Data update

Task/Blum-integer/Common-Lisp/blum-integer.lisp

@@ -0,0 +1,47 @@
+(defun is-factor (x y)
+  (zerop (mod x y)))
+
+(defun is-congruent (num a n)
+  (= (mod num n) a))
+
+(defun is-prime (n)
+  (cond ((< n 4) (or (= n 2) (= n 3)))
+        ((or (zerop (mod n 2)) (zerop (mod n 3))) nil)
+        (t (loop for i from 5 to (floor (sqrt n)) by 6
+                 never (or (is-factor n i)
+                           (is-factor n (+ i 2)))))))
+
+(defun first-factor (n)
+  (loop for i from 2 to (floor (sqrt n))
+        thereis (if (is-factor n i) i nil)))
+
+(defun is-blum (n)
+  (let ((factor (first-factor n)))
+    (and factor
+         (is-congruent factor 3 4)
+         (/= factor (/ n factor))
+         (is-congruent (/ n factor) 3 4)
+         (is-prime factor)
+         (is-prime (/ n factor)))))
+
+(defun main ()
+  (let ((n 0)
+        (i 1)
+        (blums '())
+        (counts '()))
+    (dotimes (i 10) (push (cons i 0) counts))
+    (loop while (<= n 400000)
+          do (setf i (+ i 2))
+             (when (is-blum i)
+               (incf n)
+               (incf (cdr (assoc (mod i 10) counts)))
+               (when (<= n 50)
+                 (push i blums)
+                 (when (= n 50)
+                   (format t "First 50 Blum integers:~%")
+                   (format t "~{~5d~5d~5d~5d~5d~5d~5d~5d~5d~5d~%~}~%" (reverse blums))))
+               (if (find n '(26828 100000 200000 300000 400000))
+                   (format t "The ~7:dth Blum integer is: ~9:d~%" n i))))
+    (format t "~%% distribution of the first 400,000 Blum integers:~%")
+    (dolist (x '(1 3 7 9))
+      (format t "~3$% end in ~a~%" (/ (cdr (assoc x counts)) 4000) x))))