Section 6.4.1, due Monday October 25

1. (Difficult) I understand the method of finding the numbers 9398, 19095, etc., but why does that method guarantee that the squares of that number are factored into small primes? Why are small primes important in this factorization method as well?

2. (Reflective) It is amazing how factorization has improved over the last 50 years. They showed the table on page 185 that shows the factorization methods. We have certainly come a long way. I still feel like factoring should not be so hard, but when the numbers get large it makes sense that it is difficult to find the prime factors. Is the reason why small prime factors are important in the numbers 9398, 19095, etc. because we can quickly check those and find the prime factorization? We don't have to go all the way up to the sqrt(n) to factor if we know that the numbers are a product of small prime numbers.