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diff --git a/hw3/mr.py b/hw3/mr.py
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--- /dev/null
+++ b/hw3/mr.py
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+import random
+
+_mrpt_num_trials = 5 # number of bases to test
+
+def is_probable_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.
+
+    >>> is_probable_prime(1)
+    Traceback (most recent call last):
+        ...
+    AssertionError
+    >>> is_probable_prime(2)
+    True
+    >>> is_probable_prime(3)
+    True
+    >>> is_probable_prime(4)
+    False
+    >>> is_probable_prime(5)
+    True
+    >>> is_probable_prime(123456789)
+    False
+
+    >>> primes_under_1000 = [i for i in range(2, 1000) if is_probable_prime(i)]
+    >>> len(primes_under_1000)
+    168
+    >>> primes_under_1000[-10:]
+    [937, 941, 947, 953, 967, 971, 977, 983, 991, 997]
+
+    >>> is_probable_prime(6438080068035544392301298549614926991513861075340134\
+3291807343952413826484237063006136971539473913409092293733259038472039\
+7133335969549256322620979036686633213903952966175107096769180017646161\
+851573147596390153)
+    True
+
+    >>> is_probable_prime(7438080068035544392301298549614926991513861075340134\
+3291807343952413826484237063006136971539473913409092293733259038472039\
+7133335969549256322620979036686633213903952966175107096769180017646161\
+851573147596390153)
+    False
+    """
+    assert n >= 2
+    # special case 2
+    if n == 2:
+        return True
+    # ensure n is odd
+    if n % 2 == 0:
+        return False
+    # write n-1 as 2**s * d
+    # repeatedly try to divide n-1 by 2
+    s = 0
+    d = n-1
+    while True:
+        quotient, remainder = divmod(d, 2)
+        if remainder == 1:
+            break
+        s += 1
+        d = quotient
+    assert(2**s * d == n-1)
+
+    # test the base a to see whether it is a witness for the compositeness of n
+    def try_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 # n is definitely composite
+
+    for i in range(_mrpt_num_trials):
+        a = random.randrange(2, n)
+        if try_composite(a):
+            return False
+
+    return True # no base tested showed n as composite