# A survey on primes formulas

1. Mar 18, 2003

### eljose79

a survey on primes formulas....

let be the function a(x) defined as:

1 Iff x is prime
0 x is not prime

then appliying Abel,s summation formula.it would be

S(p)f(p)= c+I(0,Infinite)Pi(x)f´(x)

where f(x) is a differentiable function and S(p) means summ over all the primes....Pi(x) is the usual formula of a number of primes <or = x.....¿is this formula true?.

b)I think i have discovered a formula to summ all primes by using euler,s transformation to summ alternate series .
in fact if you take the serie with general term:

(-1)**n(Pi(n)-Pi(n-1))f(n) and apply Euler,s transformation you can find and approach to the summ of the series above and this series is equal to:

S(0,Infinite)(-1)**nf(n)+S(p)f(n) .

So you can obtain an approach to S(p)f(n).....