The Allies forbid the Germans from manufacturing pistols with barrels longer than 100mm and the standard for Alphabet commercial Lugers such as the OP's seems to have been 98mm or 3.86 inches. I recall reading somewhere that some barrels of 95mm were used but I can't find a reference for that. 95mm would be 3.74 inches so perhaps someone measured 3 3/4 inches and converted it to mm.
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