Consider the following sum:
The summand is zero for non-primes, and finite and non-decreasing for primes
For more details see the key paper: Connes' paper on Wilson's theorem
Is there any way we can prove infinitude of primes using above series ?
I tried to attack this problem in my previous questions . I just posted this separately new question (without stating any of my work) to start fresh and expecting new methods and views from users .
Any suggestions and comments are welcome .
Possible unified Applications: We can apply it to other primes of special forms whose Infinitude is unknown. (as Γ is nicely analytic):