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049/main.py

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+'''
+The arithmetic sequence, 1487, 4817, 8147, in which each of the terms increases by 3330, is unusual in two ways: (i) each of the three terms are prime, and, (ii) each of the 4-digit numbers are permutations of one another.
+
+There are no arithmetic sequences made up of three 1-, 2-, or 3-digit primes, exhibiting this property, but there is one other 4-digit increasing sequence.
+
+What 12-digit number do you form by concatenating the three terms in this sequence?
+'''
+
+import math
+import numpy as np
+from itertools import permutations
+
+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:]
+
+def digitToList(n):
+    return [int(c) for c in str(n)]
+
+def listToDigit(l):
+    res = 0
+    for i in l:
+        res = 10 * res + i
+    return res
+
+def main():
+    print("Hello this is Patrick")
+
+    primeSet = set(sieve(10000)) - set(sieve(1000))
+    primeList = list(primeSet)
+
+    for p in primeList:
+        perms = list(set(map(listToDigit, list(permutations(digitToList(p))))))
+
+        for perm in perms:
+            if p != perm and perm in primeSet:
+                if max(p, perm) + abs(p - perm) in primeSet and max(p, perm) + abs(p - perm) in perms:
+                    print(min(p, perm), max(p, perm), max(p, perm) + abs(p - perm))
+
+    
+
+if __name__ == "__main__":
+    main()