What are the implications of this?
The new work has no immediate applications, although understanding large prime gaps could ultimately have implications for cryptography algorithms. If there turn out to be longer prime-free stretches of numbers than even Cramér’s conjecture predicts, that could, in principle, spell trouble for cryptography algorithms that depend on finding large prime numbers, Maynard said. “If they got unlucky and started testing for primes at the beginning of a huge gap, the algorithm would take a very long time to run.”
Wouldn't it also mean that the first prime after such gaps will be selected more often, assuming a random starting point for prime searches? That might be a bigger problem than having to wait longer for the selection to finish.
(The "noise threshold" is provided by the fact that processors are not in fact 100% accurate, but do indeed have a low-but-non-zero error rate. When the probability of a randomized algorithm failing drops below the probability that the processor literally got the computation wrong, it ceases to matter in practice. And one could argue it ceases to matter even before that, but it certainly ceases to matter at that point. Hence I call it the "noise floor". It's so low we are used to just assuming it is zero, but in fact it is not.)