- Hello:

I found a new mathematical constant.

Can someone find some algebraic relation with other constants?

F[n_]:=

Product[(Prime[i]-1)/2,{i,3,n,2}]*Product[(Prime[i]+1)/2,{i,2,n,2}]/

(Product[(Prime[i]+1)/2,{i,3,n,2}]*Product[(Prime[i]-1)/2,{i,2,n,2}])

(The last one 2 means step 2)

Do[Print[N[F[n],15]],{n,1000000,1004000,1000}]

1.62172686861764

1.62172686850817

1.62172686840166

1.62172686829112

1.62172686818162

[Non-text portions of this message have been removed] - --- In primenumbers@yahoogroups.com, Sebastian Martin <sebi_sebi@...> wrote:
>

It looks like you started the primes at 3, rather than 2. (And, the dividing by two thing is

>

>

> Hello:

>

> I found a new mathematical constant.

> Can someone find some algebraic relation with other constants?

>

>

> F[n_]:=

> Product[(Prime[i]-1)/2,{i,3,n,2}]*Product[(Prime[i]+1)/2,{i,2,n,2}]/

> (Product[(Prime[i]+1)/2,{i,3,n,2}]*Product[(Prime[i]-1)/2,{i,2,n,2}])

>

> (The last one 2 means step 2)

>

>

> Do[Print[N[F[n],15]],{n,1000000,1004000,1000}]

>

> 1.62172686861764

> 1.62172686850817

> 1.62172686840166

> 1.62172686829112

> 1.62172686818162

>

unnecessary.) If you started at 2 or 5 or 7 ect, you would have obtained other constants.

So, I don't think the constant you obtained is anything more special than the other ones

that could be produced. So many constants, so little time. Speaking of constants, thank

goodness for some willingness to *change* shown by our neighbours to the south last

night.

Mark - --- In primenumbers@yahoogroups.com,

"Mark Underwood" <mark.underwood@...> wrote:

> Speaking of constants, thank goodness for some willingness

Amen to that.

> to *change* shown by our neighbours to the south last night.

I left this group in April 2003, shortly after posting

http://tech.groups.yahoo.com/group/primenumbers/message/12037

I now feel able to return, for reasons unrelated to number theory,

though I do not expect to contribute anything of mathematical

substance before 20th January 2009.

David Broadhurst