Prime factorisation

By definition, a prime number 'n' is a number that is not divisible by anything else but 1 and n.

Let us analyse each of the 3 options:

A)1747 : try the usual way. 41^2= 1681, so you need to check for all numbers from 1 to 41 to see if there are any divisors of 1747. You wont find any. Thus 1747 is a prime number.

B)139^3 + 1: no need to solve. Recognise that 9^3 ends in 9 and thus the last digit 9+1 = last digit of 0. As 0 is an even number (divisible by 2)---> the resulting number 139^3+1 is NOT a prime.

C)47^8 - 37^8 ---> apply a^2-b^2=(a+b)(a-b) ---> 47^8 - 37^8 = (47^4+37^4)(47^4-37^4) = (odd+odd)(odd+odd) = even*even = even . NOT a prime number.

Hope this helps.