Expressing the sum of primes as a function

I'd appreciate sum feedback on this expression for p the sum of primes. To evaluate consider is a prime then:

sin((pi*a)/b is only 0 when a is divisible by b

product of the above is 0 when a has any factors and approaches 0 from 1 when it has none as a goes to infinity

0\^0=1 and 0\^(a number approaching 0 from 1)=0

a*cos(pi/2)=0 for factorable numbers and a*cos(0)=a for primes

a starts at 3 so the sum of all primes over 3 plus 2 is the sum of all primes

So it's essentially a sieve in function form. Curious on thoughts? Thanks

Author: In_the_year_3535