Three sides of a triangle are A, B and C, where C is the hypotenuse.
B & C share a digit, A & C share another digit and are prime numbers.
A+B+C=D where D is a three digit number made up of three consecutive digits, which may or may not be in order.
BONUS CLUE: D is also [(A-1)/2] more than the lowest three digit Mersenne Prime
What are A, B and C?
Create the number 24 using only a 1, 3, 4, and 6. You may only use +, -, /, and *. Parenthesis are allowed.