Question 35
A set of positive integers is called fragrant if it contains at least two elements and each of its elements has a prime factor in common with at least one of the other elements. Let $P(n) = n^2 + n + 1$. What is the least possible value of the positive integer $b$ such that there exists a non-negative integer $a$ for which the set
$$
\{P(a + 1), P(a + 2), \dots, P(a + b)\}
$$
is fragrant?
$$
\{P(a + 1), P(a + 2), \dots, P(a + b)\}
$$
is fragrant?