Since p-1 will be even for any odd prime, 2 must be a prime factor of n, and as it is also one less than a prime, so is 3.
Since 2x3 is one less than a prime, 7 is also a prime factor of n. Of the products of subsets of 2,3,7, only 2x3x7 is one less than a prime, so 43 is also a prime factor of n.
Of the products of subsets of 2,3,7,43, none are one less than a prime, so we can stop there.
n = 2x3x7x43 = 1806.