As the article says, one could consider this a matter of definition. The definition of choice for me (and some other category theorists?) is that the prime numb

As the article says, one could consider this a matter of definition. The definition of choice for me (and some other category theorists?) is that the prime numbers are the second row in the devisibility lattice. (That is, n < m iff n | m.) Then, the number 1 is the single element of the first row and all the prime numbers are the atoms immediately above 1.