Re: Is the twin prime constant irrational?

Expand Messages
• 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
• 0 Attachment
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
• 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
• 0 Attachment

(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
>
>
>
>
>
>
> ------------------------------------
>
> Unsubscribe by an email to: primenumbers-unsubscribe@yahoogroups.com
> The Prime Pages : http://primes.utm.edu/
>