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051/main.py

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+'''
+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.
+'''
+
+import numpy as np
+import math
+import time
+
+def sieve(n):
+    assert n > 1
+
+    ns = [True] * n
+
+    for i in range(2, math.ceil(np.sqrt(n))):
+        if ns[i]:
+            j = pow(i, 2)
+
+            while j < n:
+                ns[j] = False
+                j = j + i
+
+    return [i for i,val in enumerate(ns) if val][2:]
+
+# Does generate all families that can be made for that number, so that consists of multiple families together
+def families(num):
+    result = []
+    variedDigits = set()
+    digits = [int(d) for d in str(num)]
+
+    for i in range(len(digits)):
+        if not i in variedDigits:
+            buddies = []
+
+            for j in range(len(digits)):
+                if digits[i] == digits[j]:
+                    buddies.append(j)
+                    variedDigits.add(j)
+
+            r = digits[:]
+
+            for n in range(10):
+                for bud in buddies:
+                    r[bud] = n
+                maybeResult = int("".join([str(_r) for _r  in r]))
+                result.append(maybeResult)
+    
+    return result
+
+def findPrimeFamily(length):
+    primes = sieve(1000000)
+    primeSet = set(primes)
+
+    for p in primes:
+        primeFamilies = families(p)
+
+        for i in range(len(primeFamilies) // 10):
+            counter = 0
+            for pf in primeFamilies[10*i:10*i+10]:
+                if pf in primeSet and len(str(pf)) == len(str(p)):
+                    counter += 1
+            if counter >= length:
+                return [x for x in primeFamilies[10*i:10*i+10] if x in primeSet]
+
+def main():
+    print("Hello this is Patrick")
+
+    t0 = time.time()
+
+    print(findPrimeFamily(8), time.time() - t0)
+
+if __name__ == "__main__":
+    main()