All 499 even integers from 4 through 1000 have a Goldbach witness.
sample witnesses : 4=2+2; 28=5+23; 100=3+97; 998=7+991; 1000=3+997
The checker caches primes up to the configured bound and then searches each even number E for a prime P not greater than E/2 where E-P is also prime.
No counterexample is found in the bounded range, so the bounded Goldbach condition succeeds for this dataset.