Data commit

Task/Carmichael-3-strong-pseudoprimes/Python/carmichael-3-strong-pseudoprimes.py

@@ -0,0 +1,71 @@
+class Isprime():
+    '''
+    Extensible sieve of Eratosthenes
+
+    >>> isprime.check(11)
+    True
+    >>> isprime.multiples
+    {2, 4, 6, 8, 9, 10}
+    >>> isprime.primes
+    [2, 3, 5, 7, 11]
+    >>> isprime(13)
+    True
+    >>> isprime.multiples
+    {2, 4, 6, 7, 8, 9, 10, 11, 12, 14, 15, 16, 18, 20, 21, 22}
+    >>> isprime.primes
+    [2, 3, 5, 7, 11, 13, 17, 19]
+    >>> isprime.nmax
+    22
+    >>>
+    '''
+    multiples = {2}
+    primes = [2]
+    nmax = 2
+
+    def __init__(self, nmax):
+        if nmax > self.nmax:
+            self.check(nmax)
+
+    def check(self, n):
+        if type(n) == float:
+            if not n.is_integer(): return False
+            n = int(n)
+        multiples = self.multiples
+        if n <= self.nmax:
+            return n not in multiples
+        else:
+            # Extend the sieve
+            primes, nmax = self.primes, self.nmax
+            newmax = max(nmax*2, n)
+            for p in primes:
+                multiples.update(range(p*((nmax + p + 1) // p), newmax+1, p))
+            for i in range(nmax+1, newmax+1):
+                if i not in multiples:
+                    primes.append(i)
+                    multiples.update(range(i*2, newmax+1, i))
+            self.nmax = newmax
+            return n not in multiples
+
+    __call__ = check
+
+
+def carmichael(p1):
+    ans = []
+    if isprime(p1):
+        for h3 in range(2, p1):
+            g = h3 + p1
+            for d in range(1, g):
+                if (g * (p1 - 1)) % d == 0 and (-p1 * p1) % h3 == d % h3:
+                    p2 = 1 + ((p1 - 1)* g // d)
+                    if isprime(p2):
+                        p3 = 1 + (p1 * p2 // h3)
+                        if isprime(p3):
+                            if (p2 * p3) % (p1 - 1) == 1:
+                                #print('%i X %i X %i' % (p1, p2, p3))
+                                ans += [tuple(sorted((p1, p2, p3)))]
+    return ans
+
+isprime = Isprime(2)
+
+ans = sorted(sum((carmichael(n) for n in range(62) if isprime(n)), []))
+print(',\n'.join(repr(ans[i:i+5])[1:-1] for i in range(0, len(ans)+1, 5)))