KnowingD={p|p is a  polynomial evaluating to 0 for some assignment of integers to its variables} is not decidable, how can I prove that E={p|p is a  polynomial evaluating to a prime for some assignment of integers to its variables} is not decidable?Proving that D is mapping reducible or Turing reducible to E would be enough, since if D < E ( where < means mapping reducible), then E decidable => D decidable, and using the contrapositive we get D not decidable => E not decidable.Is showing that D is mapping or Turing reducible to E the right approach? I don't see how it can be proved. Thanks!
Proving the undecidability of a language knowing the language of polynomials evaluating to 0 is undecidable
turing machines;reductions;undecidability
Yes like you say, you have to show that an algorithm that solves $E$ can be used to solve $D$. A practical approach is to give a polynomial $p_E$ for every polynomial $p$ such that $p$ evaluates to $0$ iff $p_E$ evaluates to a prime number. 