In the context of discussing the status of the firstborn Israelites in the desert (see yesterday’s daf) the Gemara relates the following conversation:
A Roman general Kontrokos questioned Rabban Yoḥanan ben Zakkai. ‘In the detailed record of the numbering of the Levites, you find the total is twenty-two thousand three hundred, whereas in the sum total you only find twenty-two thousand. Where are the remaining three hundred?’ He replied to him: ‘The sum total includes only those Levites who redeemed the Israelite firstborn. The remaining three hundred were Levite firstborn, and a firstborn Levite cannot abrogate the sanctity of a firstborn Israelite.’ What is the reason? Abaye says: It is sufficient for a Levite firstborn to abrogate his own firstborn sanctity.
According to the initial counting by family, the families of Gershom numbered seven thousand and five hundred (see 3:22), the families of Kehat numbered eight thousand and six hundred (see 3:28), and the families of Merari numbered six thousand and two hundred (see 3:34), making a grand total of the families of the Levites of twenty-two thousand and three hundred. Nevertheless, when the number is totaled at the end of the counting, three hundred are missing (see 3:39). Rabban Yoḥanan ben Zakkai’s response is that this last number must be viewed as an introduction to the discussion that immediately follows in the Torah, whose focus is the need to exchange the levi’im for the firstborn bekhorim. According to the Talmud Yerushalmi, the reason for this exchange was the participation of the firstborn in sacrificing to the Golden Calf, something that the members of the Tribe of Levi did not do.
The Maharsha points out that this was not an innocent question asked by Kontrokos, rather it was an accusation that Moshe Rabbeinu had deliberately reduced the number of Levites so that more of the firstborn would need to pay the five shekel redemption fee (see the continuation of, Chapter 3), and Moshe’s brother Aharon and his children would benefit by means of this deception.