The smallest positive integer $n$ for which the numbers $n^2+1$, $n^2+3$, $n^2+7$, $n^2+9$, $n^2+13$, and $n^2+27$ are consecutive primes is $10$. The sum of all such integers $n$ below one-million is $1242490$.

What is the sum of all such integers $n$ below $150$ million?