added Project Eular: 60

DIRECTORY.md

@@ -632,7 +632,7 @@
 
 ## Physics
   * [Horizontal Projectile Motion](physics/horizontal_projectile_motion.py)
-  * [Lorenz Transformation Four Vector](physics/lorenz_transformation_four_vector.py)
+  * [Lorentz Transformation Four Vector](physics/lorentz_transformation_four_vector.py)
   * [N Body Simulation](physics/n_body_simulation.py)
   * [Newtons Second Law Of Motion](physics/newtons_second_law_of_motion.py)
 
@@ -792,6 +792,8 @@
     * [Sol1](project_euler/problem_058/sol1.py)
   * Problem 059
     * [Sol1](project_euler/problem_059/sol1.py)
+  * Problem 060
+    * [Sol1](project_euler/problem_060/sol1.py)
   * Problem 062
     * [Sol1](project_euler/problem_062/sol1.py)
   * Problem 063

project_euler/problem_060/sol1.py

@@ -0,0 +1,154 @@
+"""
+Project Euler 60
+https://projecteuler.net/problem=60
+
+
+
+The primes 3, 7, 109, and 673, are quite remarkable.
+By taking any two primes and concatenating them in any order the
+result will always be prime.
+For example, taking 7 and 109, both 7109 and 1097 are prime.
+The sum of these four primes, 792, represents the lowest sum for a
+set of four primes with this property.
+
+Find the lowest sum for a set of five primes for which any two primes
+concatenate to produce another prime.
+
+"""
+
+from math import sqrt
+
+pairs: list[str] = []
+minimum_sum = 0
+primes: list[str] = []
+
+
+def is_prime(number: int) -> bool:
+    """Checks to see if a number is a prime in O(sqrt(n)).
+    A number is prime if it has exactly two factors: 1 and itself.
+
+    Taken from /maths/prime_check.py
+
+    >>> is_prime(0)
+    False
+    >>> is_prime(1)
+    False
+    >>> is_prime(2)
+    True
+    >>> is_prime(3)
+    True
+    >>> is_prime(27)
+    False
+    >>> is_prime(87)
+    False
+    >>> is_prime(563)
+    True
+    >>> is_prime(2999)
+    True
+    >>> is_prime(67483)
+    False
+    """
+
+    # precondition
+    assert isinstance(number, int) and (
+        number >= 0
+    ), "'number' must been an int and positive"
+
+    if 1 < number < 4:
+        # 2 and 3 are primes
+        return True
+    elif number < 2 or number % 2 == 0 or number % 3 == 0:
+        # Negatives, 0, 1, all even numbers, all multiples of 3 are not primes
+        return False
+
+    # All primes number are in format of 6k +/- 1
+    for i in range(5, int(sqrt(number) + 1), 6):
+        if number % i == 0 or number % (i + 2) == 0:
+            return False
+    return True
+
+
+def combiner(index: int, length: int) -> bool:
+    """
+    This function goes through all the combinations of the primes list in
+    ascending order, and finds pairs that satisfy the question until the
+    minimum_sum is low enough that it can stop and the minimum_sum is the minimum.
+
+    Returns True if the recursion should continue else False.
+
+    >>> combiner(1,2)
+    False
+    >>> combiner(2,3)
+    False
+    """
+
+    global pairs, minimum_sum
+    j = i = index  # local variable j retains the original index and i gets changed
+
+    if len(pairs) == length:  # if it is one of the pairs we want
+        s = sum(int(x) for x in pairs)
+        if s < minimum_sum:
+            minimum_sum = s
+        primes.insert(i, pairs.pop(-1))
+        return True
+
+    while i < len(primes):
+        for prime in pairs:
+            if not is_prime(int(prime + primes[i])):
+                break
+            if not is_prime(int(primes[i] + prime)):
+                break
+        else:
+            pairs.append(primes.pop(i))
+            if not combiner(i, length):
+                return False
+
+        if pairs:
+            i += 1
+
+    if primes:
+        if j + len(pairs) - 1 != 0:
+            primes.insert(j, pairs.pop(-1))
+            return True
+        else:
+            if int(pairs.pop(-1)) > minimum_sum / (
+                2 * 10 ** (length - 2)
+            ):  # works for most test cases
+                return False
+            return True
+    return False
+
+
+def solution(prime_count: int = 5, limit: int = 10000) -> int:
+    """
+    The function returns the lowest sum for a set of n primes (prime_count) for which
+    any two primes concatenate to produce another prime.
+
+    Limit is the maximum number of natural numbers to be checked up to.
+
+
+    >>> solution(2,10)
+    10
+    >>> solution(3,100)
+    107
+    >>> solution(4,1000)
+    792
+    """
+
+    global minimum_sum, primes, pairs
+    primes = []
+    pairs = []
+    for i in range(1, limit + 1):
+        if is_prime(i):
+            primes.append(str(i))
+    minimum_sum = limit * 5
+    combiner(0, prime_count)
+    return minimum_sum
+
+
+if __name__ == "__main__":
+    import doctest
+
+    doctest.testmod()
+
+    print(f"{solution() = }")

project_euler/problem_104/sol.py

@@ -13,6 +13,10 @@
 the last nine digits are 1-9 pandigital, find k.
 """
 
+import sys
+
+sys.set_int_max_str_digits(0)  # type: ignore
+
 
 def check(number: int) -> bool:
     """