def is_prime_v1(n):
    if n == 1:
        return  False #1 is not prime
    for d in range(2,n):
        if n % d == 0:
            return False
    return  True

for n in range(1,21):
    print(n, is_prime_v1(n))


1 False
2 True
3 True
4 False
5 True
6 False
7 True
8 False
9 False
10 False
11 True
12 False
13 True
14 False
15 False
16 False
17 True
18 False
19 True
20 False

t0 = time.time()
for n in range(1,100000):
   is_prime_v1(n)
t1 = time.time()
print('Time required: ',t1-t0)
# Time required:  46.61776304244995




# 优化后
import time
import math
def is_prime_v2(n):
    if n ==1:
        return False
    max_divisor = math.floor(math.sqrt(n))
    for d in range(2,1+ max_divisor):
        if n % d ==0:
            return False
    return True

t0 = time.time()
for n in range(1,100000):
   is_prime_v2(n)
t1 = time.time()
print('Time required: ',t1-t0)
# Time required:  0.29659509658813477


# 继续在上述案例上优化
def is_prime_v3(n):
    if n ==1:
        return False
    if n ==2:
        return True
    if n > 2 and n %2 == 0:
        return False

    max_divisor = math.floor(math.sqrt(n))
    for d in range(3,1+ max_divisor,2):
        if n % d ==0:
            return False
    return True

t0 = time.time()
for n in range(1,100000):
   is_prime_v3(n)
t1 = time.time()
print('Time required: ',t1-t0)
# Time required:  0.268629789352417