Somewhat: you want the number to be as unsmooth (having few small factors) as possible. Since the factorial is the product of all numbers up to a given number,

Somewhat: you want the number to be as unsmooth (having few small factors) as possible. Since the factorial is the product of all numbers up to a given number, that happens when the top number is a prime, since the next number is necessarily divisible by 2 (and therefore more likely to be smooth).