hasdiv n == hasdiv1 (n - 1) n
hasdiv1 0 n == false
hasdiv1 1 n == false
hasdiv1 a n == true <| n % a = 0 |> hasdiv1 (a - 1) n

prime 1 == false
prime n == not (hasdiv n)

howmanydivisors n == hmd1 2 n
hmd1 a a == 0
hmd1 a b == 1 + n <| b % a = 0 |> n                                      \
                    where { n == hmd1 (a + 1) b }

primesbetween a b == 0     <| a > b |>                                   \
                     1 + n <| prime a |>                                 \
                     n                                                   \
                               where { n == primesbetween (a + 1) b }