Proving Riemann Hypothesis is a million dollar problem, but I am more interested in understanding its ramifications in the practical world. According to many sources, one such effect will be jeopardising the cryptography framework underlying the internet which enables us to use passwords and transfer private information.

According to Britannica

A proof of the Riemann hypothesis would have far-reaching consequences for number theory and for the use of primes in cryptography.

My question is why cant we assume the hypothesis true and go ahead with it? In other words why aren't hackers able to leverage RH yet ?

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    $\begingroup$ See this question for more discussion on the same topic: math.stackexchange.com/questions/3700497/… linked from that post is: math.stackexchange.com/questions/69540/… and math.stackexchange.com/questions/1272296/… (both very directly relevant to your question) $\endgroup$ Jul 29, 2021 at 19:47
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    $\begingroup$ Never trust the hype; people have proved results assuming RH for a century and more now, while in our times RH has been verified as far as computers go and still cryptography is safe at least from this $\endgroup$
    – Conrad
    Jul 29, 2021 at 19:48
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    $\begingroup$ Nothing is stopping a code breaker from assuming the RH is true, and get to work on cracking codes under that assumption, with all the consequences that has for prime distributions and factorisations. If that were enough to break modern cryptography, it would've happened already. $\endgroup$
    – Arthur
    Jul 29, 2021 at 20:52
  • $\begingroup$ Whether RSA is safe is another story. But whether the Riemann hypothesis is true or not is neither relevant for integer factoring nor for finding huge primes. Hence, the safety of RSA is utterly independent of the truth of the Riemann hypothesis. The dangers for RSA come from other directions. $\endgroup$
    – Peter
    Jul 30, 2021 at 8:27
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    $\begingroup$ @Arthur Not that I assume that someone has already broken RSA. But If someone does have success, I do not think that this will be discovered fast. Incidents can have many reasons and it will be difficult to find out whether an RSA break is responsible or not. And the security of RSA has anyway not been proven , not even that the enemy must factor the public number to break the code. $\endgroup$
    – Peter
    Jul 30, 2021 at 8:37


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