In an anlaogy with the Euler product of the Riemann function we make:(adsbygoogle = window.adsbygoogle || []).push({});

[tex] \prod_{p}(1+e^{-sp})=f(s) [/tex] of course we have that:

[tex] f(p1+p2+p3)=f(p1)f(p2)f(p3) [/tex] f(x)=exp(-ax) if Goldbach Conjecture is true then p1+p2= even and p5+p6+p8=Odd for integer n>5? then this product should be equal to:

[tex] f(s)=\sum_{n=0}^{\infty}a(n)e^{-sn} [/tex] where the a(n) is the function that tells in how many ways and odd or even number can be descomposed as a sum of 2 or 3 primes, we now define:

[tex] A(x)=\sum_{n=0}^{x}a(n) [/tex] if a(n)=1 for every n then using Perron formula we get that A(x)=[x] (floor function) so we would have that:

[tex] f(s)=(1-e^{-s}) [/tex] then if correct take numerical values to proof that the product and f(s) are equal.

**Physics Forums | Science Articles, Homework Help, Discussion**

Join Physics Forums Today!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

# Euler product and Goldbach conjecture

**Physics Forums | Science Articles, Homework Help, Discussion**