On page 17 in section 5.2 The Prime Is Bigger there is a mistake in the first print run of the book.
The explanation should read:
For Natural number n let the square be n2. To have a difference of 1, either n2 - 1 is the prime or n2 + 1 is the prime.
However, n2 - 1 = (n + 1)(n - 1) which means that n2 - 1 is composite, not prime, unless one factor (necessarily n - 1, the smallest factor) is zero, or the smallest factor is 1 and the other factor is prime.
If n - 1 = 0 then n = 1, meaning that n2 - 1 has the value 0, which is not prime.
If n - 1 = 1 then n = 2, meaning that n2 - 1 = 3, giving prime 3 and square 4. These form the only possible exception to the rule.
On page 33 in section 9.5 Divisibility Testing the middle line of the middle proof is jumbled.
The middle line should terminate with = 8 multiplied by 9n + 9n - 1