## Re: 2/p +..

Expand Messages
• I realized my error almost the moment I sent the message - but thanks to those who replied. Tom ... times ... 3, can ... 2/5 + 2/7 + ... the ... then sum. I
Message 1 of 7 , Apr 21, 2004
• 0 Attachment
I realized my error almost the moment I sent the message - but thanks
to those who replied.
Tom

> In a message dated 20/04/04 18:50:06 GMT Daylight Time,
>
>
> > >> If you take every prime in sequence and make a sequence of 2
times
> > >> the reciprocal of each, then if you exclude the primes 2 and
3, can
> > >> it be shown that the sum of all of them will never total 1?
> > >>
> > >> thanks,
> > >> Tom
> > >
> > >I'm not sure I understand your question. Do you want to compute
2/5 + 2/7 +
> > >2/11 + 2/13 + ...? In that case, the sum of these four terms of
the
> > sequence
> >
> > Apparently he means multiply by 2, THEN take the reciprocal,
then sum. I
> > wrote a program to do this, and I found the sum exceeds 1 at this
prime:
> >
> > 483281 1.000000724689930
> >
>
> Here's a proper proof, involving no computation at all.
>
> Suppose that, for some prime P >= 5,
> 1/(2*5) + 1/(2*7) + 1/(2*11) + .. + 1/(2*P) = 1.
> Multiply both sides by the product of all primes < P.
> Eevery term except the one before the "=" sign is an integer.