Proving the Riemann Hypothesis would somehow affect AI development indirectly. This would be possible because it would provoke several changes, such as: enhancing several methods that might help the AI systems from several perspectives, such as cryptography and algorithmic efficiency; providing new tools and systems by supporting mathematical discovery, promoting efficient machine learning and data optimization; and influencing complexity theory through the overcoming of new computational limitations by finding and optimizing new algorithms, for instance. As a result, this discovery would advance the field of mathematics and a better understanding of the laws of the universe; however, the ability to create a self-conscious algorithm relies on many more distinguishing points besides the proof of the Riemann Hypothesis.

It won't, because developing such algorithms doesn't rely on proving the Riemann hypothesis.

Cryptography doesn't rely on either the Riemann hypothesis, or on how to prove it. It relies on the difficulty of factoring large numbers into their prime factors.

The Riemann hypothesis is a statement about the distribution of primes; this doesn't affect factoring large numbers.