I'm studying Richter's "A new elementary proof of the Prime Number Theorem" paper and I'm finding some problems understanding some parts of it. For example I don't see how to get, in Lemma 3.4, that we can find two non-consecutive $$a,b\in{0,...,K-1}$$ such that the intervals $$(8^{t+aε^4} , 8^{t+(a+1)ε^4} ], (8^{t+bε^4} , 8^{t+(b+1)ε^4}]$$contain at least $$O(\frac{ε^48^n}{n})$$ many primes. Here's the reference to the paper: https://arxiv.org/abs/2002.03255 Can someone help me?

I'm studying Richter's "A new elementary proof of the Prime Number Theorem" paper, and I'm finding some problems understanding some parts of it. For example, I don't see how to get, in Lemma 3.4, that we can find two non-consecutive $$a,b\in\{0,\ldots,K-1\}$$ such that the intervals $$(8^{t+aε^4} , 8^{t+(a+1)ε^4} ], (8^{t+bε^4} , 8^{t+(b+1)ε^4}]$$ contain at least $$O\left(\frac{ε^48^n}{n}\right)$$ many primes.

Here's the reference to the paper: https://arxiv.org/abs/2002.03255. Can someone help me?