Solution to problem 51

src/Python/Problem051.py

@@ -0,0 +1,58 @@
+#!/usr/bin/env python3
+"""
+Created on 24 Sep 2021
+
+@author: David Doblas Jiménez
+@email: daviddoji@pm.me
+
+Solution for problem 52 of Project Euler
+https://projecteuler.net/problem=52
+"""
+
+from utils import timeit, list_primes, is_prime
+
+
+@timeit("Problem 52")
+def compute():
+    """
+    By replacing the 1st digit of the 2-digit number *3, it turns out that 
+    six of the nine possible values: 13, 23, 43, 53, 73, and 83, are all prime.
+
+    By replacing the 3rd and 4th digits of 56**3 with the same digit, this 5-digit 
+    number is the first example having seven primes among the ten generated numbers, 
+    yielding the family: 
+    
+        56003, 56113, 56333, 56443, 56663, 56773, and 56993. 
+    
+    Consequently 56003, being the first member of this family, is the smallest prime 
+    with this property.
+
+    Find the smallest prime which, by replacing part of the number (not necessarily 
+    adjacent digits) with the same digit, is part of an eight prime value family.
+    """
+    
+    primes = sorted(set(list_primes(1_000_000)) - set(list_primes(57_000)))
+    digits = {'0':[], '1':[], '2':[],'3':[], '4':[], '5':[],'6':[], '7':[], '8':[], '9':[]}
+    for d in digits.keys():
+        for p in primes:
+            p = str(p)
+            if p.count(d) == 3 and p[-1] != d:
+                digits[d].append(p)
+    for d in {'0', '1', '2'}:
+        for p in digits[d]:
+            res = 0
+            i = 10
+            for D in {'0', '1', '2', '3', '4', '5', '6', '7', '8', '9'}-{d}:
+                i -= 1
+                q = int(p.replace(d, D))
+                if is_prime(q) and q > 57_000:
+                    res += 1
+                if i + res < 7:
+                    break
+            if res == 7:
+                return p
+
+
+if __name__ == "__main__":
+
+    print(f"Result for Problem 52: {compute()}")