[EnPissant]

In programmer terms, imagine you had to define the product function in Python. The most natural way to write it is:

    >>> def product(ints):
    ...   result = 1
    ...   for int in ints:
    ...     result *= int
    ...   return result

In which case there is no need to make 1 a prime as you already have:

    >>> product([])
    1