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24028Re: [PrimeNumbers] The history of the primality of one

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  • Jack Brennen
    Feb 2, 2012
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      phi(1) has to equal 1 in order to preserve the multiplicative
      nature of phi(). In other words,

      If gcd(a,b) == 1, then phi(a)*phi(b)==phi(a*b).

      1 is the only value for phi(1) which preserves this property,
      and the property is too important to give up.

      Note that one definition of primality, which could include
      negative primes, would be that abs(phi(X))+1 == abs(X) if
      and only if X is prime. By such a definition, 1 would then
      not be prime.



      On 2/2/2012 12:41 PM, Walter Nissen wrote:
      > A most interesting subject .
      >
      > I think the most accessible definition of prime is geometrical ,
      > rectangularization forces linearization ,
      > http://upforthecount.com/math/nnnp1np1.html
      > Trivially , 1 is prime .
      >
      > I'd be happy to live in a world where 1 is both prime and perfect .
      > If 1 is not perfect , then by what stretch of the imagination is
      > Euler's phi ( 1 ) = 1 ?
      > I find the equality in phi ( 1 ) = 1 jarring .
      > Are units the easiest or hardest part of algebra ?
      >
      >
      >
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