Calculate ω(12! - 9!); this prime omega function returns the number of distinct prime divisors

Definition: ω(n) = ∑ (p|n) 1
Factoring 12! - 9! along with the number theoretic result: n is prime if n has no prime divisors less than √n. The contrapositive of this result is slightly easier to prove imo, namely n is composite if it has at least one prime divisor less than or equal to square root of n.(Mohammad Afzaal Butt)
Norway mathematician, Fredrik Meyer and Michael Hardy January 2012 proved this theorem, but Arturo Magidin doubted the validity.
June 2019, PHD mathematician financial analyst Xiang Yu, Shanghai, China seemed amazed that ω(n) achieves a maximum at primorial numbers, for example ω(2*3*5*7*11*13*17)=7 which is quite expected so I don't see what is so impressive about that obvious truth. Perhaps I am missing something?