Part 2

Note $2017\equiv 2\pmod{5},46\equiv1\pmod{5}$ . Therefore,

$2017^{46}+46\equiv 2^{46}+1\equiv 4^{23}+1\equiv(-1)^{23}+1\equiv 0\pmod {5}$ .

Thus, $2017^{46}+46$ is divisible by $5$ but is not equal to $5$ , so $2017^{46}+46$ is not prime.

47 is a prime number and by Fermat's little theorem , 2017^{47 - 1} = 1 (mod 47) implies that 2017^{46} = 1 (mod 47). Again , 46 = -1 (mod 47). Hence, 2017^{46} + 46 = 0 (mod 47) ,or 2017^{46} + 46 is divisible by 47 and greater than 47. Which indicates that it can't be a prime.

The last digit of 2017^46 is 9, so +46 the last digit is 5.