Created
April 10, 2013 15:03
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| import abc | |
| import collections | |
| class BasePrime(collections.Sequence): | |
| '''Base class for any primes number sequence | |
| ''' | |
| __metaclass__ = abc.ABCMeta | |
| class EvklideSieve(BasePrime): | |
| '''Evklide sieve prime numbers sequence | |
| ''' | |
| def __init__(self): | |
| self.primes = [2, 3] | |
| self.last_num = 0 | |
| self.primes_num = 2 | |
| self.start = self.end = self.step = 5 | |
| def _generate_primes(self): | |
| '''Get the numbers starting from start with the count based on primes | |
| ''' | |
| sieve = range(self.start, self.end) | |
| for prime in self.primes: | |
| # Get the start value for primes striking | |
| start_value = prime ** 2 | |
| if start_value > self.end: | |
| break | |
| if start_value < self.start: | |
| num = self.start / prime | |
| if self.start % prime: | |
| num += 1 | |
| start_value = num * prime | |
| # Strike out complex | |
| for index in xrange(start_value, self.end, prime): | |
| sieve[index - self.start] = False | |
| # Get the numbers was not striked out | |
| self.primes.extend([number for number in sieve if number]) | |
| def __len__(self): | |
| '''Get current length''' | |
| return self.primes_num | |
| def __getitem__(self, number): | |
| '''Get the n-th prime number''' | |
| while self.primes_num < number: | |
| # Get a new step size for prime sieve | |
| self.last_num = self.primes_num | |
| self.primes_num = len(self.primes) | |
| self.last_prime = self.primes[self.primes_num - 1] | |
| self.start = self.end | |
| self.end = self.last_prime ** 2 | |
| if self.primes_num > self.last_num: | |
| self.step *= (number - self.primes_num) * 1. / (self.primes_num - self.last_num) | |
| if self.start + self.step < self.end: | |
| self.end = self.start + int(self.step) | |
| else: | |
| self.step = self.end - self.start | |
| # Get new primes | |
| self._generate_primes() | |
| return self.primes[number - 1] | |
| evklide_sieve = EvklideSieve() | |
| print evklide_sieve[100001] |
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