I think you can be fairly sure that your watch was made in 1959 or so and certainly not in 1948. The 1601 reference was not made that early. The conflict comes because of the numbering system that Rolex used. When they reached the one millionth OYSTER CASE, they simply began again at zero. Some say 100,000 but we have seen many cases from the 50's with serial numbers with only 5 figures so this must not exactly be the case, rather that they started seemingly at zero again. Add a one for the millions place and the appropriate number of zeros to make a 7 digit number, in your case none, and that should get you very close. If you had a watchmaker remove the back there would likely be more information engraved on it by the factory. The watches from this period generally have Roman numerals I-IV and then a two digit Arabic number following that. This indicates the quarter 1st thru 4th that the watch was made during and then the year ie., 59 etc. Next time you have the watch serviced ask your watchmaker to write down this number and give it to you.

One other possibility is that because the watch is 18k and possibly worn at some point on a strap, the 7th digit may have been worn away slightly. Get a very powerful loupe and hold the watch at several angles in good light to see...there might be a 2,3,4, or 5 there indicating a later production but still before 77.

Best regards,