I went down this rabbit hole numerous times, most recently looking at A&D pun's. Bottom line is - there is no consistency and thus you cannot use these numbers to date a gun, unless it's very early on or is one of the last numbers used before the expiration of a patent. Believe me.. I assembled databases, created graphs, did the research, looked over several popular patents. Don't even try to go there except for fun.
And by the way, the A&D patent expired on 10 May 1889 which should mean your gun is pre- that date. (Or at least the action was built before that date).
https://www.doublegunshop.com/forums/ubbthreads.php?ubb=showflat&Number=567037For what it's worth in my Reilly database of extant guns (and PUN's are rarely published in ads) the last known Reilly gun with a published/known A&D PUN is 30768 - E.M. Reilly & Co., 16, New Oxford Street, London. 12 ga. Shotgun SxS. BLE.
A&D patent use #8245. The Reilly SN dates per my chart to fall 1888. Reilly probably built another 300 box-locks between 30768 and the expiration of the A&D patent - those guns no longer exist or have yet to come to light.
And Chris, how about some information on your gun. That is always interesting; photos included.