  A positive integer $n$ is called an abundant number if $\sigma (n)\ge 2n$,
where $\sigma (n)$ is the sum of all positive divisors of $n$. Let $E(x)$ be
the largest number of consecutive abundant numbers not exceeding $x$. In 1935,
P. Erd\H os proved that there are two positive constants $c_1$ and $c_2$ such
that $c_1\log\log\log x\le E(x)\le c_2\log\log\log x$. In this paper, we
resolve this old problem by proving that, $E(x)/\log \log\log x$ tends to a
limit as $x\to +\infty$, and the limit value has an explicit form which is
between $3$ and $4$.
