A horrible abuse of spec and laziness

prime.clj

(ns prime
  (:require [clojure.spec.alpha :as s]))


(s/def ::prime-number
  (fn [x]
    (cond (<= x 1) false
          (= 2 x) true
          :else
          (let [naturals (drop 2 (map inc (range)))
                primes (lazy-seq [2])]
            (letfn
              [(divisible-by? [numer denom]
                 (= (mod numer denom)
                    0))
               (find-next-prime [naturals primes]
                 (let [factor-predicates (map (fn [p] #(divisible-by? % p)) primes)
                       factor-of-primes? (fn [i] (some (fn [pred] (pred i)) factor-predicates))]
                   (drop-while factor-of-primes? naturals)))
               (sieve [naturals primes]
                 (let [[next-prime & rest-of-naturals] (find-next-prime naturals primes)]
                   (lazy-seq
                     (cons next-prime (sieve rest-of-naturals
                                             (cons next-prime primes))))))]
              (contains?
                (->> (sieve naturals primes)
                     (take-while #(>= x %))
                     (into #{}))
                x))))))