Who knows thirteen?
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13 are the midos of Yishmael.
(Obvious, but it fits the rhythm!)
13 are the "mechilin" in Aramaic to correspond to any 13 "midos" in Hebrew, which we usually translate as "measures." If exegetic techniques are considered "measures", that explains why the exegetic work on Exodus is called the Mechilta.
Thirteen are the shofaros* in the Beis Hamikdash (Mishnah, Shekalim 6:5).
* Money boxes, shaped like a shofar (narrow on top, wide on the bottom, to prevent theft of the contents). They were used for various kinds of contributions to the Beis Hamikdash and its operations.
Thirteen months in a Jewish leap year.
Thirteen are the number of covenants associated with bris milah (Nedarim 31b).
Thirteen years for a boy to be bar mitzva
There are 13 Ani Maamins
There were thirteen men born mahul as listed in the Medrash Tehilim chapter nine.
אדם הראשון. שת. חנוך. נח. שם. תרח. יעקב. יוסף. משה. שמואל. דוד. ישעיה. ירמיה.
Thirteen are the number of knots and strings on each corner of the tzitzis (5 knots, 8 strings (four doubled over)).
Thirteen is the Gematria of Ehad, ...which leads us back to... Bas613's answer at Echad - mi yodeya? ! (Thank you Shalom! My short term memory is not doing too well these days!)
1) 13 middos of HaShem (hashem, hashem, kel rachum...)
Thirteen at which Yishmael had Bris Mila. בראשית י״ז , כה
Thirteen(th) is the Maalah tovah that He gave us the Torah. (Haggadah Shel Pesah) (Doesn't fit the meter perfectly but you can squeeze it in better than my Zaidy used to squeeze in half of Kol Mikadesh Shivi'i and Baruch Hashem Yom Yom into their respective tunes!)
13 is the number of tribes which Eretz Israel will be divided in the future (Bava Basra 122a).
Thirteen is the number of young bulls that are offered on the alter on the 1st day Sukkot 13You shall offer up a burnt offering, a fire offering for a spirit of satisfaction to the Lord: thirteen young bulls, two rams, fourteen lambs in the first year; they shall [all] be unblemished.
במדבר כט י״ג אִשֵּׁ֨ה רֵ֤יחַ נִיחֹ֨חַ֙ לַֽיהֹוָ֔ה פָּרִ֧ים בְּנֵֽי־בָקָ֛ר שְׁלשָׁ֥ה עָשָׂ֖ר אֵילִ֣ם שְׁנָ֑יִם כְּבָשִׂ֧ים בְּנֵֽי־שָׁנָ֛ה אַרְבָּעָ֥ה עָשָׂ֖ר תְּמִימִ֥ם יִֽהְיֽוּ:
The people of Chedorlaomer served him for twelve years then rebelled against him in the thirteenth year.
בראשית יד ד
שְׁתֵּ֤ים עֶשְׂרֵה֙ שָׁנָ֔ה עָבְד֖וּ אֶת־כְּדָרְלָעֹ֑מֶר וּשְׁלֹשׁ־עֶשְׂרֵ֥ה שָׁנָ֖ה מָרָֽדוּ׃ Twelve years they served Chedorlaomer, and in the thirteenth year they rebelled.
Thirteen were the number of towns that were allocated to the children of Gershon.
יהושע כ״א ו
וְלִבְנֵ֣י גֵרְשׁ֗וֹן מִמִּשְׁפְּח֣וֹת מַטֵּֽה־יִשָּׂשכָ֣ר וּמִמַּטֵּֽה־אָ֠שֵׁר וּמִמַּטֵּ֨ה נַפְתָּלִ֜י וּ֠מֵחֲצִי מַטֵּ֨ה מְנַשֶּׁ֤ה בַבָּשָׁן֙ בַּגּוֹרָ֔ל עָרִ֖ים שְׁלֹ֥שׁ עֶשְׂרֵֽה׃
To the Gershonites [there fell] by lot 13 towns from the clans of the tribe of Issachar, the tribe of Asher, the tribe of Naphtali, and the half-tribe of Manasseh in Bashan.