diff --git a/maths/prime_check.py b/maths/prime_check.py
index ed8fbbae809a..ef987901abb3 100644
--- a/maths/prime_check.py
+++ b/maths/prime_check.py
@@ -4,26 +4,21 @@
 import unittest
 
 
-def prime_check(number: int) -> bool:
-    """
-    Check to See if a Number is Prime.
+def prime_check(number):
+    """Checks to see if a number is a prime.
 
-    A number is prime if it has exactly two dividers: 1 and itself.
+    A number is prime if it has exactly two factors: 1 and itself.
     """
-    if number < 2:
-        # Negatives, 0 and 1 are not primes
-        return False
-    if number < 4:
+
+    if 1 < number < 4:
         # 2 and 3 are primes
         return True
-    if number % 2 == 0:
-        # Even values are not primes
+    elif number < 2 or not number % 2:
+        # Negatives, 0, 1 and all even numbers are not primes
         return False
 
-    # Except 2, all primes are odd. If any odd value divide
-    # the number, then that number is not prime.
-    odd_numbers = range(3, int(math.sqrt(number)) + 1, 2)
-    return not any(number % i == 0 for i in odd_numbers)
+    odd_numbers = range(3, int(math.sqrt(number) + 1), 2)
+    return not any(not number % i for i in odd_numbers)
 
 
 class Test(unittest.TestCase):
@@ -40,12 +35,15 @@ def test_primes(self):
         self.assertTrue(prime_check(29))
 
     def test_not_primes(self):
-        self.assertFalse(prime_check(-19), "Negative numbers are not prime.")
         self.assertFalse(
-            prime_check(0), "Zero doesn't have any divider, primes must have two."
+            prime_check(-19), "Negative numbers are excluded by definition of prime numbers.")
+        self.assertFalse(
+            prime_check(
+                0), "Zero doesn't have any positive factors, primes must have exactly two."
         )
         self.assertFalse(
-            prime_check(1), "One just have 1 divider, primes must have two."
+            prime_check(
+                1), "One only has 1 positive factor, primes must have exactly two."
         )
         self.assertFalse(prime_check(2 * 2))
         self.assertFalse(prime_check(2 * 3))
diff --git a/searches/breadth_first_search.py b/searches/breadth_first_search.py
new file mode 100644
index 000000000000..7b639586f17b
--- /dev/null
+++ b/searches/breadth_first_search.py
@@ -0,0 +1,238 @@
+"""
+Python implementation of the breadth-first search algorithm for pathfinding.
+
+Find an explanation of this algorithm here: 
+https://en.wikipedia.org/wiki/Breadth-first_search
+
+Also included is a simple node class, maze generation and maze visualisation
+to show the results of the algorithm.
+
+For doctest testing run: python3 -m doctest -v breadth_first_search.py
+
+For manual testing and visualisation run: python3 breadth_first_search.py
+"""
+import random
+import queue
+
+
+class Node:
+    """
+    Objects of this class make up the grid (2d array) which will be
+    traversed by the algorithm.
+    """
+
+    def __init__(self, value, row, col):
+        self.value = value
+        self.row = row
+        self.col = col
+        self.neighbours = []
+
+    def __str__(self):
+        return f"Node ({self.row}, {self.col})"
+
+    def update_neighbours(self, i: int, j: int, grid: list) -> None:
+        """
+        Appends adjacent nodes which are not walls to self.neighbours.
+        """
+
+        if i > 0 and grid[i - 1][j].value:
+            self.neighbours.append(grid[i - 1][j])
+        if i < len(grid) - 1 and grid[i + 1][j].value:
+            self.neighbours.append(grid[i + 1][j])
+        if j > 0 and grid[i][j - 1].value:
+            self.neighbours.append(grid[i][j - 1])
+        if j < len(grid) - 1 and grid[i][j + 1].value:
+            self.neighbours.append(grid[i][j + 1])
+
+    def make_path(self):
+        self.value = "x"
+
+    def make_start(self):
+        self.value = "S"
+        return self
+
+    def make_end(self):
+        self.value = "E"
+        return self
+
+
+def random_value():
+    """
+    Used for very simple maze generation, every 1 in 4 nodes becomes a
+    wall.
+
+    This is done just so the algorithm has some obstacles to get around.
+
+    Examples:
+    >>> rand = random_value()
+    >>> rand in [" ", None]
+    True
+
+    >>> rand = random_value()
+    >>> rand in ["", 0, "hello"]
+    False
+    """
+
+    return random.choices([" ", None], weights=[4, 1])[0]
+
+
+def make_grid(size: int, random_maze=True) -> list:
+    """
+    Returns a list containing lists of nodes (the grid).
+
+    Option to just have a grid with no walls generated
+    by giving the second parameter as False.
+
+    Examples:
+    >>> grid = make_grid(2)
+    >>> print(grid[1][1])
+    Node (1, 1)
+
+    >>> grid = make_grid(16)
+    >>> print(grid[0][0])
+    Node (0, 0)
+
+    >>> grid = make_grid(4)
+    >>> len(grid) == len(grid[0]) == 4
+    True
+
+    >>> len(make_grid(0))
+    0
+
+    >>> grid = make_grid(3, False)
+    >>> grid[0][0].value
+    ' '
+    """
+
+    grid = []
+    for i in range(size):
+        row = []
+        for j in range(size):
+            value = random_value() if random_maze else " "
+            row.append(Node(value, i, j))
+        grid.append(row)
+    return grid
+
+
+def print_grid(grid: list, message: str) -> None:
+    """
+    Prints out the grid so the maze and the algorithm can be visualised.
+    """
+
+    key = "\nKey: \n|=wall S=start E=end x=path"
+    print(f"{key}\n\n{message}\n", "_" * len(grid))
+    for row in grid:
+        print()
+        for node in row:
+            if node.value:
+                print(node.value, end="")
+            else:
+                print("|", end="")
+    print("\n", "_" * len(grid))
+
+
+def construct_path(path: dict, current: Node, start: Node) -> None:
+    """
+    Takes a dictionary, path, and makes all nodes along the shortest
+    path into path nodes.
+
+    Only called if the end node was reached.
+
+    Examples:
+    >>> grid = make_grid(2, False)
+    >>> start = grid[1][1]
+    >>> path = {grid[0][0]: grid[1][0], grid[1][0]: grid[1][1]}
+    >>> construct_path(path, grid[0][0], grid[1][1])
+    >>> grid[1][0].value
+    'x'
+    >>> grid[0][0].value
+    ' '
+
+    >>> grid = make_grid(4, False)
+    >>> start = grid[2][3]
+    >>> path = {grid[1][2]: grid[1][3], grid[1][3]: grid[2][3]}
+    >>> construct_path(path, grid[1][2], grid[2][3])
+    >>> grid[1][3].value
+    'x'
+    >>> grid[0][0].value
+    ' '
+    """
+
+    while path.get(current, None):
+        current = path[current]
+        if current is start:
+            break
+        current.make_path()
+
+
+def breadth_first_search(grid, start, end):
+    """
+    Searches every traversible node outwards from the starting
+    node until the end node is reached.
+
+    This algorithm ensures the shortest path.
+
+    Examples:
+    >>> grid = make_grid(4, False)
+    >>> start, end = grid[1][1], grid[2][2]
+    >>> breadth_first_search(grid, start, end)
+    True
+
+    >>> grid = make_grid(25, False)
+    >>> start, end = grid[24][24], grid[0][0]
+    >>> breadth_first_search(grid, start, end)
+    True
+
+    >>> grid = make_grid(100, False)
+    >>> start, end = grid[0][99], grid[99][0]
+    >>> breadth_first_search(grid, start, end)
+    True
+
+    >>> grid = make_grid(10, False)
+    >>> for row in grid: row[5].value = None
+    >>> start, end = grid[9][9], grid[0][0]
+    >>> breadth_first_search(grid, start, end)
+    False
+    """
+    open_set = queue.Queue()
+    open_set.put(start)
+
+    # Will be used to construct the best path using the construct_path function
+    path = {node: None for row in grid for node in row if node.value}
+
+    while not open_set.empty():
+        current = open_set.get()
+
+        if current is end:
+            construct_path(path, current, start)
+            return True
+
+        current.update_neighbours(current.row, current.col, grid)
+        for neighbour in current.neighbours:
+            if path[neighbour]:
+                continue
+
+            open_set.put(neighbour)
+            path[neighbour] = current
+
+    return False
+
+
+if __name__ == "__main__":
+
+    # **CHANGE THESE VARIABLES FOR DIFFERENT RESULTS**
+    size = 50  # grid = size x size 2d array
+    x1, y1 = 1, 1  # Sets the starting node to grid[x1][y1]
+    x2, y2 = 48, 48  # Sets ending node to grid[x2][y2]
+
+    # Grid generation
+    grid = make_grid(size)
+    start = grid[x1][y1].make_start()
+    end = grid[x2][y2].make_end()
+
+    # Output
+    print_grid(grid, "Maze before:")
+    if breadth_first_search(grid, start, end):
+        print_grid(grid, "Maze after:")
+    else:
+        print("No path was found :(")