(ns primes.primes)

(defn debug-on? []
  "debug print statements :)"
  false)

(defn sieve [n] 
  (let [n (int n)] 
    "Returns a list of all primes from 2 to n (from: http://paste.lisp.org/display/69952)" 
    (let [root (int (Math/round (Math/floor (Math/sqrt n))))] 
      (loop [i (int 3) 
             a (int-array n) 
             result (list 2)] 
            (if (>= i n) (reverse result) 
                (recur (+ i (int 2)) 
                       (if (< i root) (loop [arr a inc (+ i i) j (* i i)] 
                                            (if (>= j n) arr 
                                                (recur (do (aset arr j (int 1)) arr) inc (+ j inc)))) 
                           a) 
                       (if (zero? (aget a i)) (conj result i) 
                            result)))))))

(defn get-primes
  "take n primes from the set of all primes"
  [n]
  (take n (sieve (* n n))))

(defn nary-dec 
  "map base_n -> decimal (for placement of values in the matriies"
  [n num]
  (int (reduce + (map-indexed (fn [i v] (* (Math/pow n i) v)) (reverse num)))))

(defn psq [n]
  "get the next (i,j,value) sequence of primes for the matrix"
  (let [primes (get-primes (* n n))] 
    (for [i (range n) j (range n)]
       [i j (nth primes (nary-dec n (list i j)))])))

(defn amatrix
  "make a matrix given (i,j,value) tuples"
  [i_j_v-list]
  (if (zero? (count i_j_v-list)) [[]]
  (let [size (inc (first (last i_j_v-list)))]
    (vec (for [u (range size)]
         (vec (for [v (range size)]
            (last (nth i_j_v-list (nary-dec size [u v]))))))))))

(defn gpm
  "get n x n prime matrix"
  [n]
  (amatrix (psq n)))

(defn sumrows
  [matrix]
  (map (partial reduce +) matrix))

(defn summat
  "sum of a matrix is the sum of the sum of each row"
  [matrix]
  (reduce + (sumrows matrix)))

(defn get-pair
  [n]
  [(gpm n) (gpm (inc n))])

(defn op-pair
  [op pair]
  (op (summat (first pair)) (summat (second pair))))

(defn reduce-primes-with [op n]
  (map (partial op-pair op) (map get-pair (range (inc n)))))

(println (reduce-primes-with * 15))