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The numbers $14$ and $21$ are quite interesting.

The prime factorisation of $14$ is $2\cdot 7$ and the prime factorisation of $14+1$ is $3\cdot 5$. Note that $3$ is the prime after $2$ and $5$ is the prime before $7$.

Similarly, the prime factorisation of $21$ is $7\cdot 3$ and the prime factorisation of $21+1$ is $11\cdot 2$. Again, $11$ is the prime after $7$ and $2$ is the prime before $3$.

In other words, they both satisfy the following definition:

Definition: A positive integer $n$ is called interesting if it has a prime factorisation $n=pq$ with $p

e q$ such that the prime factorisation of $n+1$ is $p'q'$ where $p'$ is the prime after $p$ and $q'$ the prime before $q$.

Are there other interesting numbers?