2. Let $D(k)$ denote the number of positive divisors of $k$. For a quadruple of positive integers $(a, b, c, d)$, if
$$
b=a^{2}+1, c=b^{2}+1, d=c^{2}+1 \text {, }
$$

and $D(a)+D(b)+D(c)+D(d)$ is odd, then it is called "green". How many green quadruples $(a, b, c, d)$ are there with $a, b, c, d$ less than 1000000?
2. Notice that, $D(k)$ is odd if and only if $k$ is a perfect square.
For any positive integer $m$, we have
$$
m^{2}d>c^{2}>b^{4}>a^{8}$, which gives
$$
\begin{array}{l}
2^{10}=1024>10^{3}>a^{4} \\
\Rightarrow 6^{2}>2^{5}>a^{2} \Rightarrow a<6 \\
\Rightarrow a=1,4 .
\end{array}
$$

Thus, the two green number arrays are
$$
(1,2,5,26),(4,17,290,84101) \text {. }
$$

Therefore, the required conclusion is 2.