Do the primers differentiate between Gram-positive and Gram-negative bacteria?

Do the primers differentiate between Gram-positive and Gram-negative bacteria?

The Set of Eubacterial Sequencing primers

contains one primer, SeqGN16, which mainly targets Gram-negative bacteria,
and a second one, SeqGN16, which mainly targets Gram-positive bacteria.
But both sequencing primers show exceptions, a few Gram-negative species will be detected by the SeqGP16 and some Gram-positive species will be detected by the SeqGN16.
The exceptions of the sequencing primers are listed here.