方法一
#%%timeit
#打印10万以内的素数
n = 100000
#除了2 以外的素数，都是奇数
count=1
#print(2,end=' ')
for i in range(3,n,2):
flag = False
if i > 10 and i % 5 == 0 :
continue
for j in range(3,int(i**0.5)+1,2):
if i % j == 0:
break
else:
print(i,end=' ')
count += 1
print()
print(count)
方法二
#%%timeit
n = 100000
count = 0
primenumber = []
flag = False
for x in range(2,n):
edge = int(x**0.5)
for i in primenumber:
if x % i == 0:
flag = True
break
# if i > x ** 0.5.如果每次进入循环重新计算，就会消耗性能
if i > edge:
flag = False
break
if not flag :
primenumber.append(x)
count += 1
print(count)
方法三
#%%timeit
count = 2
#print(2, end=' ')
#print(3, end=' ')
number = 100000
for num in range(5,number,2):
#大于6的质数除以6，余数都是1或者5
if num % 6 != 1 and num % 6 != 5:
continue
else :
flag = False
if num < 30 :
for i in range(3,num,2):
if not ( num % i ):
flag = False
break
else:
flag = True
else:
for i in range(5,int(num**0.5 + 1),6):
if ( not num % i ) or ( not num % (i+2) ):
flag = False
break
else:
flag = True
if flag :
print(num, end= ' ')
count += 1
print()
print(count)
方法四
#%%timeit
count = 2
lst = [2,3]
n = 100000
x = 5 # 6的倍数前后都是奇数
step = 2
#大于3的素数只有6N-1和6N+1两种形式，如果6N-1和6N+1都是素数成为孪生素数
while x <= n: #被除数从5开始，7，11，13....
for i in range(3,int(x**0.5)+1,2): # 除数是素数列表
if x % i == 0 :
break
else:
count += 1
lst.append(x)
x += step
step = 4 if step == 2 else 2
print(count)
方法五 效率最快
#%%timeit
count = 2
lst = [2,3]
n = 100000
x = 5
step = 2
while x <= n: #被除数从5开始，7，11，13....
edge = int(x**0.5)
for i in lst: # 除数是素数列表
if x % i == 0 :
break
if i > edge:
break
else:
count += 1
lst.append(x)
x += step
step = 4 if step == 2 else 2
print(count)
