3 ms·

Is that fact that 7 is prime relevant?

• lvh 7y ago
  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).
• pfortuny 7y ago
  Possibly that all the odd factors of 5040 are prime and they are all the primes less than pr equal to the largest prime divisor of 5040. Only happens for 7!
  • lisper 7y ago
    > all the odd factors of 5040 are prime No, they aren't. 15, 21, 35 are all factors of 5040. In fact, any number with more than two factors will necessarily have at least one non-prime odd factor.
    • pfortuny 7y ago
      Sorry, my bad. Silly comment.
• impendia 7y ago
  Yes. For example, 7! is already divisible by 8. The smallest integer that 8! is divisible by, and that 7! isn't, is 32 -- much less small.