Yes the numeric examples often don't work. The consequences of this though are similar to a failed web search. As in it's not a big deal and when it does work it's very helpful.

Maths is one of those things with so much objectivity that even the LLM usually realizes it has failed to create a numeric example. "Here the numeric example breaks down since we cannot find a congruence of squares in this example without finding more B-smooth numbers in step 1". Ok that's a shame, i would have loved to see an end to end numeric example.

I think people get too hung up on any possibility of LLMs not being perfect while still being extremely helpful.