According to this thread the 3837004 indicates a 56 or 57 engine block. The 1266 would indicate either Jan 26 '56 or Dec 6 '56 date. The serial number F prefix indicates it was made in the Flint Factory, and the A suffix means it was originally installed in a car and would have hydraulic lifters. No idea on the SPECIAL casting.

Kevin
1951 Chevy 3100 work truck
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1929 Ford pickup restored from the ground up. | 1929 Ford Special Coupe (First car)
Busting rust since the mid-60's
If you're smart enough to take it apart, you darn well better be smart enough to put it back together.