Add own bitarray and Miller-Rabin primality test.

python/lib_prime.py

@@ -1,4 +1,5 @@
 from functools import lru_cache
+from lib_bitarray import Bitarray
 try:
     from lib_misc import get_item_counts
     from lib_misc import product
@@ -65,6 +66,29 @@ def is_prime(n):
     return True
 
 
+def is_prime_rabin_miller(number):
+    """ Rabin-Miller Primality Test """
+    if number % 6 not in [1,5]:
+        return False
+
+    r, s = 1, number - 1
+    while s % 2 == 0:
+        s //= 2
+        r += 1
+
+    for witness in [2, 3, 5, 7, 11, 13, 17, 23, 29, 31, 37, 41, 43, 47, 53]:
+        remainder = pow(witness, s, number)
+        if remainder == 1:
+            continue
+        for _ in range(1, r):
+            if remainder == number - 1:
+                break
+            remainder = pow(remainder, 2, number)
+        else:
+            return False
+    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.
@@ -97,12 +121,8 @@ def primes(n_max):
 
     :param n_max:
     """
-    try:
-        import bitarray
-        b = bitarray.bitarray(n_max)
-        b.setall(True)
-    except ModuleNotFoundError:
-        b = [True for _ in range(n_max)]
+    b = Bitarray(n_max)
+    b.setall(True)
     n = 1
     b[n - 1] = False
     while n * n <= n_max: