显示所有奇数而不是质数

Question

def prime_num_gen():
    
    try:
        r = int(input('Type in the number till which you want to generate your prime numbers : '))
    
        if r <= 2:
             print('There is no prime number smaller than 2, 2 is the smallest prime number')
    
        #A list to store primes
        #Storing 2 already, because I need a number to start with
        prime_num = [2] 
    
        #Counter
        #Counter will be divided and if it's a prime; will append it
        x = 3
    
        #Starting with 3 cus 2 is already considered
        #Having a jump of 2, cus no even num is prime, so considering only odd nums
        while x <= r:
            for num in range(3,x,2):
    
                if num % x == 0:
                    x += 2
                    break 
    
            else:
                prime_num.append(x)
                x += 2 
    
        print(prime_num)
    
    except:
        print('Please only give input as a number!\nTry again')

出于某种原因，此代码将所有奇数都包含为素数。我是编码方面的新手，即使这看起来是一个非常明显的错误，也请告诉我。

任何帮助将不胜感激！！

Answer 1

您的代码中有一个小错误。而不是条件

if num % x == 0:

你应该做

if x % num == 0:

由于 num 总是小于或等于 x，所以它对 x 的模数总是再次给出数字。

Answer 2

这里是一个略有不同的实现，可以在不同的范围内更快。 基本算法很简单。

def isprime(n):
    for i in range(2,int(n**0.5)+1):
        if n%i == 0: 
            return False
    return True
for i in range (1,100):
    if isprime(i) == True:
        print(i)

找到所有小于 N 的素数需要 O(N log (log N)) 时间。

显示所有奇数而不是质数

Showing all odd numbers instead of prime numbers

python

primes