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Another Qaudratic form??

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  • Cletus Emmanuel
    Guys, I ve been looking at the following equation; R=4^k +/- P*2^(k-1) - 1, where k = 2,3,4 ... and P is a prime number. The two (or four) most interesting
    Message 1 of 2 , Jan 10 12:00 PM
      Guys,
      I've been looking at the following equation; R=4^k +/- P*2^(k-1) - 1, where k = 2,3,4 ... and P is a prime number. The two (or four) most interesting ones so far are:

      1. 4^k +/- 61*2^(k-1) - 1

      2. 4^k +/- 139*2^(k-1) - 1

      If P is not prime, then R would not be prime for k values (of course, there are one or two exceptions like a small k-value). These equations yield lots of primes "compared". If one looks at P =+/- 61, they'll find that for k = 2 through 7 R is prime. Can anyone write a sieve for these numbers? Phil, maybe? I've search several thousand k values, but would love a sieve to be more efficient.


      ---Cletus Emmanuel



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    • Rob Binnekamp
      Your equations are a special form of the more general form 2^a +/- b*2^c +/- 1 Phil C. wrote a sieve base-10 of this form for me; you could ask him to write a
      Message 2 of 2 , Jan 11 7:10 AM
        Your equations are a special form of the more general form

        2^a +/- b*2^c +/- 1

        Phil C. wrote a sieve base-10 of this form for me;
        you could ask him to write a sieve base-2 for you
        or a variable base.
        Why you assume that b (your P) must be prime for
        the expression to be prime?

        gr. rob


        ----- Original Message -----
        From: Cletus Emmanuel
        To: primenumbers@yahoogroups.com
        Sent: Monday, January 10, 2005 9:00 PM
        Subject: [PrimeNumbers] Another Qaudratic form??


        Guys,
        I've been looking at the following equation; R=4^k +/- P*2^(k-1) - 1, where k = 2,3,4 ... and P is a prime number. The two (or four) most interesting ones so far are:

        1. 4^k +/- 61*2^(k-1) - 1

        2. 4^k +/- 139*2^(k-1) - 1

        If P is not prime, then R would not be prime for k values (of course, there are one or two exceptions like a small k-value). These equations yield lots of primes "compared". If one looks at P =+/- 61, they'll find that for k = 2 through 7 R is prime. Can anyone write a sieve for these numbers? Phil, maybe? I've search several thousand k values, but would love a sieve to be more efficient.


        ---Cletus Emmanuel



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        Yahoo! Mail - 250MB free storage. Do more. Manage less.

        [Non-text portions of this message have been removed]



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