Kommentar zu Bamidbar 3:48

As a redemption for those whose numbers are in excess. The meaning of this is that one must give specifically for the intention of redemption. The same applies for future generations — if one gave five silver coins to the Kohein and did not specify that they are for the redemption of the firstborn, he did not fulfill his obligation.

ונתת הכסף לאהרן ולבניו, “you are to give the money to Aaron and his sons; just as the Levites who had redeemed the firstborn now took the place of them, so the money realized from the 273 firstborn for whom no Levites were found to redeem them, now was given to the priests, seeing that the Levites themselves were also subservient to the priests.