I emailed one of the most known vintage Rolex dealers (Interview of him on Hoodink@@)with a request to find me a 1976 5513. Here is his reply.
"4,4XX,XXX serial are all replacement cases and I can't recall every finding a 5513 off the top of my head from that SN range. That being said, watches are made in batches by Rolex, so quite possibly none fall in that range."
This is the correct answer.. Just like during 2009 recently there were no new serial prefixes released.
Internet charts used to find a "1976" will give you false information. Charts are interpolations of a few numbers reported throughout the years, then they are simply filled in by guessing.. It is likewise guessing to state that "Rolex must have sold only a few that year".
Rolex stamps cases or allocates numbers to cases, then they are tossed into a warehouse until needed. There is no real way to "know" when a watch was actually manufactured as Rolex has never released that information..
Regarding the 4.4xxxxx numbers and 4.7xxxxx numbers, since those were allocated as replacement case numbers, Rolex would have skipped over that entire range during a production run, so for your target year you will need to look earlier or later (do some math, discounting the notoriously innacurate charts) and then feel comfortable that you did your best research and found your "tgarget" watch.. :cheers: