  In this paper, we investigate the 2-adic valuations of the Stirling numbers
$S(n, k)$ of the second kind. We show that $v_2(S(4i, 5))=v_2(S(4i+3, 5))$ if
and only if $i\not\equiv 7\pmod {32}$. This confirms a conjecture of
Amdeberhan, Manna and Moll raised in 2008. We show also that $v_2(S(2^n+1,
k+1))= s_2(n)-1$ for any positive integer $n$, where $s_2(n)$ is the sum of
binary digits of $n$. It proves another conjecture of Amdeberhan, Manna and
Moll.
