tasks a-s

Task/Prime-decomposition/Python/prime-decomposition-1.py

@@ -0,0 +1,47 @@
+import sys
+
+def is_prime(n):
+    return zip((True, False), decompose(n))[-1][0]
+
+class IsPrimeCached(dict):
+    def __missing__(self, n):
+        r = is_prime(n)
+        self[n] = r
+        return r
+
+is_prime_cached = IsPrimeCached()
+
+def primes():
+    yield 2
+    n = 3
+    while n < sys.maxint - 2:
+        yield n
+        n += 2
+        while n < sys.maxint - 2 and not is_prime_cached[n]:
+            n += 2
+
+def decompose(n):
+    for p in primes():
+        if p*p > n: break
+        while n % p == 0:
+            yield p
+            n /=p
+    if n > 1:
+        yield n
+
+if __name__ == '__main__':
+    # Example: calculate factors of Mersenne numbers to M59 #
+
+    import time
+
+    for m in primes():
+        p = 2 ** m - 1
+        print( "2**{0:d}-1 = {0:d}, with factors:".format(m, p) )
+        start = time.time()
+        for factor in decompose(p):
+            print factor,
+            sys.stdout.flush()
+
+        print( "=> {0:.2f}s".format( time.time()-start ) )
+        if m >= 59:
+            break

Task/Prime-decomposition/Python/prime-decomposition-2.py

@@ -0,0 +1,18 @@
+primelist = [2,3]
+def is_prime(n):
+	for y in primes():
+		if not n % y: return False
+		if n > y * y: return True
+
+def primes():
+	for n in primelist: yield n
+
+	n = primelist[-1] + 2
+	while True:
+		n += 2
+		for x in primelist:
+			if not n % x: break
+			if x * x > n:
+				primelist.append(n)
+				yield n
+				break

Task/Prime-decomposition/Python/prime-decomposition-3.py

@@ -0,0 +1,21 @@
+def fac(n):
+    step = lambda x: 1 + x*4 - (x/2)*2
+    maxq = long(math.floor(math.sqrt(n)))
+    d = 1
+    q = n % 2 == 0 and 2 or 3
+    while q <= maxq and n % q != 0:
+        q = step(d)
+        d += 1
+    res = []
+    if q <= maxq:
+        res.extend(fac(n//q))
+        res.extend(fac(q))
+    else: res=[n]
+    return res
+
+if __name__ == '__main__':
+    import time
+    start = time.time()
+    tocalc =  2**59-1
+    print "%s = %s" % (tocalc, fac(tocalc))
+    print "Needed %ss" % (time.time() - start)