To make divinity, first beat egg whites with an electric stand mixer at high speed until soft peaks form. Set aside.
Combine sugar, corn syrup, water, and salt in a heavy 2-quart saucepan. Bring to a boil, stirring constantly. Wash down any sugar crystals on the sides of the pan with a brush dipped in hot water.
Boil for about 10 minutes or until mixture reaches hard ball stage, which is 260 degrees on a candy thermometer.
With mixer running at high speed, pour syrup over egg whites in a pencil-size stream.
Add vanilla. And beat for about 8 to 10 minutes or until mixture thickens and mounds slightly when dropped from a spoon. Stir in pecans.
Quickly drop candy onto wax paper by rounded teaspoonfuls. To make the process a little easier, use one spoon for scooping out the candy and another spoon to scrape the candy from the spoon onto the paper. Let cool completely.