Gale didn't kill Prim. It was actually that Coin lady. Which at first I thought it was Snow.
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After the reaping before she leaves District 12, she is visited by Madge who gives her the mockingjay pin, Gale, Prim and her mom, and the Baker who gives her cookies.
Katniss doesn't kill Prim, Coin does. She does because she was afraid Katniss might want to stand up and be president.
Prim dies on page 406
The locket that Peeta gave Katniss in Catching Fire is gold and has a mockingjay ingraved in the front, inside the locket there is a picture of Gale and her mother and her sister Prim.
*SPOILER ALERT* He does not kill her directly. He is the one who created the bomb design of the bomb that killed her. Katniss dislikes him now for this.