Feller-Torier constant equals this sum involving the prime zeta function?

Question

According to the Wikipedia and Mathworld pages, the Feller-Tornier constant can be defined by this sum involving the prime zeta function $$C_{\text{FT}}=\frac{1}{2}\left(1+\exp\left[-\sum_{n=1}^\infty \frac{2^n P(n)}{n}\right]\right)$$

When I evaluate this, I get $1/2$ because of the divergent sum, not $0.6613170494\ldots$ as it should be.

Both Wikipedia and Mathworld give this formula. What am I missing here?

Answer 1

It's a typo, they meant $$\log \prod_p (1-\frac{2}{p^2}) = -\sum_{n=1}^\infty 2^n\frac{P(\color{red}{2}n)}{n}$$