The Guardian reports today, in an article with an over-the-top title of Maths holy grail could bring disaster for internet, that 2 of the seven millenium problems, the Riemann Hypothesis and the Pincaré Conjecture may have been solved.
The article links a proof of the Riemann Hypothesis, to knowing more about primes, to cracking of codes based on prime numbers. This is tenuous at best. Yes, the proof may lead to further understanding of primes, but why that means that the codes become useless is beyond me. There are many results which depend on the Riemann Hypothesis (they say things like assuming the Riemann Hypothesis is true then …) so knowing the Riemann Hypothesis is true just makes these results true. If one of these results had led to cracking of codes it would be known about now.
On the other hand if someone shows that the Riemann Hypothesis is false, then that would cause a drastic rethink in many areas of mathematics.