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61 lines
1.3 KiB
Python
61 lines
1.3 KiB
Python
"""Find the 10001st prime.
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By listing the first six prime numbers: 2, 3, 5, 7, 11, and 13, we can see that the 6th prime is 13.
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What is the 10001st prime number?
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"""
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import math
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def is_prime(n):
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if n == 1:
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return False
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if n < 4:
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return True
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if n % 2 == 0:
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return False
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if n < 9:
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return True
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if n % 3 == 0:
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return False
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r = math.floor(math.sqrt(n))
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f = 5
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while f <= r:
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if (n % f == 0) or (n % (f + 2) == 0):
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return False
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f = f + 6
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return True
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def prime_generator():
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i = 1
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yield 2
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while True:
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i += 2
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if is_prime(i):
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yield i
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def primes(max_count = 0, max_value = 0):
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if not max_count and not max_value:
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raise Exception('There must be a constraint on how many primes to return!')
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primes = [2]
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i = 1
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while (not max_count or len(primes) < max_count) \
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and (not max_value or i < max_value):
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i = i + 2
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if is_prime(i):
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primes.append(i)
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return primes
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def main():
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i = 0
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prime = 0
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generator = prime_generator()
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while i < 10000:
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i += 1
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prime = generator.next()
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if i == 6:
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print '6th Prime', prime
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print '10001st Prime', prime
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if __name__ == '__main__':
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main()
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