Looking for a formula on primes

I am looking for a formula that gives me a good estimate of the
product:

F(P) = П(Рk-2)/Pk, where Pk are primes from 3 to P.

I came up with an estimate that this should be close to

1/(log(P)*log(P) multiple a constant or a value that is close to
constant.

Your suggestions are very appreciated!

.