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15696RE: [PrimeNumbers] another way to calculate primes

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  • Mazzarello Gianni
    Dec 6, 2004
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      It seems correct, but we can say it in an equivalent way:

      the set of prime numbers = 2, 5 PLUS all odd numbers > 5, not ending by
      5 and not composite.

      Following your way we could perform primality test on a number N
      searching odd numbers ending by 1, 3, 7, 9 and less than sqrt(N).

      Moreover, considering the least significant digit:

      ...1 => 1 x 1 or 3 x 7 or 9 x 9
      ...3 => 1 x 3 or 7 x 9
      ...7 => 1 x 7 or 3 x 9
      ...9 => 1 x 9 or 7 x 7 or 3 x 3

      we can limit our search to a set of the order of sqrt(N) x 2/10 or
      sqrt(N) x 3/10 elements.
      That is: numbers ending by 1, 3, 9 (or 1, 7, 9) if N ends by 1 and so
      on.

      I was wondering this: for a fixed M, are there more primes < M ending
      with 3 and 7 than primes < M ending with 1 and 9?

      Gianni


      >-----Original Message-----
      >From: Jim Doyle [mailto:ozyjim2004@...]
      >Sent: Friday, December 03, 2004 1:53 AM
      >To: primenumbers@yahoogroups.com
      >Subject: [PrimeNumbers] another way to calculate primes
      >
      >
      >Hi
      >
      >I'm not sure if this is a new idea but I have not come across
      >it . Its based on the fact that apart from 2 and 5 all primes
      >have a last digit of 1,3,7 or 9.
      >
      >...
      >...
      >
      >Jim
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