n:{1...}. 
f:(Prime
). f is a factorization of nn:{1...}.
Thm*
h:({2..(n+1)
}).
Thm* n =
{2..n+1}(h) & is_prime_factorization(2; (n+1); h)a,b:
, f:({a..b}), x:.
Thm*
a 
x < b 
complete_intseg_mset(a; b; f)(x) = 0f:(Prime), x:Prime. prime_mset_complete(f)(x) = f(x)a,b:, f:({a..b}), x:{a..b}. complete_intseg_mset(a; b; f)(x) = f(x)f:(Prime), x:. prime(x) prime_mset_complete(f)(x) = 0