Question 177
A positive integer $n$ is called *divisor primary* if for every positive divisor $d$ of $n$ at least one of the numbers $d-1$ and $d+1$ is prime. For example, $8$ is divisor primary, because its positive divisors $1$, $2$, $4$, and $8$ each differ by $1$ from a prime number ($2$, $3$, $5$, and $7$, respectively), while $9$ is not divisor primary, because the divisor $9$ does not differ by $1$ from a prime number (both $8$ and $10$ are composite).
Determine the largest divisor primary number.
Determine the largest divisor primary number.