区间内整数的二进制表示1的个数是质数的个数-算法题

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网易有道面试算法题

"""
判断一个区间内数字的二进制表示是质数的数目
"""

import math

def count_1_binary(n):
    """
    统计二进制表示1的个数
    """
    count = 0
    while n:
        count += 1
        n = n&(n-1)
    return count

def is_prim(n):
    """
    判断是否是质数
    """
    for i in range(2, n/2):
        if n%i==0: return 0
    return 1

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

def is_prime_3(n):
    """
    质数分布规律，大于等于5的质数一定和6的倍数相邻
    6i+1 6i-1的情况，循环步长定位为6，每次判断k和k+2的情况
    理论上比srqt快3倍
    """
    if n==2 or n==3: return 1
    if n%6!=1 and n%6!=5: return 0
    temp = int(math.sqrt(n))
    for i in range(5,temp,6):
        if n%i==0 or n%(i+2)==0: return 0
    return 1

def test():
    x = [1,100]
    # print(count_1_binary(7))
    count = 0
    for i in range(x[0],x[1]+1):
        u = count_1_binary(i)
        if is_prime_3(u)==1:
            count += 1
    print(count)


test()