September 2017 Update

Task/Carmichael-3-strong-pseudoprimes/Clojure/carmichael-3-strong-pseudoprimes.clj

@@ -0,0 +1,27 @@
+(ns example
+  (:gen-class))
+
+(defn prime? [n]
+  " Prime number test (using Java) "
+  (.isProbablePrime (biginteger n) 16))
+
+(defn carmichael [p1]
+  " Triplets of Carmichael primes, with first element prime p1 "
+  (if (prime? p1)
+    (into [] (for [h3 (range 2 p1)
+          :let [g (+ h3 p1)]
+          d (range 1 g)
+          :when (and (= (mod (* g (dec p1)) d) 0)
+                     (= (mod (- (* p1 p1)) h3) (mod d h3)))
+          :let [p2 (inc (quot (* (dec p1) g) d))]
+          :when (prime? p2)
+          :let [p3 (inc (quot (* p1 p2) h3))]
+          :when (prime? p3)
+          :when (= (mod (* p2 p3) (dec p1)) 1)]
+         [p1 p2 p3]))))
+
+; Generate Result
+(def numbers (mapcat carmichael (range 2 62)))
+(println (count numbers) "Carmichael numbers found:")
+(doseq [t numbers]
+  (println (format "%5d x %5d x %5d = %10d" (first t) (second t) (last t) (apply * t))))