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Fix MathJAX, esp. { and } versus \{ and \}; catch a couple missing commas while here

Difficulty with "A new elementary proof of the Prime Number Theorem" by Richter

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?

rr_math
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