@jens @virtuous_sloth The purpose of a definition of a prime is to reproduce the sequence 2,3,5,7,11… because that is the sequence which is interesting and useful to discuss. We pick whatever rules produce that. The fact that, as you observe, any number can be divided by one an infinite number of times is exactly what makes it useless for calculating a prime factorization. By your argument, 3 would not be prime because it has 3 possible factors, 3, 1, and 1.
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@mcc @virtuous_sloth No, my argument merely implements the requirements naively with a simple Boolean statement.
Sorry, this is not a maths argument in the slightest. I feel people let that part get out of hand here.