# Week 5 Bonus Exercise

18. June 2024

Prime numbers are natural numbers greater than 1 which are not divisible by any number beside 1 and the number itself. In other words, the number cannot be composed as a product of two natural numbers other than 1 and the number itself. There are infinite prime numbers and the first ones are:

2, 3, 5, 7, 11, ...

Write a program, that gets an integer through input and creates a list containing all prime numbers until this input. To do so, two functions have to be implemented:

- The function
`is_prime()`

gets an integer as input and returns`True`

if this integer is prime, and`False`

if the integer is not prime. - The function
`prime_list()`

gets an integer as input and checks each number from 2 to input, if it is prime by calling the above function. If a number is prime, it is appended to a list. This list is given back as the return value of prime_list().

The program finally outputs the list of all prime numbers.

### Example 1:

```
Up to which number do you want all prime numbers: 100
[2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47, 53, 59, 61, 67, 71, 73, 79, 83, 89, 97]
```

### Example 2:

```
Up to which number do you want all prime numbers: 13
[2, 3, 5, 7, 11, 13]
```