6. Show that there are infinitely many primes of the form $5 k+4$. (Hint: Let $n$ be a positive integer and form $Q=5(n!)^{2}+4$. Show that $Q$ has a prime divisor of the form $5 k+4$ greater than $n$. To do this, use the law of quadratic reciprocity to show that if a prime $p$ divides $Q$, then $\left(\frac{p}{5}\right)=1$.)