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Topic: Prime numbers and pi
Replies: 33   Last Post: Dec 10, 2012 3:43 PM

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Franz Gnaedinger

Posts: 330
Registered: 4/30/07
Re: Prime numbers and pi
Posted: Apr 16, 2009 8:33 AM
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Stairway approximations of ln2 :

'1
'1x2 '5
'1x2 '3x4 '9
'1x2 '3x4 '5x6 '14
'1x2 '3x4 '5x6 '7x8 '19
'1x2 '3x4 '5x6 '7x8 '9x10 '24

ln2 = '1x2 '3x4 '5x6 '7x8 '9x10 '11x12 '13x14 '15x16 ...

9/10

1x3/2x2 x 14/15

1x3/2x2 x 5x7/6x6 x 19/20

1x3/2x2 x 5x7/6x6 x 9x11/10x10 x 24/25

ln2 = 1x3/2x2 x 5x7/6x6 x 9x11/10x10 x 13x15/14x14 ...

ln2 = 1/2 x 3/2 x 5/6 x 7/6 x 9/10 x 11/10 x 13/14 ...

By playing with this product and looking out for
partial products Euler could have left out all factors
whose numerators are composites and would have obtained

1/2 x 3/2 x 5/6 x 7/6 x 11/10 x 13/14 ... = pi/4

At least half an explanation for that amazing link
between pi and the primes.


Date Subject Author
4/12/09
Read Prime numbers and pi
James A. Landau
4/13/09
Read Re: Prime numbers and pi
Franz Gnaedinger
4/13/09
Read Re: Prime numbers and pi
Franz Gnaedinger
4/13/09
Read Re: Prime numbers and pi
James A. Landau
4/14/09
Read Re: Prime numbers and pi
Franz Gnaedinger
4/14/09
Read Re: Prime numbers and pi
Franz Gnaedinger
6/26/12
Read Re: Prime numbers and pi
hashim shah
4/14/09
Read Re: Prime numbers and pi
James A. Landau
4/15/09
Read Re: Prime numbers and pi
Franz Gnaedinger
4/16/09
Read Re: Prime numbers and pi
Franz Gnaedinger
4/16/09
Read Re: Prime numbers and pi
Franz Gnaedinger
4/16/09
Read Re: Prime numbers and pi
Franz Gnaedinger
4/16/09
Read Re: Prime numbers and pi
Franz Gnaedinger
4/16/09
Read Re: Prime numbers and pi
Franz Gnaedinger
4/18/09
Read Re: Prime numbers and pi
Franz Gnaedinger
4/18/09
Read Re: Prime numbers and pi
Franz Gnaedinger
4/23/09
Read Re: Prime numbers and pi
Franz Gnaedinger
4/23/09
Read Re: Prime numbers and pi
Milo Gardner
4/25/09
Read Re: Prime numbers and pi
Franz Gnaedinger
4/25/09
Read Re: Prime numbers and pi
Milo Gardner
4/26/09
Read Re: Prime numbers and pi
Franz Gnaedinger
4/26/09
Read Re: Prime numbers and pi
Milo Gardner
4/27/09
Read Re: Prime numbers and pi
Franz Gnaedinger
4/27/09
Read Re: Prime numbers and pi
Franz Gnaedinger
4/27/09
Read Re: Prime numbers and pi
Milo Gardner
4/28/09
Read Re: Prime numbers and pi
Franz Gnaedinger
4/28/09
Read Re: Prime numbers and pi
Milo Gardner
4/29/09
Read Re: Prime numbers and pi
Franz Gnaedinger
4/15/09
Read Re: Prime numbers and pi
John Bibby, QED of York, York, England
6/27/12
Read Re: Prime numbers and pi
Milo Gardner
6/27/12
Read Re: Prime numbers and pi
Milo Gardner
12/5/12
Read Re: Prime numbers and pi
kevin
12/6/12
Read Re: Prime numbers and pi
Milo Gardner
12/10/12
Read Re: Prime numbers and pi
Milo Gardner

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