Initial commit

primes.py

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+
+def sieve(limit):
+    '''https://stackoverflow.com/a/3941967
+    '''
+    a = [True] * limit                          # Initialize the primality list
+    a[0] = a[1] = False
+
+    for (i, isprime) in enumerate(a):
+        if isprime:
+            yield i
+            for n in range(i*i, limit, i):     # Mark factors non-prime
+                a[n] = False
+
+
+def is_prime(n):
+    '''Returns True if n is prime.
+    https://stackoverflow.com/a/18833845'''
+    if n == 1:
+        return False
+    if n == 2:
+        return True
+    if n == 3:
+        return True
+    if n % 2 == 0:
+        return False
+    if n % 3 == 0:
+        return False
+
+    i = 5
+    w = 2
+
+    while i * i <= n:
+        if n % i == 0:
+            return False
+        i += w
+        w = 6 - w
+
+    return True
+
+
+def prime_factors(n):
+    '''https://stackoverflow.com/a/22808285
+    '''
+    i = 2
+    factors = []
+    while i * i <= n:
+        if n % i:
+            i += 1
+        else:
+            n //= i
+            factors.append(i)
+    if n > 1:
+        factors.append(n)
+    return factors