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24026The history of the primality of one

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  • Chris Caldwell
    Feb 2, 2012
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      I have a couple undergraduate students researching the history of the primality of one. For example, most of the early Greeks did not consider one to be a number, so one could not be a prime number for them. (A few considered primeness a subcategory of oddness, so two wasn't prime either!) As we move forward to the middle ages and later it is quite a mixture. For Cataldi, Euler, Gauss, and Landau, one appears not to be a prime. For Goldbach, Lebesgue, and Lehmer, it was a prime.

      Here is my question: if you have any good references on what was believe by who in the past (preferably before 1900 and especially if it says why), please let me know off the list: caldwell@...<mailto:caldwell@...>. I would be glad to share what we have collected so far, but we are just beginning (for example, trying to find copies the sources cited in Dickson history...), so it might be far more productive to wait a bit (it will eventually be web page on the prime pages).

      This is of course just a matter of definition, but definitions are motivated by their usage. Usage now demands that one be (a number,) a unit
      and neither prime nor composite, but as the names above suggests, that was not always the case.

      Chris Caldwell

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