Are Riemann hypothesis and Goldbach conjecture related?

In summary, the conversation discusses the relationship between the Riemann hypothesis (RH) and Goldbach conjecture. It is suggested that proving the RH would imply the Goldbach conjecture and vice versa. Additionally, there is a question about whether there exists a generating function for the number of ways a natural number can be split into a sum of r-primes, which could potentially aid in proving the Goldbach conjecture. It is also mentioned that proving the RH may also prove that there are infinitely many twin primes. However, at this time, there is no known result linking the two together.
  • #1
eljose
492
0
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)

[tex]\zeta(s)=0 [/tex] then [tex]s=1/2+it [/tex]

Goldbach conjecture,let be n a positive integer then:

[tex]2n=p1+p2 [/tex] , [tex]2n+1=p3+p4+p5 [/tex]

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..
 
Physics news on Phys.org
  • #2
an additional question, would proving the RH also prove that there are infinitely many twin primes
 
  • #3
As of now i don't think there is any result linking both together but you can always try.
good luck.
 

1. How are the Riemann hypothesis and Goldbach conjecture related?

The Riemann hypothesis and Goldbach conjecture are two famous unsolved mathematical problems that have been studied for centuries. While they are not directly related, they both deal with prime numbers and have connections through theorems and mathematical concepts.

2. Are there any similarities between the Riemann hypothesis and Goldbach conjecture?

Both the Riemann hypothesis and Goldbach conjecture involve prime numbers. The Riemann hypothesis deals with the distribution of prime numbers, while the Goldbach conjecture states that every even number can be expressed as the sum of two prime numbers. Additionally, both problems have been studied extensively by mathematicians and remain unsolved.

3. Can solving one problem lead to a solution for the other?

There is currently no evidence to suggest that solving one of these problems would lead to a solution for the other. While they have connections through mathematical concepts, they are distinct problems with their own unique challenges and approaches.

4. Has any progress been made towards solving these problems?

Many mathematicians have attempted to solve the Riemann hypothesis and Goldbach conjecture, but as of yet, no one has been able to find a definitive solution. However, there have been notable discoveries and advancements in understanding these problems, such as the proof of the weak Goldbach conjecture in 2013.

5. Why are the Riemann hypothesis and Goldbach conjecture considered important in mathematics?

The Riemann hypothesis and Goldbach conjecture are considered important because they have implications for other areas of mathematics. The Riemann hypothesis, if proven true, would have far-reaching consequences in number theory and could potentially lead to a better understanding of prime numbers. The Goldbach conjecture, on the other hand, has connections to other areas of mathematics such as probability and cryptography. Additionally, these problems have captivated mathematicians for centuries and their solutions would be a significant achievement in the field.

Similar threads

Very simple (Dis)proof of Riemann hypothesis, Goldbach, Polignac, Legendre conjecture
    • Linear and Abstract Algebra
Replies
2
Views
4K
Elliott-Halberstam conjecture and the Riemann Hypothesis
    • Linear and Abstract Algebra
Replies
1
Views
4K
Solution for Goldbach Conjecture
    • Linear and Abstract Algebra
Replies
6
Views
7K
I Connection of zeta to primes: less Euler than error or L-functions?
    • General Math
Replies
2
Views
1K
Extended Goldbach: every odd number the sum of 5 primes
    • Linear and Abstract Algebra
Replies
1
Views
3K
B Does this help solve the Riemann Hypothesis?
    • General Math
Replies
4
Views
1K
A Question About Prime Numbers and Goldbach's Conjecture
    • Linear and Abstract Algebra
Replies
6
Views
6K
Legendre and Riemann: A Conjecture Comparison
    • Linear and Abstract Algebra
Replies
6
Views
3K
(Not a Proof of) Goldbach's Conjecture
    • Linear and Abstract Algebra
Replies
6
Views
4K
MHB What is the Riemann Hypothesis?
    • Math Guides, Tutorials and Articles
Replies
10
Views
21K

Hot Threads

Recent Insights

Back
Top