Problem 8
A prime number is a number that only has factors of 1 and itself. For example, 7 is a prime number since 1 and 7 are the only factors of 7. Something like 32 is not prime because 2 is a factor, so is 4, and so on. If we multiply any two numbers together to get a larger one, then that result is not prime. Example: 2*3 = 6, the value 6 is not prime because 2 and 3 are factors.
---------------------------------------------------------------
Problem 9
Let's say that we added 7 to itself. The value 7 is prime but 7+7 = 14 is composite (since 7 is a factor). We can do this with any prime we want. Let p be some prime. Add p to itself and we have p+p = 2*p so the number has 2 and p as factors. There may other other factors as well. Since 2 and p are factors, this proves that 2*p is composite.
