All positive integers can be partitioned in such a way that each and every term of the partition can be expressed as $2^i\times 3^j$, where $i,j\ge 0$.

Let's consider only such partitions where none of the terms can divide any of the other terms.
For example, the partition of $17=2+6+9=(2^1\times 3^0+2^1\times 3^1+2^0\times 3^2)$ would not be valid since $2$ can divide $6$. Neither would the partition $17=16+1=(2^4\times 3^0+2^0\times 3^0)$ since $1$ can divide $16$. The only valid partition of $17$ would be $8+9=(2^3\times 3^0+2^0\times 3^2)$.

Many integers have more than one valid partition, the first being $11$ having the following two partitions.
$11=2+9=(2^1\times 3^0+2^0\times 3^2)$
$11=8+3=(2^3\times 3^0+2^0\times 3^1)$

Let's define $P(n)$ as the number of valid partitions of $n$. For example, $P(11)=2$.

Let's consider only the prime integers $q$ which would have a single valid partition such as $P(17)$.

The sum of the primes $q<100$ such that $P(q)=1$ equals $233$.

Find the sum of the primes $q<1000000$ such that $P(q)=1$.