Very simple (Dis)proof of Riemann hypothesis, Goldbach, Polignac, Legendre conjecture

In summary, the conversation discussed a claimed disproof of the Riemann Hypothesis, which included undefined variables and unjustified equalities. It also mentioned the Goldbach, Polignac, and Legendre conjectures in relation to the disproof. The validity and accuracy of the disproof were questioned and further calculations were suggested.
  • #1
choe
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(Dis)proof of Riemann hypothesis,Goldbach,Polignac,Legendre conjecture

I'm just an amateur and not goot at english ^^;
 

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  • #2
wwwconjec

wwwww
 
  • #3


In your claimed disproof of the Riemann Hypothesis, introduction:

1. Line 2: i is undefined.
2. Line 3: j is not properly defined; is this counted with or without multiplicity?
3. Line 4, third equality: Since D_i is finite and the expression in the sum is constant wrt n, the sum diverges and thus is not equal to the preceding expression which is convergent for all s with Re(s) > 1.
4. Line 4, fourth equality: The sum is not equal to the zeta function for any real s > 2, which can be verified by subtracting the series. (More precise results are possible; I don't care to calculate them.)
5. Line 6: The equality is totally unjustified and usually wrong.
 

1. What is the Riemann hypothesis?

The Riemann hypothesis is a famous unsolved problem in mathematics that deals with the distribution of prime numbers. It states that all non-trivial zeros of the Riemann zeta function lie on the critical line of 0.5+it, where t is a real number.

2. How does the Riemann hypothesis relate to the Goldbach, Polignac, and Legendre conjectures?

The Riemann hypothesis is closely related to these other conjectures because it provides a deeper understanding of the distribution of prime numbers. These conjectures all deal with patterns and relationships among prime numbers, and a proof of the Riemann hypothesis would provide insights into these patterns.

3. What is the significance of proving the Riemann hypothesis, Goldbach, Polignac, and Legendre conjectures?

Proving these conjectures would have major implications in mathematics. It would provide a deeper understanding of prime numbers and their distribution, which has many practical applications in fields such as cryptography and number theory. It would also contribute to solving other long-standing mathematical problems.

4. How does the (dis)proof of these conjectures impact the wider scientific community?

The (dis)proof of these conjectures would have a significant impact on the wider scientific community, particularly in the field of mathematics. It would open up new avenues for research and potentially lead to the development of new mathematical tools and techniques. It would also generate excitement and interest among mathematicians and inspire them to tackle other difficult problems.

5. What progress has been made towards proving these conjectures?

There have been many attempts to prove these conjectures over the years, but none have been successful so far. However, there have been some breakthroughs and progress made in related areas of mathematics, which have shed more light on these conjectures. Many mathematicians continue to work on these problems, and it is possible that we may see a proof or (dis)proof in the future.

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