# euler / clojure / 27.clj

 ``` 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41``` ```; Euler published the remarkable quadratic formula: ; ; n² + n + 41 ; ; It turns out that the formula will produce 40 primes for the consecutive ; values n = 0 to 39. However, when n = 40, 40^(2) + 40 + 41 = 40(40 + 1) + 41 ; is divisible by 41, and certainly when n = 41, 41² + 41 + 41 is clearly ; divisible by 41. ; ; Using computers, the incredible formula n² − 79n + 1601 was discovered, which ; produces 80 primes for the consecutive values n = 0 to 79. The product of the ; coefficients, −79 and 1601, is −126479. ; ; Considering quadratics of the form: ; ; n² + an + b, where |a| < 1000 and |b| < 1000 ; ; where |n| is the modulus/absolute value of n ; e.g. |11| = 11 and |−4| = 4 ; ; Find the product of the coefficients, a and b, for the quadratic expression ; that produces the maximum number of primes for consecutive values of n, ; starting with n = 0. ; ; Answer: -59231 (defn prime? [n] (.isProbablePrime (bigint n) 10)) (defn quad [a b n] (+ (* n n) (* n a) b)) (defn num-primes [a b] (let [func (partial quad a b)] (count (take-while prime? (map func (iterate inc 0)))))) (let [abs (for [a (range -999 1001) b (range -999 1001)] [a b]) results (pmap (fn [[a b]] [a b (num-primes a b)]) abs) [a b _] (apply max-key #(% 2) results)] (println (* a b))) (shutdown-agents) ```