# Are Riemann hypothesis and Goldbach conjecture related?

1. Aug 24, 2005

### eljose

this is a question i have i mean are RH and Goldbach conjecture related? i mean in the sense that proving RH would imply Goldbach conjecture and viceversa:

RIemann hypothesis: (RH)

$$\zeta(s)=0$$ then $$s=1/2+it$$

Goldbach conjecture,let be n a positive integer then:

$$2n=p1+p2$$ , $$2n+1=p3+p4+p5$$

with p1,p2,p3,p4 and p5 prime numbers...

Another question is there a generating function for the number of ways a natural number can be split into a sum of r-primes?....
this would be interesting because if existed with r=2 and r=3 it would aid to prove Goldbach conjecture..

2. Aug 24, 2005

### nate808

an additional question, would proving the RH also prove that there are infinitely many twin primes

3. Aug 24, 2005

### hello3719

As of now i don't think there is any result linking both together but you can always try.
good luck.