listing prime numbers from 3 to 21 in python 3

Question

for x in range (3,21):
    if(x%2==0):
        print (x,'is a not a prime number')
    else:
        print (x,'is a prime number')

This is my code but when it prints it says 9 is a prime number and 15 is a prime number.

Which is wrong because they aren't so how do I fix that?

Possible duplicate of [Find prime numbers in range](https://stackoverflow.com/questions/23079761/find-prime-numbers-in-range) — eyllanesc, Dec 13 '18 at 02:30
Your code does nothing to test for prime numbers. It is looking at whether a number is odd or even — sacuL, Dec 13 '18 at 02:31
Possible duplicate of [isPrime Function for Python Language](https://stackoverflow.com/questions/15285534/isprime-function-for-python-language) — Håken Lid, Dec 13 '18 at 02:33

score 0 · Answer 1 · answered Dec 13 '18 at 02:35

0

Your code only checks if a number is even. All odd numbers are not prime. So write a for-loop that checks if a odd number is divisible by any of the odd number less than that. Sometying like:

For i in (3 to n): If n mod i == 0, n is not prime.

answered Dec 13 '18 at 02:35

nnut

35
7

I know the issue is with the if loop, but every other method of finding a prime number ends up messing up the whole list somehow. When I run the program I want it to say '3 is a prime number' '4 is not a prime number' all the way to 20 all at once – Brendo Campos Dec 13 '18 at 03:00

JoshuaCS · Accepted Answer · 2018-12-13T03:46:15.910

.

def isPrime(N):
    i = 2
    while i**2 <= N:
        if N % i == 0:
            return False
        i+=1
    return True

for i in range(3, 21 + 1):
    if isPrime(i):
        print(i, 'is prime')
    else:
        print(i, 'is not a prime number')

First of all, create a function for determining whether or not a given number is prime (this is not a requirement but just a good practice). That function is not that hard: it just starts at i = 2 (starting at 1 makes no sense because every number can be divided by it) and check if N can be divided by it. If that is the case, we have found a divisor of N and thus, it isnt prime. Otherwise, continue with the next number: i += 1. The most tricky part of the loop is the stoping condition: i**2 <= N: we dont have to look further, because if some j > i is a divisor of N, then there is some other k < i that is also a divisor of N: k * j == N. If such k exists, we will find it before getting to the point where i * i == N. Thats all. After that, just iterate over each number you want to check for primality.

Btw, the best way to check for the primality of a set of number is using the Sieve of Eratosthenes

thank you! do you mind explaining how this works really quickly? Like why the +1 in the range and what the first part is? Sorry I'm a complete beginner. — Brendo Campos, Dec 13 '18 at 03:09
@BrendoCampos I edited the answer explaining what that code does. The +1 in the range is just to ensure that 21 is included in the checks, because `range(3, 21)` returns an open interval on the right: **[3, 21)** — JoshuaCS, Dec 13 '18 at 03:54

listing prime numbers from 3 to 21 in python 3

2 Answers2