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Re: [PrimeNumbers] On the 1, 3, 7, 9

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  • Phil Carmody
    ... Modulo 10, there are phi(2)*Phi(5) = 1*4 = 4 possible non-zero-divisors (or units, or numbers coprime to 10). 1, 3, 7, 9 Therefore the 16 possible numbers
    Message 1 of 2 , Nov 28, 2002
      --- Juan Ignacio Casaubon <jicasaubon@...> wrote:
      >
      > Hi,
      >
      > A result of Juan Pablo Cosentino juancosentino@...
      >
      > From 10 to 20 the primes are 11, 13, 17, 19
      >
      > he puts 101000101 where 1 indicate prime
      >
      > From 20 to 30 the primes are 23, 29
      >
      > he puts 1000001
      >
      > AND SO ON...
      >
      > Now he transform these 16 possible binary numbers

      Modulo 10, there are phi(2)*Phi(5) = 1*4 = 4 possible non-zero-divisors (or
      units, or numbers coprime to 10).
      1, 3, 7, 9

      Therefore the 16 possible numbers are
      {0,2^8}+{0,2^6}+{0,2^2}+{0,2^0}

      > in arabic, he found four WELL SEPARATED bands
      >
      > of exactly 5 numbers (width)
      >
      > 0-5
      >
      > 64-69
      >
      > 256-261
      >
      > 320-325

      My expresion above is equivalent to
      {0,2^6,2^8,2^8+2^6} + {0,2^0,2^2,2^2+2^0}
      or
      {0, 64, 256, 320} + {0, 1, 4, 5}

      There're the 4 bands, and here are the "5" numbers.

      > Take this into account: Do not steal this result, Juan Pablo is a student
      > in Engineering.
      >
      > My students are ever very inteligent!

      As were Eratosthenes and many others. However, they got to the topic
      2 millennia ago.

      Phil


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