Are Riemann hypothesis and Goldbach conjecture related?

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SUMMARY

The Riemann Hypothesis (RH) and the Goldbach Conjecture are two significant unsolved problems in number theory. The Riemann Hypothesis posits that all non-trivial zeros of the Riemann zeta function, ζ(s), lie on the critical line s = 1/2 + it. The Goldbach Conjecture asserts that every even integer greater than two can be expressed as the sum of two prime numbers. While there is currently no established result linking the two conjectures, exploring generating functions for the partitioning of natural numbers into sums of prime numbers may provide insights into their potential relationship.

PREREQUISITES
  • Understanding of the Riemann zeta function and its properties
  • Familiarity with prime number theory
  • Knowledge of number partitioning concepts
  • Basic grasp of mathematical conjectures and proofs
NEXT STEPS
  • Research the implications of the Riemann Hypothesis on prime distribution
  • Explore generating functions related to prime partitions
  • Study existing proofs and attempts related to the Goldbach Conjecture
  • Investigate connections between analytic number theory and combinatorial number theory
USEFUL FOR

Mathematicians, number theorists, and students interested in advanced mathematical conjectures and their interrelations.

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

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