程序分析：判断素数的方法：用一个数分别去除2到sqrt(这个数)，如果能被整除，则表明此数不是素数，反之是素数。

例如：输出100-200范围内符合条件的素数

#!/usr/bin/python#coding:utf-8#author:菜就多练呀from math import sqrtc = 0leap = 1for m in range(101, 201):    k = int(sqrt(m + 1))    for i in range(2, k + 1):        if m % i == 0:            leap = 0            break    if leap == 1:        print('%4d' % m)        c += 1    leap = 1print('范围内的素数共有%d个' % c)

判断素数的常用方法：

1.试除法

def is_prime(n):    if n <= 1:        return False    for i in range(2, int(n**0.5) + 1):        if n % i == 0:            return False    return Trueprint(is_prime(100))

2.米勒-拉宾素性测试

#!/usr/bin/python#coding:utf-8#author:菜就多练呀import randomdef miller_rabin(n, k=5):    if n <= 1:        return False    if n == 2 or n == 3:        return True    if n % 2 == 0:        return False    r, s = 0, n - 1    while s % 2 == 0:        r += 1        s //= 2    for _ in range(k):        a = random.randrange(2, n - 1)        x = pow(a, s, n)        if x == 1 or x == n - 1:            continue        for _ in range(r - 1):            x = pow(x, 2, n)            if x == n - 1:                break        else:            return False    return Truedef is_prime(n):    if n <= 1:        return False    if n == 2 or n == 3:        return True    if n % 2 == 0:        return False    return miller_rabin(n)print(is_prime(5))

3.素数筛法

#!/usr/bin/python#coding:utf-8#author:菜就多练呀def sieve_of_eratosthenes(n):    primes = [True] * (n + 1)    primes[0], primes[1] = False, False    for i in range(2, int(n**0.5) + 1):        if primes[i]:            for j in range(i*i, n + 1, i):                primes[j] = False    return [x for x in range(n + 1) if primes[x]]def is_prime(n):    if n <= 1:        return False    if n in sieve_of_eratosthenes(n):        return True    return Falseprint(is_prime(100))

4.费马小定理

#!/usr/bin/python#coding:utf-8#author:菜就多练呀import randomdef fermat_little_theorem(n):    if n <= 1:        return False    if n == 2 or n == 3:        return True    if n % 2 == 0:        return False    a = random.randint(2, n - 1)    if pow(a, n - 1, n) != 1:  # 修改：检查 pow 结果是否为 1        return False    return Truedef is_prime(n):    if n <= 1:        return False    if n == 2 or n == 3:        return True    if n % 2 == 0:        return False    return fermat_little_theorem(n)# 测试print(is_prime(7))  # 输出：True