Related for Bekhorot 115:41

What does it mean "half [פרס]" before Passover and "half [פרס]" before Pentecost and "half [פרס]" before of Tabernacles? R. Yose the son of R. Yehuda says: Not less than fifteen days before the [relevant] pilgrimage festival. And why is it written on the baskets [which contain the shekels in the temple] "Alef, Beit, Gimel"? They write "Alef, Beit, Gimel" on it, because they started with the first and bring out of it. When the first was empty, you bring out from the second. When the second was empty, you bring out from the third. When all three were empty, and the time came to separate the [next] appropriation, one gives from the new, but if not, from the old one.

[If] the portion of the Shekalim fell [as part of the normal cycle] next to Adar, either before it or after it, we read it [at its normal time] and then we read it a second time [for purposes of Purim], and so two for the second [portion], and so too for the third, and so too for the fourth. And so too for Chanukah (בחנוכה not בפורים). They ask about the halachot of Passover on Passover, and the halachot of Shevuot on Shevuot, and the halachot of Sukkot on Sukkot. In the study hall they ask about the halachot of Passover thirty days before Passover. Rabban Shimon ben Gamaliel says, two weeks.