how many digits 2 ^ 400 has ?
"2 ^ 10 = 1.024 * 10 ^ 3 = > 2 ^ 100 = ( 1.024 ) ^ 10 * 10 ^ 120 therefore 121 digits would be my best guess e"
floor(add(const_1, multiply(divide(log(2), log(const_10)), 400)))