使用列表理解查找素數

Question

我試圖編寫代碼到 select 列表中的素數。 用戶給出一個極限，程序顯示從 2 到極限的所有素數。 我試圖盡可能減少行數，但對一些我無法理解的情況感到驚訝。 如果你能幫助我，我將不勝感激。

我寫了這段代碼：

# returns all integers from 2 to a limit given by the user. 

def primes(limit):
    # generates the numbers. 
    lista = range(2, limit + 1)
    
    p = 2
    
    while p < limit:
        #filters the prime numbers and places in a list.
        lista = [i for i in lista if i == p or i % p != 0]
    
        p += 1
    

    return lista

        
def main():
    #asks the user for the limit number.
    l = int(input("Enter the limit: "))
    
    #call the function which selects the numbers and returns the result. 
    return print(primes(l))

#Ensures that the main program only runs when the functions have not been imported into another file.
if __name__ == '__main__':
    main()

它按我的預期運行，但是當我嘗試刪除第一個列表分配行並將范圍 function 直接包含到理解中時，它不起作用。 為什么？

# returns all integers from 2 to a limit given by the user. 

def primes(limit):
    p = 2
    
    while p < limit:
        #filters the prime numbers and places in a list.
        lista = [i for i in range(2, limit + 1) if i == p or i % p != 0]
    #or lista = [i for i in range(2, limit + 1) if i == p or i % p != 0]
    #or lista = [i for i in [*range(2, limit + 1)] if i == p or i % p != 0]
    
        p += 1
    

    return lista

        
def main():
    #asks the user for the limit number.
    l = int(input("Enter the limit: "))
    
    #call the function which selects the numbers and returns the result. 
    return print(primes(l))

#Ensures that the main program only runs when the functions have not been imported into another file.
if __name__ == '__main__':
    main()

其他問題。 由於范圍行不是列表，我修復它只是為了改進代碼，但是當我將值的名稱從“lista”更改為另一個名稱時，我發現它也不起作用。 為什么？

# returns all integers from 2 to a limit given by the user. 

def primes(limit):
    # generates the numbers. 
    nums = range(2, limit + 1)

    p = 2
    
    while p < limit:
        #filters the prime numbers and places in a list.
        lista = [i for i in nums if i == p or i % p != 0]
    
        p += 1
    

    return lista

        
def main():
    #asks the user for the limit number.
    l = int(input("Enter the limit: "))
    
    #call the function which selects the numbers and returns the result. 
    return print(primes(l))

#ensures that the main program only runs when the functions have not been imported into another file.
if __name__ == '__main__':
    main()

感謝您的關注。

Answer 1

這個單線完美地工作：

def primes(val):
    return [x for x in range(2, val) if all(x % y != 0 for y in range(2, x))]

print(primes(10))

Answer 2

感謝您的關注。我喜歡我們的朋友 Yash Makan 的回答，但是當我嘗試更大的數字時，比如 100000，它從來沒有讓我得到結果（或者我沒有耐心等待）。 所以我繼續思考這個問題並得到以下是計算這個問題的最快方法，我可以通過列表理解實現。 請注意計算數百萬個數字的速度。

# returns all integers from 2 to a limit given by the user. 

def primes(limit):
    
    l = [i for i in range(2, limit + 1) if all(i % j != 0 for j in [2, 3, 5])]    
    lista = []
    return [2, 3, 5] + [lista.append(i) or i for i in l if all( i % j != 0 for j in lista[:int((len(lista) ** .5) + 1)])]

        
def main():
    l = int(input("Enter the limit: "))
    
    return print(primes(l))

if __name__ == '__main__':
    main()