old hat? or just not true?

Let z(n) be the nth zero with real part 1/2 of the Zeta function (z(n)= 14.13, 21.02,...etc.).

?? Product[1/(1-(1/z(n)^s)]= Sum[1/z(n)^s] + 1

s real

This is not even a conjecture and before I invest more time in improving my approximation and trying to figure out why this might be true, I thought I'd see if this is old or ancient hat.
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