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Re: [PrimeNumbers] A New Kind of Prime Number

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  • Andy Swallow
    ... - Suppose that n is a first order prime. Then n-1 is either prime, or a power of 2. - Suppose n is a 2nd order prime. Then n-2 is either prime, or a
    Message 1 of 3 , Sep 29, 2003
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      > I introduce the concept of higher order primes. Zero order primes
      > are just the familiar primes; 2,3,5,7 etc. A zero order prime, X,
      > if divided by any number less than X and more than one never
      > yields a remainder of zero. A first order prime, X, if divided by
      > any number less than X?1 and more than 2 never yields remainder
      > of
      > one. Prime1 numbers are 3, 4, 5, 6, 8, 12, 14 etc. In general, a
      > prime Y number ,X, when divided by any number less than X ?
      > Y
      > and more than Y + 1 never yields a remainder of Y.

      - Suppose that n is a first order prime. Then n-1 is either prime, or
      a power of 2.
      - Suppose n is a 2nd order prime. Then n-2 is either prime, or a product
      of powers of 2 and 3 only.
      - Do we see a pattern yet? Since 4 is not prime, it follows (I think)
      that n is 2nd order iff n+1 is 3rd order.

      And so on. My point is, why should the word 'prime' be associated with
      these n? I mean, your definition says things about the factorisation of
      n-1, or n-2, or whatever, but that doesn't say much about the factors of
      n itself.

      A sequence of m'th order primes can basically be split into two parts.
      One part is a shifted prime sequence, i.e. p+m. The other part is
      essentially boring, from a prime point of view, since it is just all
      those numbers consisting of prime factors from a finite set.

      I don't see anything new in this definition, sorry.

      Andy
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