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Re: Is the twin prime constant irrational?

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  • Kermit Rose
    Re: Is the twin prime constant irrational? Twin prime constant = (3/2)(1/2)(5/4)(3/4)(7/6)(5/6)(11/10)(9/10)...(p/(p-1))((p-2)/(p-1))... I expected that it
    Message 1 of 7 , Feb 15, 2013
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      Re: Is the twin prime constant irrational?



      Twin prime constant
      = (3/2)(1/2)(5/4)(3/4)(7/6)(5/6)(11/10)(9/10)...(p/(p-1))((p-2)/(p-1))...


      I expected that it would have been easily determined whether or not
      the twin prime constant was rational or irrational.

      It would not be possible for the twin prime constant to be rational
      because the infinite numerator is odd, and the infinite denominator is
      divisible by
      2 infinitely many times.

      Kermit
    • Jack Brennen
      How about this infinite product here? (99/10)*(111/110)*(1111/1110)*(11111/11110)*... The partial products are: 9.9 9.99 9.999 9.9999 and so on... The product
      Message 2 of 7 , Feb 15, 2013
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        How about this infinite product here?

        (99/10)*(111/110)*(1111/1110)*(11111/11110)*...

        The partial products are:
        9.9
        9.99
        9.999
        9.9999
        and so on...

        The product quite obviously converges to an even number (10), but all of
        the numerators are odd and all of the denominators are even. Even and
        odd really have no meaning when it comes to infinity and limits. As
        this example shows, a series of partial products, all of which have
        odd numerator and even denominator, can converge to not only a rational
        number, but an even integer.


        On 2/15/2013 8:53 AM, Kermit Rose wrote:
        > Re: Is the twin prime constant irrational?
        >
        >
        >
        > Twin prime constant
        > = (3/2)(1/2)(5/4)(3/4)(7/6)(5/6)(11/10)(9/10)...(p/(p-1))((p-2)/(p-1))...
        >
        >
        > I expected that it would have been easily determined whether or not
        > the twin prime constant was rational or irrational.
        >
        > It would not be possible for the twin prime constant to be rational
        > because the infinite numerator is odd, and the infinite denominator is
        > divisible by
        > 2 infinitely many times.
        >
        > Kermit
        >
        >
        >
        >
        >
        >
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