Lazy list of primes, as implemented in 15 minutes on the subway on my phone

primes.clj

(defn divides [m n]
  (= 0
     (mod n m)))

(defn my-and [x y]
  (and x y))

(defn all? [pred xs]
  (reduce my-and true
    (map pred xs)))

(defn prime? [n]
  (and
    (not (== n 1))
    (not (== n 0))
    (all?
      #(not (divides % n))
      (range 2 (+ 0.1 (Math/sqrt n))))))

(def primes
  (filter prime?
    (range)))

my-and is hacky. I had to do that because and is a macro, not a function. Looking back, I kind of like this way of defining all?:

(defn all? [pred xs]
  (not (some #(not (pred %)) xs)))

And it's faster because unlike reducing with my-and, this will short circuit. I still think it's silly that this all? function isn't built in.

Another hacky thing is adding 0.1 to the square root passed to range. I did this because range excludes the stop value. If I don't add anything to the sqrt, perfect squares like (prime? 9) incorrectly become true. If I add 1, then 2 is incorrectly reported as not prime. A more elegant way would be to use

(range 2 (Math/ceil (Math/sqrt n)))