What you have here is a "1956 6B/159 recase". I'd venture a guess that the serial number on the back is actually 3xxx/56 as I'm unaware of any of these being issued in 1959, although I freely admit I am not an expert!
Basically these Omegas started life in the 1940's with a light coloured face and black or blued(?) hands. In 1956 a whole pile of them were stripped down by a government contractor and had their movements put into somewhat larger cases. At the same time the dial was repainted black and the hands covered with white luminous compound. My understanding is that this was not done without Omega's knowledge, involvement, or blessing. So you could think of them as an "officially supplied frankenwatch" if you like. :)
Some good info here: http://www.mwrforum.net/forums/showt...6b-159-Watches
I'm sure someone with more details will be along shortly, but that's how I understand it...