ClearAll[GoldbachFuncion]
GoldbachFuncion[e_Integer] := Module[{ps},
  ps = Prime[Range[PrimePi[e/2]]];
  Total[Boole[PrimeQ[e - ps]]]
]
Grid[Partition[GoldbachFuncion /@ Range[4, 220, 2], 10]]
GoldbachFuncion[10^6]
DiscretePlot[GoldbachFuncion[e], {e, 4, 2000}, Filling -> None]