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primes in clojure
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(ns primes) | |
(defn divides? [number divisor] | |
(zero? (mod number divisor))) | |
(divides? 4 2) ;; => true | |
(divides? 8 1) ;; => true | |
(divides? 3 2) ;; => false | |
(divides? 2 4) ;; => false | |
(defn is-prime? [p] | |
(let [possible-divisors (range 2 p) | |
divides-p? (partial divides? p)] | |
(not-any? divides-p? possible-divisors))) | |
(is-prime? 5) ;; => true | |
(is-prime? 9) ;; => false | |
;; counting primes in a range | |
(let [numbers (range 2 1000)] | |
(-> (filter is-prime? numbers) | |
count ;; remove/comment this line to see the numbers | |
)) | |
(defn sieve [s] | |
(cons (first s) | |
(lazy-seq (sieve (remove #(zero? (mod % (first s))) s))))) | |
(take 100 (sieve (iterate inc 2))) ;; works fine, but 10000 explodes the stack | |
(defn not-divisable-by-any | |
[number primes] | |
(when (not-any? (partial divides? number) primes) | |
number)) | |
(defn next-prime [primes] | |
(let [last-prime (last primes) | |
next-possible (iterate inc (inc last-prime))] | |
(->> (inc last-prime) | |
(iterate inc) | |
(some #(not-divisable-by-any % primes)) | |
(conj primes)))) | |
(next-prime [2 3 5 7]) ;; [2 3 4 5 7 11] | |
(defn nth-prime [n] | |
(last (last (take n (iterate next-prime [2]))))) | |
(time (nth-prime 20000)) ;; |
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