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Task/Semiprime/Racket/semiprime-1.rkt

@@ -0,0 +1,15 @@
+#lang racket
+(require math)
+
+(define (pair-factorize n)
+  "Return all two-number factorizations of a number"
+  (let ([up-limit (integer-sqrt n)])
+    (map (λ (x) (list x (/ n x)))
+	 (filter (λ (x) (<= x up-limit)) (divisors n)))))
+
+(define (semiprime n)
+  "Determine if a number is semiprime i.e. a product of two primes.
+Check if any pair of complete factors consists of primes."
+  (for/or ((pair (pair-factorize n)))
+    (for/and ((el pair))
+      (prime? el))))

Task/Semiprime/Racket/semiprime-2.rkt

@@ -0,0 +1,12 @@
+#lang racket
+(require math)
+
+(define (semiprime n)
+  "Alternative implementation.
+Check if there are two prime factors whose product is the argument
+or if there is a single prime factor whose square is the argument"
+  (let ([prime-factors (factorize n)])
+    (or (and (= (length prime-factors) 1)
+	     (= (expt (caar prime-factors) (cadar prime-factors)) n))
+	(and (= (length prime-factors) 2)
+	     (= (foldl (λ (x y) (* (car x) y)) 1 prime-factors) n)))))