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What is the significance of the two letter shins (ש) on tefillin?

One side of tefillin has a regular shin (ש) and the second has four-prongs.

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up vote 5 down vote accepted

From here, quoting the Beit Yosef to Orach Chaim 32:

The Verse says, "And all the nations of the land will see that the name of God is called upon you and they will fear you" (Devarim 28:10). The Talmud says that this refers to the the Tefillin Shel Rosh (Tefillin of the Head).

G-d Name, The Tetragramaton, is the numerical value of 300, using the Gematria Method known as AT-BASH:

Yud == Mem (40)

Hey == Tzadi (90)

Vav == Peh (80)

Hey == Tzadi (90)

So the 3 pronged Shin represents G-d's name.

According to the Sefer Mitzvos Gedolos, quoted by the Beit Yosef, the writing in the Luchos (Tablets) were sunken in. If so, a Shin had 4 prongs, and the 4 progned Shin on the Tefillin Shel Rosh commemorates that.

The Talmud (Menachot 35A - page 130 of here) says:

Abaye also said, The shin of the tefillin is a law given to Moses at Sinai

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