Only every time they claim a major mathematical breakthrough using regular expressions.

Nobody claimed that.

It's true, the article doesn't make that claim. We think of primes as being mysterious and out of reach, and we're conditioned to think "mathematical / computational breakthrough" when we read the words "prime number" in a headline, but this is only because we've found all of them that aren't huge enough to be mysterious. Computing prime numbers is trivial as long as you don't mind them being the same ones everybody else already found.

Not sure what you mean by "trivial", I mean a simple prime finding algorithm is easy to write down, but it will be very inefficient, especially for large primes (the very ones you use in cryptography).

Coming up with an efficient prime-finding algorithm like Miller-Rabin* is far from trivial.

* Technically it's just a prime-checking algorithm, but you can just generate random numbers until you've verified one of them is prime.

I do find it useful to know that regular expressions in JS(and many other languages really) are not actually regular and why - allows one to decide if a given problem can be solved at all using them.