使用列表理解查找素数

Question

I was trying to write a code to select the prime numbers in a list. The user gives a limit and the program displays all prime number from 2 to the limit. I was trying to reduce the maximum amount of lines I could and was surprised with some situations I can't understand. If you can help me, I'd be grateful.

I wrote this code:

# 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()

It runs as I expected, but when I tried deleting the first list assignment line and include the range function directly into the comprehension, it doesn't work. Why?

# 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()

Other problem. As the line with range is not a list I fixed it only to improve the code, but when I changed the name of the value from 'lista' to another name, I saw that it doesn't work too. Why?

# 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()

Thanks for your attention.

Answer 1

This one-liner works perfectly:

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

Thank you for your attention.I liked the answer of our friend Yash Makan, but when I tried larger numbers, like 100000, it never led me to the result (or I was not so patient to wait). So I continued thinking about the problem and got the following that is the fastest way to compute this problem I could achieve with list comprehension. Note how fast you can compute millions of numbers.

# 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()