Question 26
Let $p\geq5$ be prime, let $q$ be the smallest prime greater than $p$, and let $n$ be the number of positive divisors of $p+q$, including 1 and $p+q$.
a. Prove that $n\geq4$ for every such $p$.
b. Find the smallest possible value $m$ of $n$ over all choices of $p$:
$b_1)$ Give a prime $p$ attaining $m$.
$b_2)$ Prove that no prime $p$ gives $n\lt m$.
a. Prove that $n\geq4$ for every such $p$.
b. Find the smallest possible value $m$ of $n$ over all choices of $p$:
$b_1)$ Give a prime $p$ attaining $m$.
$b_2)$ Prove that no prime $p$ gives $n\lt m$.