如何找到用户定义范围内的所有素数？

Question

I want to get a script to: a) check if a number within the user defined range is prime or not b) print the result of a check c) print amount of numbers checked and how many of these numbers were primes d) print the last prime number

Here is what I have so far:

lower = int(input("Lower boundry: "))
upper = int(input("Upper boundry: "))
for n in range(lower, upper + 1):
    if (n <= 1):
        print(n, "error")
    elif (n > 1):
        for x in range(2, n):
            if ((n % x) == 0):
                print(n, "not prime, because", x, "*", int(n/x),"=", n)
                break
        else:
            print(n, "prime")
            last = [n]  
print("Checked", n, "numbers, of which","XXX","were prime.")
print("Last prime number found was", *last)

Question:

1. The tool im using gives me an error. Lets say, I check the numbers 1-10. On 1 I get a notification that 1 is not prime (as intended, as n <= 1). Number 2 is a prime and the programme notifies me of this. However, on 3 i get an error - "incorrect output: your program printed "prime3", but should have printed "prime.". I don't get it. Is it the white space python seems to like so much? Or did I fail with else if use?

2. For checking the number of primes within the specified range - am I supposed to use a list to store the values generated in the for loop? The material will cover lists during later sessions, so I am guessing I am meant to use some other method. But lets say I want to use the list. Is it something like:

    list=[] for y in [1,10]: for z in [0,1,2,3]: x=y+z list.append(x)

and the use len(list) where the XXX placeholder is ATM?

Edit: Got the c) and d) to work - used list as a storage for values. Printed last value in the list for d) and used the length of the list for c). Fixed the indentation issue pointed out to me in the comments below. Still cannot get the code to run properly. In I in put 1 and 10 as bounds, the programme identifies 1 as not prime, 2 as prime and then gives error. Error text is: "Incorrect output: your program printed "prime3", but should have printed "prime." " Not really sure what is up with that.

Answer 1

Fist of all: Please pose your question in the title. For Example: "How do I find all primes in a user-defined range?"

The Algorithm

To find out whether or not a number is prime you can divide it by all primes smaller than the number, since all non-primes can be divided by primes. This is significantly faster than checking all numbers

Generating primes

I would first define a function to generate the next prime. For this I take the last prime number and then continue to add 2 to it until we find the next prime:

def dividable_by_any_in_list(x, list):
    for n in list:
        if x%n == 0:
            return True

    return False

def next_prime(known_primes):
    """
    Takes a list of known primes and returns the next prime.
    """

    current = known_primes[-1]+2

    while True:
        if dividable_by_any_in_list(current, known_primes):
            current += 2
        else:
            return current

I tested that with this main function:

def main():
    # Not what you want to copy-paste
    known_primes = [2,3,5,7,11,13,17,19]

    next = next_prime(known_primes)
    print(next)

if __name__ == '__main__':
    main()

and it returned 23, which is correct.

Finding all primes in range

Now we can write a function to find all primes below an upper boundary:

def find_primes_below(known_primes, max):
    last = known_primes[-1]

    while last <= max:
        last = next_prime(known_primes)
        known_primes.append(last)

    return known_primes[:-1]

Using this we can write a function that takes the return value of this function and cuts out all primes below the lower bound:

def find_primes_in_range(known_primes, min, max):
    all_primes = find_primes_below(known_primes, max)

    l = 0
    while all_primes[l] < min:
        l+=1

    u = len(all_primes)-1
    while all_primes[u] > max:
        u -= 1

    return all_primes[l:u]

Output

Now we can define the main function:

def main():
    known_primes = [2,3,5,7,11,13,17,19]

    lower = int(input("Lower boundry: "))
    upper = int(input("Upper boundry: "))

    primes = find_primes_in_range(known_primes, lower, upper)

    print("Found Primes:")
    print(primes)

    print(f"Checked {upper-lower} numbers, of which {len(primes)} were prime.")
    print("Last prime number found was", primes[-1])


if __name__ == '__main__':
    main()

Answer 2

How about this.

# define a flag variable
lower = int(input("Lower boundry: "))
upper = int(input("Upper boundry: "))
prime_list=[]
for num in range(lower,upper+1):
    flag = False

# prime numbers are greater than 1
    if num > 1:
    # check for factors
        for i in range(2, num):
            if (num % i) == 0:
            # if factor is found, set flag to True
                flag = True
            # break out of loop
                break

# check if flag is True
    if flag:
        flag=False
    else:
        prime_list.append(num)
print("Checked:",len(list(range(lower,upper+1))),"numbers where",len(prime_list),"were prime.")
print("Last prime number checked: ",prime_list[-1])
print("All prime numbers are: ",','.join(str(n) for n in prime_list))

Output

Lower boundry: 1
Upper boundry: 30
Checked: 30 numbers where 11 were prime.
Last prime number checked:  29
All prime numbers are:  1,2,3,5,7,11,13,17,19,23,29

Answer 3

The indentation of your else clause is wrong. It should belong to the for loop. This means it will be executed when the loop is not terminated by the break statement.

I can't answer your question about the error message, because I don't know the test tool in question.

To keep track of the number of primes found, you can use a simple integer variable: Initialize it as zero and increment it by 1 whenever a prime is found.

lower = int(input("Lower boundry: "))
upper = int(input("Upper boundry: "))

n_primes = 0

for n in range(lower, upper + 1):
    if (n <= 1):
        print(n, "error")
    else:
        for x in range(2, n):
            if ((n % x) == 0):
                print(n, "not prime, because", x, "*", int(n/x),"=", n)
                break
        else:
            print(n, "prime")
            n_primes += 1
            last = n  
            
print("Checked", upper - lower + 1, "numbers, of which", n_primes, "were prime.")
print("Last prime number found was", last)