388 = 22 x 97.
388 has a representation as a sum of two squares: 388 = 82 + 182.
The number 388 followed by 388 sevens is a prime number.
388 is the maximum value of n so that there exist 6 denominations of stamps so that every postage from 1 to n can be paid for with at most 6 stamps.
The Junkers Ju 388 was a German World War II aircraft.
Source: Prime Curios!