Explain how a Turing machine can be used to determine whether a given number is prime. Suppose you are given two algorithms for solving the same problem. One algorithm has time complexity n^4 and the...

Explain how a Turing machine can be used to determine whether a given number is prime. Suppose you are given two algorithms for solving the same problem. One algorithm has time complexity n^4 and the other has time complexity 4n. For what size inputs is the former more efficient than the latter?