Your understanding is skewed because the source you are reading
doesn't make it clear at all.
There would be no four-digit Model 51 serial numbers without
an M prefix, that is correct. You said yours has an M prefix.
The Model 51 serial number series from 1960 to 1969 supposedly
ended at 135465. Other models also used that series.
The new serial number series began in 1969 at M1 and went up
from there for the Model 51 until it was discontinued in 1974, but
the M serial numbers continued on after that for the other models
using the M prefix. The M series serials ended in 1983 when all
S&Ws were converted to the new alphanumeric serial number
system.