37 lines
1.3 KiB
Python
37 lines
1.3 KiB
Python
'''
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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.
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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.
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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.
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'''
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import numpy as np
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import math
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def sieve(n):
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assert n > 1
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ns = [True] * n
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for i in range(2, math.ceil(np.sqrt(n))):
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if ns[i]:
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j = pow(i, 2)
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while j < n:
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ns[j] = False
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j = j + i
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return [i for i,val in enumerate(ns) if val][2:]
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def main():
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print("Hello this is Patrick")
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primes = sieve(1000000)
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# So instead of going past all number families and see if they are prime I think it's better to look for families in the primes
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# Quite the combinatorial problem indeed, lots of permutations and I don't immediately see an easy way to fix it
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if __name__ == "__main__":
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main()
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