Data commit

Task/Miller-Rabin-primality-test/Racket/miller-rabin-primality-test.rkt

@@ -0,0 +1,32 @@
+#lang racket
+(define (miller-rabin-expmod base exp m)
+  (define (squaremod-with-check x)
+    (define (check-nontrivial-sqrt1 x square)
+      (if (and (= square 1)
+               (not (= x 1))
+               (not (= x (- m 1))))
+          0
+          square))
+    (check-nontrivial-sqrt1 x (remainder (expt x 2) m)))
+  (cond ((= exp 0) 1)
+        ((even? exp) (squaremod-with-check
+                      (miller-rabin-expmod base (/ exp 2) m)))
+        (else
+         (remainder (* base (miller-rabin-expmod base (- exp 1) m))
+                    m))))
+
+(define (miller-rabin-test n)
+  (define (try-it a)
+    (define (check-it x)
+      (and (not (= x 0)) (= x 1)))
+    (check-it (miller-rabin-expmod a (- n 1) n)))
+  (try-it (+ 1 (random (remainder (- n 1) 4294967087)))))
+
+(define (fast-prime? n times)
+  (for/and ((i (in-range times)))
+    (miller-rabin-test n)))
+
+(define (prime? n(times 100))
+  (fast-prime? n times))
+
+(prime? 4547337172376300111955330758342147474062293202868155909489) ;-> outputs true