Is it undecidable if the language of a given Turing Machine is the set of composite numbers?
Hint 1: Do you know Rice's theorem? It's the go-to result for any version of "Prove it's undecidable whether $L(M) =\,$ something."

Hint 2: You can reduce from "Does this TM accept everything?" You're given a Turing machine&nbsp;$M$ and you want to produce a new machine&nbsp;$T$ such that $T$&nbsp;accepts the set of composites iff $L(M)=\Sigma^*$. Have $T$&nbsp;reject its input if it's prime.  If the input is composite, use its factors to decide what input you'll feed to&nbsp;$M$. You need to do this in a way that every possible input to&nbsp;$M$ corresponds to some combination of factors of $T$'s input.

Hint 2.5: Alternatively, go from "Does this TM accept nothing?" Similar idea but now $T$ will accept if its input is composite and you'll use prime inputs to&nbsp;$T$ to code inputs to&nbsp;$M$. Actually, this one might be slightly easier to see.