There are some discrepancies in the case numbering system that have been discussed many times here. Since you seem to be "new" to the hobby I will try and go over a bit of it again for your benefit. When Rolex reached the 1,000,000th oyster case, they simply started over at O. Some reports say they started over at 100,000 but obviously by your watch and others like it we see that this is untrue. They did generally date the cases on the inside of the case back. Yours should have some marking with a Roman numeral I-IV and then 55 to indicate that it was made during one of the 4 quarters of the year 1955. An easy way to approximate this without opening the case is just to add a 1 and the appropriate amount of zeros to make a 6 place serial number. I know this to be the case with your watch without seeing it because the perpetual movement was not issued until 1934 some 4 or 5 years later than your case number in its present state would indicate. Is your case solid or a "shell" case. The shell is a 14k overlay or shell over a stainless case. This would be assertained by seeing if the lugs were silver or gold on the back and also the case back itself. If it is solid your case could be either 18, 14, or 9 karat. The appropriate band would be a rivited oyster bracelet or an older jubilee style in the appropriate carat content. There are a few different sizes of cases during that era with perpetual movements so you would want to be sure to get the correct measurements of the space between the lugs to get the proper fit. It is likely between 17mm and 20mm. Hope this helps.