prime numbers and expressing non-prime numbers My textbook says if $b$ is a non-prime number then it can be expressed as a product of prime numbers. But if $1$ isn't prime how it can be expressed as a product of prime numbers?


An empty product is still a product.

Lulu's comment is sufficient to answer what you asked. Although you didn't state any constraints on $b$, I understand your question to be specifically about the case $b = 1$. And that's neatly addressed just by the concept of the empty product alone.

But then why is everyone talking about the fundamental theorem of arithmetic? Its overuse is part of the reason.
But also because it's kind of implied by the idea of $b$ being the product of primes. For, after all, if a number domain does not have unique factorization, then it probably has numbers that are divisible by irreducible non-primes but not by any primes.
However, even if we're only talking about $\mathbb Z$, I think it's still more productive (pun fully intended) to say numbers in a unique factorization domain are divisible by units and primes: the units may vary in infinitely many ways, but the primes can only vary in regards to order.
And so we're not the least bit baffled about the number 1, since it's a product of units in several different ways (e.g., $(-1)^2 =$ $ (-1)^4 \times 1 = $ $\ldots$) and an empty product of primes.
Nor are we baffled by negative numbers, even if we stubbornly refuse the sensible idea that negative numbers can be prime. For example, $-14 = (-1) \times 2 \times 7$.
And $-1$ is the product of the unit $-1$ and an empty product of primes, which is, of course, 1.
This only leaves out the very special case of 0.
