Well, I learned two things from this.  If you want a lot of mail, give your 
idea a catchy title.  Second I learned of another crazy idea, which will be 
sent as soon as the first couple of terms of checked.  It's on the same basic 
principle as the one I showed you, except the next one will no doubt be more 
useful when it comes to twin primes.

I spent a whole day organizing the zeta function (which I learned 2 minutes 
before organizing …) to get:

Z(n) = 1 + (1/(2^n - 1)) + (1/(3^n -1)) + (1/(5^n - 1)) + ...

with the same x' group.  This maybe way to obvious, or it might not (I need 
to check my math history...  I think It's more fun to prove what other people 
have.  It's much more fun : - D) But this is where I thought I might mess up 
since it's subtracting infinity from infinity.  I set n = 1 and got:

1 + 1/2 + 1/3 + 1/4 + 1/5 + 1/6 +... = 1 + 1 + (1/2) + (1/4) + (1/5) + (1/6) 
+ (1/9) + ...

Where the left includes all terms, and the right includes all terms in the 
set x'', which is (x' - 1)

Canceling like terms I got:

(1/3) + (1/7) + (1/8) + (1/15) + ... = 1

Now, x' is the set that does not contain integral powers.  So, the left side 
is the side that does contain integral powers, minus 1.  So, we can put 1 = 
1/(2^2 - 1) + (1/2^3 - 1) + ... + (1/3^2 - 1) + (1/3^3 -1) + ... 

And there you have your proof.  Connie brought up an interesting point, which 
included a proof, so I can say my math was correct.  I must say, though, that 
I didn't like subtracting infinity from infinity.

Mark
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