Who knows fifteen?
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Fifteen are the extra years added to King Chizkiyahu's lifetime, after his sincere prayer and resolution to fulfill Hashem's command to marry and bear children (II Kings 20:6 and Isaiah 38:5; Talmud, Berachos 10a).
Fifteen are the women who exempt their co-wives. (Mishna Yevamot 1:1)
(from Yibum and Chalitza)
Fifteen was the depth (in cubits) of the Flood waters above the mountaintops (Gen. 7:20) - or according to R' Yehudah (Bereishis Rabbah 32:17), all over the world.
Fifteen years old to start learning Talmud. (Avot 5:24)
Fifteen are the steps from the azarah to the ezras Kohanim.
Fifteen are the Shirei HaMa'alos.
There are 15 Simanim at the Seder. Kadesh, Urchatz........
Fifteen are the unintelligent people it takes to make a minyan:
Hosheea es amecha uvarech es nachalesecha urem urem urem urem venasem urem venasem ad olam
(Yes, this is a joke.)
With Fifteen (the gematria of the name Yud-Heh) He formed the worlds.
15 are the days S'faradim are not sad during the Omer.
15 is the day of the month of Iyar that the Manna began to fall for the Jews in the desert.
Chamisha Asar B'Omer always comes out on Rosh Chodesh
Shemos 27:14 The hangings of one side of the gate shall be fifteen cubits: their pillars three, and their sockets three.
Shemot 27:15 And on the other side shall be hangings fifteen cubits: their pillars three, and their sockets three.
Vayikra 27:7 And if it be from sixty years old and above; if it be a male, then thy estimation shall be fifteen shekels, and for the female ten shekels.
Hoshea 3:2 So I bought her to me for fifteen silver, and an omer of barley, and a half omer of barley:
Yeshayahu 38:5 Go, and say to Hezekiah, Thus saith HaShem, the God of David thy father, I have heard thy prayer, I have seen thy tears: behold, I will add unto thy days fifteen years.
1- Fifteen generations from Abraham to King Solomon; then fifteen generations from Solomon until the destruction of the Beit HaMikdash.
2- There were fifteen who ruled Israel as judges
[Midrash Rabbah - Bereishis 97] The tribes are enumerated fifteen times in the Torah [together].
Shemot 25 [Fifteen things were given as donations toward the construction of the Mishkan:]  ...gold, and silver, and brass,  And blue, and purple, and scarlet, and fine linen, and goats’ hair,  And rams’ skins dyed red, and badgers’ skins, and shittim wood,  Oil for the light, spices for anointing oil, and for sweet incense, 7 Onyx stones, and stones to be set in the ephod, and in the breastplate.
Fifteen is the fifteen expressions in the berachah of Ha-Tov ve-ha-Meitiv (לחן ולחסד ולרחמים ולרוח הצלה והצלחה ברכה וישועה נחמה פרנסה וכלכלה ורחמים וחיים ושלום וכל טוב), which correspond to:
Source: פירוש ברכת המזון למוהר"ן שפירא.