## Investigating a Prime Pattern

### Problem 146

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?