We use $x\oplus y$ for the bitwise XOR of $x$ and $y$.

Define the XOR-product of $x$ and $y$, denoted by $x\otimes y$, similar to a long multiplication in base $2$, except that the intermediate results are XORed instead of the usual integer addition.

For example, $7\otimes 3=9$, or in base $2$, ${111}_2\otimes {11}_2={1001}_2$:

$$\begin{array}{r}\phantom{\otimes 111}{111}_2\\ \otimes \phantom{1111}{11}_2\\ \phantom{\otimes 111}{111}_2\\ \oplus \phantom{11}{111}_2\phantom{9}\\ \phantom{\otimes 11}{1001}_2\end{array}$$

An XOR-prime is an integer $n$ greater than $1$ that is not an XOR-product of two integers greater than $1$. The above example shows that $9$ is not an XOR-prime. Similarly, $5=3\otimes 3$ is not an XOR-prime. The first few XOR-primes are $2,3,7,11,13,...$ and the 10th XOR-prime is $41$.

Find the $5000000$th XOR-prime.