Heat and stir sugar, syrup, and water in a heavy 3-quart saucepan until sugar dissolves. Cook over medium heat to softball stage (234 degrees).
Add peanuts and salt. Cook to hard crack stage (305 degrees), stirring often.
Remove from heat. Quickly stir in butter and soda. Pour at once onto two well-buttered cookies sheets, spreading with forks until thin.
Break up into pieces when cold. Makes 1 1/2 pounds.