Generate a list in Mathematica with a conditional tested for each element

Question

Suppose we want to generate a list of primes p for which p + 2 is also prime.

A quick solution is to generate a complete list of the first n

Answer 1

You can perhaps try something like this:

Clear[f, primesList]
f = With[{p = Prime[#]},Piecewise[{{p, PrimeQ[p + 2]}}, {}] ] &;
primesList[k_] := Union@Flatten@(f /@ Range[k]);

---

If you want both the prime p and the prime p+2, then the solution is

Clear[f, primesList]
f = With[{p = Prime[#]},Piecewise[{{p, PrimeQ[p + 2]}}, {}] ] &;
primesList[k_] := 
  Module[{primes = f /@ Range[k]}, 
   Union@Flatten@{primes, primes + 2}];