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I ask myself for many years without ever having answers that suit me.

What impact would Riemann's conjecture if it had to be demonstrated as a whole? What would be the impact on our lives?

I already know that the Riemann hypothesis holds its importance in number theory, particularly on prime numbers.

The Riemann hypothesis is one of seven Millenium problems, a reputed insurmountable mathematical challenge posed by the Clay Mathematics Institute in $2000$. One of the criteria why the institute has chosen seven problems was that the resolution would be a great interest to advance mathematics and society.

Can you share me your opinion on this question?

P.S. I already know there exists a similar question : Proving the Riemann Hypothesis and Impact on Cryptography and What is so interesting about the zeroes of the Riemann $\zeta$ function?. However, the question is not exactly the same.

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    $\begingroup$ The Riemann Hypothesis has no impact on RSA/criptography/secutiry whatsoever since it although predicts stuff about the distribution of primes, it doesn't say anything about methods of factorization. RSA is powerful because factoring numbers that are a product large primes is computationally difficult, and nothing short of an algorithm that finds prime factors of a given number faster will break it. $\endgroup$
    – Felipe Jacob
    Nov 7, 2015 at 0:04
  • $\begingroup$ RSA is by no means the most important real world cryptographic system. $\endgroup$
    – André Nicolas
    Nov 7, 2015 at 0:06
  • $\begingroup$ Extremely similar question: math.stackexchange.com/questions/1272296/… $\endgroup$
    – pjs36
    Nov 7, 2015 at 0:09

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Notwithstanding Godel's proof, it would be another instance that if a conjecture seems true, it will eventually be proven to be so. I put this in the same class as the Collatz conjecture. Ed Gray

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