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Re: [PrimeNumbers] Re: Hypothesis Part 2

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  • Jack Brennen
    ... Actually, Chris, the word pedantic was wrong on my part, as it may have a negative connotation, which was certainly not intended. My intent was to say
    Message 1 of 9 , Jul 2, 2001
      > ... Yes indeed, the sign restriction was just to make the
      > statement easier. Pedantic perhaps, but as author of the page in
      > question (not the theorem!!!) I'd offer another
      > reason: laziness (or should I say simplicity).

      Actually, Chris, the word "pedantic" was wrong on my part, as it
      may have a negative connotation, which was certainly not intended.

      My intent was to say that by restricting the parameters to positive
      integers, you have "over-specified" the theorem -- that's not a bad
      thing at all, and certainly well justified since it avoids having
      to answer the question of whether a negative integer can be prime.

      Jack
    • Paul Leyland
      ... Why avoid it at all? The integers can be divided into four classes which are relevant in this context. 1) Zero (the additive identity) 2) Units (1 and
      Message 2 of 9 , Jul 3, 2001
        > thing at all, and certainly well justified since it avoids having
        > to answer the question of whether a negative integer can be prime.

        Why avoid it at all? The integers can be divided into four classes
        which are relevant in this context.

        1) Zero (the additive identity)
        2) Units (1 and -1, the integers with norm equal to the multiplicative
        identity)
        3) Primes (those integers all of whose divisors with a smaller norm are
        units)
        4) Composites (everything else).


        As the integers form a unique factorization domain we don't have to
        worry about concepts such as prime ideals.


        Paul
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