求質數，優化

優化前

import math
def prime(n):
    if n%2 == 0:
        return n==2
    if n%3 == 0:
        return n==3
    if n%5 == 0:
        return n==5
    for p in range(7,int(math.sqrt(n))+1,2):    #只考慮奇數作爲可能因子
        if n%p == 0:
            return 0
    return 1

if __name__ == "__main__":
    n = int(input(">>"))
    count = 0
    star_time = time.time()
    for i in range(2, n + 1):  # 1不是素數,從2開始
        if prime1(i):
            # print(i)
            count += 1
    print(count)
    end_time = time.time()
    print(end_time - star_time)

---

執行結果:

>>2000000
148933
5.532246351242065

優化後

def prime(n):
    flag = [1] * (n + 2)
    p = 2  # 第一個質數
    count = 0  # 用於計算質數的數量
    while (p <= n):
        # print(p)
        count += 1
        # 把質數的倍數，設爲非質數
        for i in range(2 * p, n + 1, p):
            flag[i] = 0
        # 找出下一個質數
        while 1:
            p += 1  # p自增
            if (flag[p] == 1):  # 當p是質數，跳出內層循環
                break
    print(count)


# test
if __name__ == "__main__":
    n = int(input(">>"))
    star_time = time.time()
    prime(n)
    end_time = time.time()
    print(end_time - star_time)

---

執行結果:

>>2000000
148933
0.5664565563201904