Odd Barrel Marking......

[Roundsworth]

.....on my 12 gauge 1877 vintage Hammer/Lifter. I have identified all of the markings stamped on the barrel flats and lug of my gun, but am puzzled by the number 13 stamped beneath the right barrel, just forward of the flat area. Could this be a bore size? Would the shooter use paper cases with 13 bore wads? Oh, there is also a small diamond with the letter P inside of it on the right barrel. A proof mark? Cheers!