Data commit

Task/Chernicks-Carmichael-numbers/Python/chernicks-carmichael-numbers.py

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+"""
+
+Python implementation of
+http://rosettacode.org/wiki/Chernick%27s_Carmichael_numbers
+
+"""
+
+# use sympy for prime test
+
+from sympy import isprime
+
+# based on C version
+
+def primality_pretest(k):
+    if not (k % 3) or not (k % 5) or not (k % 7) or not (k % 11) or not(k % 13) or not (k % 17) or not (k % 19) or not (k % 23):
+        return (k <= 23)
+
+    return True
+
+def is_chernick(n, m):
+
+    t = 9 * m
+
+    if not primality_pretest(6 * m + 1):
+        return False
+
+    if not primality_pretest(12 * m + 1):
+        return False
+
+    for i in range(1,n-1):
+        if not primality_pretest((t << i) + 1):
+            return False
+
+    if not isprime(6 * m + 1):
+        return False
+
+    if not isprime(12 * m + 1):
+        return False
+
+    for i in range(1,n - 1):
+        if not isprime((t << i) + 1):
+            return False
+
+    return True
+
+for n in range(3,10):
+
+    if n > 4:
+        multiplier = 1 << (n - 4)
+    else:
+        multiplier = 1
+
+    if n > 5:
+        multiplier *= 5
+
+
+    k = 1
+
+    while True:
+        m = k * multiplier
+
+        if is_chernick(n, m):
+            print("a("+str(n)+") has m = "+str(m))
+            break
+
+        k += 1