Moved 6 to 11 from ipython to python.

python/lib_prime.py

@@ -5,6 +5,9 @@ except ModuleNotFoundError:
 
 
 def prime_factors(n):
+    """
+    :param n: number for which prime factors should be returned
+    """
     # TODO: Look into using a prime wheel instead.
     factors = []
     rest = n
@@ -24,4 +27,83 @@ def prime_factors(n):
 
 
 def prime_factors_count(n):
+    """
+
+    :param n: numober for which prime factor counts are returned
+    :returns: a dict where they key is a prime vactor and the value
+              the count of how of that value occurs
+
+    """
     return get_item_counts(prime_factors(n))
+
+
+def is_prime(n):
+    """Returns True if n is prime and False otherwise.
+
+    :param n: number to be checked
+
+    """
+    if n < 2:
+        return False
+    if n == 2 or n == 3:
+        return True
+    if n % 2 == 0:
+        return False
+    d = 3
+    while d * d <= n:
+        if n % d == 0:
+            return False
+        d += 2
+    return True
+
+
+def prime_nth(n):
+    """Returns the nth prime number. The first number
+    is 1 indexed, i.e. n = 1 -> 2, n = 2 -> 3, etc.
+
+    :param n:
+
+    """
+    if n == 1:
+        return 2
+    if n == 2:
+        return 3
+    p = 5
+    i = 3
+    while i < n:
+        p = p + 2
+        if is_prime(p):
+            i += 1
+    return p
+
+
+def primes(n_max):
+    """
+    Returns a list of all primes smaller n based
+    on sieve of erasthones algorithm.
+
+    If bitarray module is installed it will be used
+    for the array, otherwise a regular Python list is
+    used. The function should work for much larger
+    numbers with bitarray.
+
+    :param n_max:
+    """
+    try:
+        import bitarray
+        b = bitarray.bitarray(n_max)
+        b.setall(True)
+    except ModuleNotFoundError:
+        b = [True for _ in range(n_max)]
+    n = 1
+    b[n - 1] = False
+    while n * n <= n_max:
+        if b[n - 1] is True:
+            for i in range(n + n, n_max + 1, n):
+                b[i - 1] = False
+        n += 1
+    ps = []
+    for i in range(1, n_max + 1):
+        if b[i - 1]:
+            ps.append(i)
+    return ps