Why isn't 1 a prime number?
Bad example, if 1 isn't prime, 2 x 1 isn't a product of prime, so not all the number can be written as <i>product of primes</i>. My point is that you can't write an introductory article, supposed to be understandable to the masses, using a form able to confuse further the readers. A student, reading this, I don't think will understand this explanation that seems contradictory.<p>"My mathematical training taught me that the good reason for 1 not being considered prime is the fundamental theorem of arithmetic, which states that every number can be written as <i>a product of primes</i> in exactly one way. If 1 were prime, we would lose that uniqueness. We could write 2 as 1×2, or 1×1×2, or 1594827×2. Excluding 1 from the primes smooths that out."