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

Yes, this is another answer. Another alternative that includes the flavour of the Reap/Sow approach and the FoldList approach would be to use Scan.

result = {1};
Scan[With[{p=Prime[#]},If[PrimeQ[p+2],result={result,p}]]&,Range[2,K] ];
Flatten[result]

Again, this involves a long list of integers, but the intermediate Prime results are not stored because they are in the local scope of With. Because p is a constant in the scope of the With function, you can use With rather than Module, and gain a bit of speed.