What exactly is the negation of Goldbach's Conjecture? The glib answer is:

Not( $\forall{\quad}n\geq{2},{\quad}\exists{\quad}p{}rimes{\quad}p,q{\quad}s.t.{\quad}p+q=2n.)$

But what does this really mean? If you are tempted to write

$\forall{\quad}n\geq{2},{\quad}there{\quad}do{\quad}not{\quad}exist{\quad}p{}rimes{\quad}p,q{\quad}s.t.{\quad}p+q=2n$