60 lines
1.4 KiB
Python
60 lines
1.4 KiB
Python
'''
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It was proposed by Christian Goldbach that every odd composite number can be written as the sum of a prime and twice a square.
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9 = 7 + 2×12
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15 = 7 + 2×22
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21 = 3 + 2×32
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25 = 7 + 2×32
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27 = 19 + 2×22
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33 = 31 + 2×12
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It turns out that the conjecture was false.
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What is the smallest odd composite that cannot be written as the sum of a prime and twice a square?
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'''
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# So I guess I just go past all odd non-prime numbers and keep subtracting all double squares that fit and see if the rest is a prime
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import math
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import numpy as np
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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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end = 10000
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primes = set(sieve(end))
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for n in range(9, end, 2):
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termination = True
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if n not in primes:
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x = 1
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while n - 2 * x*x > 0:
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if n - 2 * x*x in primes:
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termination = False
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break
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x += 1
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if termination:
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print(n)
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break
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if __name__ == "__main__":
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main() |