Moved 6 to 11 from ipython to python.

python/e006.py

@@ -1,5 +1,14 @@
-def euler_006():
-    return 0
 
-assert(euler_006() == 233168)
+def diff_between_sum_of_squares_and_square_sum(n):
+    a = sum([x for x in range(1, n + 1)])**2
+    b = sum([x**2 for x in range(1, n + 1)])
+    return a - b
+
+
+def euler_006():
+    return diff_between_sum_of_squares_and_square_sum(100)
+
+
+assert(diff_between_sum_of_squares_and_square_sum(10) == 2640)
+assert(euler_006() == 25164150)
 print("e006.py: {}".format(euler_006()))

python/e007.py

@@ -0,0 +1,32 @@
+from lib_prime import prime_nth
+
+
+def euler_007():
+    return prime_nth(10001)
+
+
+def euler_007_forum_4r0():
+    """ This solution is very naiv. I only got intrigued by
+    it because it looked so weird and simple in the beginning.
+    Turned out it is a straight forward and naiv as it gets once
+    you format the code properly and give somewhat meaningful
+    variable names. """
+    prime_count = 0
+    divisor = 2
+    prime = 2
+    while prime_count != 10001:
+        print(prime_count)
+        divisor = 2
+        while divisor <= prime:
+            if prime % divisor == 0 and divisor != prime:
+                divisor = prime
+            elif divisor == prime:
+                prime_count += 1
+            divisor += 1
+        prime += 1
+    prime -= 1
+    return prime
+
+
+assert(euler_007() == 104743)
+print("e007.py: {}".format(euler_007()))

python/e008.py

@@ -0,0 +1,44 @@
+from lib_misc import product
+
+
+def remove_newlines(s):
+    import re
+    return re.sub(r'\n', '', s)
+
+
+digits_string = """
+73167176531330624919225119674426574742355349194934
+96983520312774506326239578318016984801869478851843
+85861560789112949495459501737958331952853208805511
+12540698747158523863050715693290963295227443043557
+66896648950445244523161731856403098711121722383113
+62229893423380308135336276614282806444486645238749
+30358907296290491560440772390713810515859307960866
+70172427121883998797908792274921901699720888093776
+65727333001053367881220235421809751254540594752243
+52584907711670556013604839586446706324415722155397
+53697817977846174064955149290862569321978468622482
+83972241375657056057490261407972968652414535100474
+82166370484403199890008895243450658541227588666881
+16427171479924442928230863465674813919123162824586
+17866458359124566529476545682848912883142607690042
+24219022671055626321111109370544217506941658960408
+07198403850962455444362981230987879927244284909188
+84580156166097919133875499200524063689912560717606
+05886116467109405077541002256983155200055935729725
+71636269561882670428252483600823257530420752963450
+"""
+digits = [int(d) for d in remove_newlines(digits_string)]
+
+
+def get_largest_product_of_n_digits(digits, n):
+    return max((product(digits[i:i + n]) for i in range(len(digits))))
+
+
+def euler_008():
+    return get_largest_product_of_n_digits(digits, 13)
+
+
+assert(get_largest_product_of_n_digits(digits, 4) == 5832)
+assert(euler_008() == 23514624000)
+print("e008.py: {}".format(euler_008()))

python/e009.py

@@ -0,0 +1,10 @@
+def euler_009():
+    for a in range(1, 251):
+        for b in range(a + 1, 501):
+            c = 1000 - a - b
+            if a * a + b * b == c * c:
+                return a * b * c
+
+
+assert(euler_009() == 31875000)
+print("e009.py: {}".format(euler_009()))

python/e010.py

@@ -0,0 +1,9 @@
+from lib_prime import primes
+
+
+def euler_010():
+    return sum(primes(2 * 10**6))
+
+
+assert(euler_010() == 142913828922)
+print("e010.py: {}".format(euler_010()))

python/e011.py

@@ -0,0 +1,61 @@
+from lib_misc import product
+s = """
+08 02 22 97 38 15 00 40 00 75 04 05 07 78 52 12 50 77 91 08
+49 49 99 40 17 81 18 57 60 87 17 40 98 43 69 48 04 56 62 00
+81 49 31 73 55 79 14 29 93 71 40 67 53 88 30 03 49 13 36 65
+52 70 95 23 04 60 11 42 69 24 68 56 01 32 56 71 37 02 36 91
+22 31 16 71 51 67 63 89 41 92 36 54 22 40 40 28 66 33 13 80
+24 47 32 60 99 03 45 02 44 75 33 53 78 36 84 20 35 17 12 50
+32 98 81 28 64 23 67 10 26 38 40 67 59 54 70 66 18 38 64 70
+67 26 20 68 02 62 12 20 95 63 94 39 63 08 40 91 66 49 94 21
+24 55 58 05 66 73 99 26 97 17 78 78 96 83 14 88 34 89 63 72
+21 36 23 09 75 00 76 44 20 45 35 14 00 61 33 97 34 31 33 95
+78 17 53 28 22 75 31 67 15 94 03 80 04 62 16 14 09 53 56 92
+16 39 05 42 96 35 31 47 55 58 88 24 00 17 54 24 36 29 85 57
+86 56 00 48 35 71 89 07 05 44 44 37 44 60 21 58 51 54 17 58
+19 80 81 68 05 94 47 69 28 73 92 13 86 52 17 77 04 89 55 40
+04 52 08 83 97 35 99 16 07 97 57 32 16 26 26 79 33 27 98 66
+88 36 68 87 57 62 20 72 03 46 33 67 46 55 12 32 63 93 53 69
+04 42 16 73 38 25 39 11 24 94 72 18 08 46 29 32 40 62 76 36
+20 69 36 41 72 30 23 88 34 62 99 69 82 67 59 85 74 04 36 16
+20 73 35 29 78 31 90 01 74 31 49 71 48 86 81 16 23 57 05 54
+01 70 54 71 83 51 54 69 16 92 33 48 61 43 52 01 89 19 67 48
+"""
+
+
+def get_index(xs, index, default):
+    if index < 0:
+        return default
+    try:
+        return xs[index]
+    except IndexError:
+        return default
+
+
+def get_lists_for_all_directions():
+    # horizontal lists
+    hss = [list(map(int, h.split())) for h in s.split('\n') if h]
+    # vertical lists
+    vss = [list(vs) for vs in zip(*hss)]
+    # diagonal from top left to bottom right
+    dss_1 = [[get_index(hs, -19 + i + j, 1) for j, hs in enumerate(hss)]
+             for i in range(39)]
+    # diagonal from bottom left to top right
+    dss_2 = [[get_index(hs, -19 + i + j, 1) for j, hs in enumerate(hss[::-1])]
+             for i in range(39)]
+    # all lists
+    xss = hss + vss + dss_1 + dss_2
+    return xss
+
+
+def get_largest_product_of_n_digits(xs, n):
+    return max([product(xs[i:i + n]) for i in range(len(xs))])
+
+
+def euler_011():
+    xss = get_lists_for_all_directions()
+    return max([get_largest_product_of_n_digits(xs, 4) for xs in xss])
+
+
+assert(euler_011() == 70600674)
+print("e011.py: {}".format(euler_011()))

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

python/lib_prime_tests.py

@@ -2,9 +2,15 @@ import unittest
 try:
     from .lib_prime import prime_factors
     from .lib_prime import prime_factors_count
+    from .lib_prime import is_prime
+    from .lib_prime import prime_nth
+    from .lib_prime import primes
 except ModuleNotFoundError:
     from lib_prime import prime_factors
     from lib_prime import prime_factors_count
+    from lib_prime import is_prime
+    from lib_prime import prime_nth
+    from lib_prime import primes
 
 
 class TestPrimeMethods(unittest.TestCase):
@@ -20,6 +26,39 @@ class TestPrimeMethods(unittest.TestCase):
         self.assertEqual(prime_factors_count(2), {2: 1})
         self.assertEqual(prime_factors_count(147), {3: 1, 7: 2})
 
+    def test_is_prime(self):
+        self.assertTrue(is_prime(2))
+        self.assertTrue(is_prime(3))
+        self.assertTrue(is_prime(5))
+        self.assertTrue(is_prime(7))
+        self.assertTrue(is_prime(11))
+        self.assertTrue(is_prime(13))
+        self.assertTrue(is_prime(101))
+
+        self.assertFalse(is_prime(0))
+        self.assertFalse(is_prime(1))
+        self.assertFalse(is_prime(4))
+        self.assertFalse(is_prime(6))
+        self.assertFalse(is_prime(8))
+        self.assertFalse(is_prime(9))
+        self.assertFalse(is_prime(10))
+        self.assertFalse(is_prime(12))
+        self.assertFalse(is_prime(323))
+
+    def test_get_nth_prime(self):
+        self.assertEqual(prime_nth(1), 2)
+        self.assertEqual(prime_nth(2), 3)
+        self.assertEqual(prime_nth(3), 5)
+        self.assertEqual(prime_nth(4), 7)
+        self.assertEqual(prime_nth(5), 11)
+        self.assertEqual(prime_nth(6), 13)
+
+    def test_primes(self):
+        self.assertEqual(primes(19), [2, 3, 5, 7, 11, 13, 17, 19])
+        self.assertEqual(primes(20), [2, 3, 5, 7, 11, 13, 17, 19])
+        self.assertEqual(primes(25), [2, 3, 5, 7, 11, 13, 17, 19, 23])
+        self.assertEqual(primes(1), [])
+
 
 if __name__ == '__main__':
     unittest.main()