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It depends, rather obviously, on the serial No.
Robert quotes dates for the first two batches from 1957 and 1958 and the last batch dated Oct 1st 1960 (Olympic excepted).
By looking at the start date of production and serial 6300001 and the total production of 12,310 and Roberts batches and dates, it should be possible to date the camera to a specific batch and date.
See Page 138 of the Complete System last edition.
Gaps in the numbering do exist as the last serial known 6318306 does not correspond to the total known production.
I suppose it depends how precise you need to be. I am never clear if the batch date, precisely quoted by Robert, refers to the date the block was issued and production began or the date the block was finished and released, but that is getting very pedantic indeed. I "think" it refers to the completion date as he refers to batch two being completed on the date quoted.
The data is there you need the will to construct a table but due to gaps it may not be accurate.
Edit:
Just to add, using the "formula" my chrome S3 would be the middle of batch 5 completed 25/10/58
BUT the gaps are in the range of 6,000 serials so it is very much a best guess as that would comfortably push it forwards or backwards a batch. Which is why I suppose there is no table!!
Just to edit my edit !!
Any serial jumps from Nikon would ADD to the serial I said above push back, that could not happen. The issue is we know the dates f the blocks and the quantities but not the serials attached to the batches. Goodness knows why they "missed" so many numbers.