Initial data commit

Task/Miller-Rabin-primality-test/Python/miller-rabin-primality-test-1.py

@@ -0,0 +1,39 @@
+import random
+
+def is_Prime(n):
+    """
+    Miller-Rabin primality test.
+
+    A return value of False means n is certainly not prime. A return value of
+    True means n is very likely a prime.
+    """
+    if n!=int(n):
+        return False
+    n=int(n)
+    #Miller-Rabin test for prime
+    if n==0 or n==1 or n==4 or n==6 or n==8 or n==9:
+        return False
+
+    if n==2 or n==3 or n==5 or n==7:
+        return True
+    s = 0
+    d = n-1
+    while d%2==0:
+        d>>=1
+        s+=1
+    assert(2**s * d == n-1)
+
+    def trial_composite(a):
+        if pow(a, d, n) == 1:
+            return False
+        for i in range(s):
+            if pow(a, 2**i * d, n) == n-1:
+                return False
+        return True
+
+    for i in range(8):#number of trials
+        a = random.randrange(2, n)
+        if trial_composite(a):
+            return False
+
+    return True

Task/Miller-Rabin-primality-test/Python/miller-rabin-primality-test-2.py

@@ -0,0 +1,37 @@
+def _try_composite(a, d, n, s):
+    if pow(a, d, n) == 1:
+        return False
+    for i in range(s):
+        if pow(a, 2**i * d, n) == n-1:
+            return False
+    return True # n  is definitely composite
+
+def is_prime(n, _precision_for_huge_n=16):
+    if n in _known_primes:
+        return True
+    if any((n % p) == 0 for p in _known_primes) or n in (0, 1):
+        return False
+    d, s = n - 1, 0
+    while not d % 2:
+        d, s = d >> 1, s + 1
+    # Returns exact according to http://primes.utm.edu/prove/prove2_3.html
+    if n < 1373653:
+        return not any(_try_composite(a, d, n, s) for a in (2, 3))
+    if n < 25326001:
+        return not any(_try_composite(a, d, n, s) for a in (2, 3, 5))
+    if n < 118670087467:
+        if n == 3215031751:
+            return False
+        return not any(_try_composite(a, d, n, s) for a in (2, 3, 5, 7))
+    if n < 2152302898747:
+        return not any(_try_composite(a, d, n, s) for a in (2, 3, 5, 7, 11))
+    if n < 3474749660383:
+        return not any(_try_composite(a, d, n, s) for a in (2, 3, 5, 7, 11, 13))
+    if n < 341550071728321:
+        return not any(_try_composite(a, d, n, s) for a in (2, 3, 5, 7, 11, 13, 17))
+    # otherwise
+    return not any(_try_composite(a, d, n, s)
+                   for a in _known_primes[:_precision_for_huge_n])
+
+_known_primes = [2, 3]
+_known_primes += [x for x in range(5, 1000, 2) if is_prime(x)]