*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 *n*^{2}. To have a difference of 1, either *n*^{2} - 1 is the prime
or *n*^{2} + 1 is the prime.

However, *n*^{2} - 1 = (*n* + 1)(*n* - 1) which means that *n*^{2} - 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 *n*^{2} - 1 has the value 0, which is not prime.

If *n* - 1 = 1 then *n* = 2, meaning that *n*^{2} - 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 9^{n} + 9^{n} - 1