Most bekhorim customarily participate in a siyum masekhet (a festive ceremonial meal occasioned by the completion of a tractate of the Talmud) on Erev Pesaḥ after Shaḥarit. Afterward, refreshments are served to everyone in attendance, and the bekhorim present are permitted to partake, sharing in the joy of a se’udat mitzva and celebrating the mitzva of Torah study and the completion of the tractate. Since they break their fast with the se’udat mitzva, bekhorim are no longer obligated to fast.
However, poskim of past generations were divided over this custom. Some took a stringent position, ruling that only a bekhor who himself completed a tractate may partake of the se’udat mitzva, while other firstborns, who are not so connected to the joy of the siyum, may not break the fast by partaking in someone else’s se’uda. This is especially true when those completing the tractate do not hold a se’udat mitzva on such occasions during the course of the year, and the bekhorim as well do not generally attend their friends’ siyumim. By arranging a siyum for firstborns once a year on Erev Pesaḥ, it appears as though they are coming not to celebrate the mitzva, but to exempt themselves from the fast. Moreover, often the person making the siyum completed the tractate a week or two earlier and postponed the siyum until Erev Pesaḥ in order to exempt himself from fasting. According to the stringent opinion, it is improper to act in this manner, because the real joy is felt when one completes his study, not when he recites the last few lines so that he can make a siyum on Erev Pesaḥ (Teshuva Me-ahava 2:262; Noda Bi-Yehuda).
Nevertheless, the custom is to rely on the lenient poskim who rule that anyone who participates in the se’udat mitzva is exempt from fasting, even if he does not usually make or attend siyumim during the course of the year, and even if the siyum was delayed until Erev Pesaḥ. The simple reason for this is that when a masekhet is completed, it is fitting to celebrate, and this is therefore a se’udat mitzva. Moreover, Ta’anit Bekhorot is predicated entirely on custom, not on a binding enactment, and is not mentioned at all in the Bavli or by Rambam. Furthermore, some leading Rishonim were of the opinion that bekhorim are not obligated to fast on Erev Pesaḥ. This being the case, whenever there is a halakhic disagreement, the lenient poskim have the upper hand. What is more, in recent generations we no longer fast often, and if the bekhorim fast, their preparations for Pesaḥ will most likely suffer from the weakness it induces; they will even want to rush through the Hagada in order to get to the meal. Therefore, many leading rabbis would exempt themselves from the fast via a siyum. Only one who knows that the fast will not impair his preparations for Pesaḥ or his fulfillment of the mitzvot of Seder night may act stringently and fast on Erev Pesaḥ. Indeed, Rav Kook and his son R. Tzvi Yehuda, both of whom were firstborns, customarily fasted on Erev Pesaḥ.
The type of siyum that exempts its participants from fasting is one that marks the completion of a tractate of the Bavli or Yerushalmi, an entire seder of Mishna, or a significant Torah work. The study must involve real understanding.
Completing the intensive study of a book of Nevi’im is also a se’udat mitzva (Igrot Moshe OḤ 1:157). It seems that anyone who finishes one of the four sections of Shulḥan Arukh or a significant Torah work can also make a se’udat mitzva, since making a siyum was never essentially limited just to a tractate of the Bavli; see Ḥavot Ya’ir §70. A siyum on a Torah work that learned society deems significant exempts all participants in the siyum from fasting. But when the siyum is on a work that is significant to the one who studied it but not so significant in the general eye, only the one who makes the siyum can make a se’udat mitzva and exempt himself from fasting. Thus, one who is just beginning to study Torah and has difficulty learning a tractate of Mishna in depth may make a siyum on completing a superficial study of a tractate of Mishna or a book from Tanakh, but others are not exempted from fasting by his siyum. See Yabi’a Omer OḤ 26, Piskei Teshuvot 470:9.