Suppose is coprime with . Then every potential typical primality radius of is a multiple of . But as is a multiple of less than , and is a multiple of less than , it follows that and can’t be potential typical primality radii of since each of them shares with a residue class mod for .
Hence (since one has at least different Goldbach gaps, namely of size , or ).
The same reasoning can be applied for even and coprime with by replacing with and with .