57 lines
1.5 KiB
Python
57 lines
1.5 KiB
Python
def sievePrime(n):
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if n < 2:
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return 0
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prime = [1] * (n + 1)
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prime[0] = prime[1] = 0
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for i in range(2, int(n**0.5) + 1):
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if prime[i] == 1:
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prime[i*i:n + 1:i] = [0]*len(prime[i*i:n + 1:i])
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return [i for i in range(n+1) if prime[i] == 1]
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class primeSiever:
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'''sieve of Eratosthenes, It will be more efficient when judging many times'''
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primes = [2, 3, 5, 7, 11, 13]
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def isPrime(self, x):
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if x <= primes[-1]:
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return twoDivideFind(x, self.primes)
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while x > self.primes[-1]:
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left = self.primes[-1]
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right = (left+1)**2
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lst = []
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for i in range(left, right):
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for j in self.primes:
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if i % j == 0:
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break
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else:
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lst.append(i)
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self.primes += lst
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return twoDivideFind(x, lst)
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def nPrime(n):
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'''return the n-th prime'''
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i = n-len(self.primes)
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last = self.primes[-1]
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for _ in range(i):
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while 1:
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last += 2
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for p in self.primes:
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if last % p == 0:
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break
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else:
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self.primes.append(last)
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break
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return self.primes[n-1]
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if __name__ == "__main__":
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import sys
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if len(sys.argv) < 2:
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n = 100
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else:
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n = int(sys.argv[1])
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ans = sievePrime(n)
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print(f'primes <= {n}, nums: {len(ans)}')
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print(ans)
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