Why can't mathematica tell me the smallest prime number?

Question

I entered

MinValue[{Prime[n], n>=1 && Element[n, Integers]}, n]

But I just got back what I entered. Why can mathematica not tell me the smallest prime is 2?

Even

MinValue[{Prime[n], 1<=n<=10 && Element[n, Integers]}, n]

seems to be beyond it, which is bizarre since it only has to check 10 values.

Answer 1

Presumably the problem is that the derivative of Prime is undefined in Mathematica

D[Prime[n], n]

(*  Derivative[1][Prime][n]  *)

Use NMinValue

NMinValue[{Prime[n], 1 <= n}, n, Integers]

(*  2.  *)

NMinValue[{Prime[n], 1 <= n, Element[n, Integers]}, n]

(*  2.  *)

Round to taste.