Hi Alan,
It doesn't appear in the original parish register for Swanton Morley, but does appear in the ATs on page 73 of 151 (last Baptism on the page) at Swanton Morley Archdeacons Transcripts. A few of the other entries also do not appear in the actual Parish Register and I wonder if that is how the name has been recorded as 'Partherman' rather than the standard Parfrement that appears elsewhere in the actual register.
While I cannot 'prove' that this is the Mary that married Edward Parish neither can I find any other unattached suitable candidate!
Regards
Mitch