Chapter 4.8, Problem 30ES

Let $p_1,p_2,p_3,\mathrm{...}$ be a list of all prime numbers in ascending order. Here is a table of the first six:

a. Let $N_1=p_1,N_2=p_1\cdot p_2,N_3=p_1\cdot p_2\cdot p_3,\mathrm{...},N_6=p_1\cdot p_2\cdot p_3\cdot p_4\cdot p_5\cdot p_6$. Calculate $N_1,N_2,N_3,N_4,N_5$ , and $N_6$.
b. For each $i=\text{1},\text{ 2},\text{ 3},\text{ 4},\text{5},\text{6}$ , find whether $N_i$is itself prime or just has a prime factor less than itself. (Hint: Use the test for primality from exercise 31 in Section 4.7 to determine your answers.)