  We derive heuristically approximate formulas for the negative $k$--moments
$M_{-k}(x)$ of the gaps between consecutive primes$<x $ represented directly by
$\pi(x)$ --- the number of primes up to $x$. In particular we propose an
analytical formula for the sum of reciprocals of gaps between consecutive
primes $<x : ~ M_{-1}(x)\sim
\frac{\pi^2(x)}{x-2\pi(x)}\log\Big(\frac{x}{2\pi(x)}\Big) \sim x \log
\log(x)/\log^2(x)$. We illustrate obtained results by the enormous computer
data up to $x=4\times 10^{18}$.
