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Shulchan Aruch O.C. 470:1 codifies that firstborns fast on Erev Pesach. In my experience, the widespread practice is for firstborns to attend a siyum of the completion of a tractate of Talmud, usually at a local synagogue, and then not fast.

I am planning on starting a synagogue, and I want things to be very organized. This includes having things set up so that there will be someone to make a siyum every Erev Pesach. To make things easier, I only want to have to find someone to make a siyum if there is not already someone to make one.

Given that there is a worldwide program of people studying Daf Yomi, it should be built into the calendar that there is someone to make a siyum every couple of months or so (depending on the varying lengths of tractates). Surely, some of these would coincide with Erev Pesach.

I want to be able to calculate how often this would happen. To keep it simple, I am only interested in cases where the tractate is finished exactly on Erev Pesach. I want to plan in advance as much as possible, so I am thinking about years and even decades into the future as well.

Is there any (relatively) simple way to make this calculation? Has someone already made it? Or will I have to sit with a Daf Yomi calendar and manually check every Erev Pesach?

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    On average it's about 5-6 siyum days per year and one erev pesach. So 6/365 is about one and a half percent of years where they match. About once a century. Not so common. – Double AA Jan 5 '20 at 16:44
  • @DoubleAA I suppose that's true in theory, but how would I know if it works out that way in the actual calendar? – Alex Jan 5 '20 at 16:48
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    The only way is to check every case. Maybe someone's already done it or has a computer program that can do it quickly. But there's no math trick. These cycles are entirely independent of each other. – Double AA Jan 5 '20 at 16:52
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    You can check here, for year by year basis. dafyomi.org/machzor.php or here: dafyomi.co.il/calendars/calendar.htm – IsraelReader Jan 5 '20 at 17:34
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    Good luck on the synagogue, anyways! – Dr. Shmuel Jan 5 '20 at 20:00
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I wrote a program using scripts I wrote for TorahCalc that will calculate when this will happen.

Having it end up on the exact date is very rare. Here are the dates for the next 1,000 years where Nissan 14 will be the last day of the masechta:

Mon Mar 31 2064 / Nissan 14 5824 - Kerisus 28
Mon Apr 24 2119 / Nissan 14 5879 - Kesuvos 112
Wed Apr 23 2138 / Nissan 14 5898 - Erchin 34
Mon Apr 03 2311 / Nissan 14 6071 - Beitzah 40
Mon Apr 15 2329 / Nissan 14 6089 - Bava Batra 176
Sat Mar 27 2393 / Nissan 14 6153 - Moed Katan 29
Sat Apr 16 2546 / Nissan 14 6306 - Chulin 142
Wed Mar 30 2591 / Nissan 14 6351 - Kerisus 28
Wed Apr 22 2646 / Nissan 14 6406 - Kesuvos 112
Fri Apr 21 2665 / Nissan 14 6425 - Erchin 34
Wed Apr 27 2727 / Nissan 14 6487 - Chagigah 27
Wed Apr 07 2821 / Nissan 14 6581 - Temurah 34
Wed Mar 31 2838 / Nissan 14 6598 - Beitzah 40
Wed Apr 23 2977 / Nissan 14 6737 - Me'ilah 37

If you are interested in any time where the end of a masechta is within a week of Erev Pesach, here are the dates for the next 100 years:

Sat Mar 27 2021 / Nissan 14 5781 - Shekalim 6 (Pesachim ends 5 days before E.P.)
Wed Apr 05 2023 / Nissan 14 5783 - Sotah 7 (Nazir ends 6 days before E.P.)
Sat Apr 12 2025 / Nissan 14 5785 - Makkos 4 (Sanhedrin ends 3 days before E.P.)
Mon Apr 07 2031 / Nissan 14 5791 - Bava Kama 2 (Kidushin ends 1 day before E.P.)
Fri Apr 04 2042 / Nissan 14 5802 - Nidah 66 (Nidah ends 7 days after E.P.)
Wed Apr 18 2057 / Nissan 14 5817 - Shabbos 2 (Berachos ends 1 day before E.P.)
Fri Mar 28 2059 / Nissan 14 5819 - Chagigah 6 (Moed Katan ends 5 days before E.P.)
Mon Apr 04 2061 / Nissan 14 5821 - Bava Kama 113 (Bava Kama ends 6 days after E.P.)
Mon Mar 31 2064 / Nissan 14 5824 - Kerisus 28 (Kerisus ends on E.P.)
Wed Mar 26 2070 / Nissan 14 5830 - Horayos 11 (Horayos ends 3 days after E.P.)
Wed Apr 03 2080 / Nissan 14 5840 - Eruvin 99 (Eruvin ends 6 days after E.P.)
Wed Apr 23 2081 / Nissan 14 5841 - Ta'anis 24 (Ta'anis ends 7 days after E.P.)
Fri Mar 29 2086 / Nissan 14 5846 - Bechoros 54 (Bechoros ends 7 days after E.P.)
Wed Mar 31 2094 / Nissan 14 5854 - Berachos 6 (Nidah ends 5 days before E.P.)
Fri Apr 06 2096 / Nissan 14 5856 - Moed Katan 3 (Megilah ends 2 days before E.P.)
Wed Apr 13 2101 / Nissan 14 5861 - Temurah 32 (Temurah ends 2 days after E.P.)
Mon Apr 03 2102 / Nissan 14 5862 - Shabbos 156 (Shabbos ends 1 day after E.P.)
Sat Apr 21 2103 / Nissan 14 5863 - Sukkah 51 (Sukkah ends 5 days after E.P.)
Fri Mar 31 2113 / Nissan 14 5873 - Bava Metzia 6 (Bava Kama ends 5 days before E.P.)
Wed Apr 06 2118 / Nissan 14 5878 - Beitzah 38 (Beitzah ends 2 days after E.P.)
Mon Apr 24 2119 / Nissan 14 5879 - Kesuvos 112 (Kesuvos ends on E.P.)
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    As predicted, it's about one and half percent of years – Double AA Nov 8 '20 at 0:26

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