_Numbers.html