python素数判断

以下是Python中判断素数的五种实现方式：
1.暴力判断法

def is_prime(n):
    if n < 2:
        return False
    for i in range(2, n):
        if n % i == 0:
            return False
    return True

2.平方根暴力判断法

import math

def is_prime(n):
    if n < 2:
        return False
    for i in range(2, int(math.sqrt(n))+1):
        if n % i == 0:
            return False
    return True

3.素数表筛选法

def get_primes(n):
    primes = []
    for i in range(2, n+1):
        is_prime = True
        for j in primes:
            if i % j == 0:
                is_prime = False
                break
        if is_prime:
            primes.append(i)
    return primes

4.埃拉托斯特尼(Eratosthenes)筛法

def get_primes(n):
    primes = [True] * (n+1)
    primes[0] = primes[1] = False
    for i in range(2, int(n**0.5)+1):
        if primes[i]:
            primes[i*i: n+1: i] = [False] * len(primes[i*i: n+1: i])
    return [i for i in range(n+1) if primes[i]]

5.欧拉（Euler）筛法

def get_primes(n):
    primes = []
    is_prime = [True] * (n+1)
    for i in range(2, n+1):
        if is_prime[i]:
            primes.append(i)
        for j in primes:
            if i*j > n:
                break
            is_prime[i*j] = False
            if i % j == 0:
                break
    return primes