List all the prime numbers between 20 and 50.

Answer

To find all the prime numbers between 20 and 50, we will go through each number in that range and determine if it is prime. A prime number is defined as a number greater than 1 that has no positive divisors other than 1 and itself.

### Step-by-Step Solution:

1. **Identify the range**: We are looking for prime numbers between 20 and 50. This means we will check the numbers from 21 to 49.

2. **Check each number for primality**:
- **21**: Divisible by 3 and 7 (not prime).
- **22**: Divisible by 2 (not prime).
- **23**: Not divisible by any number other than 1 and 23 (prime).
- **24**: Divisible by 2 (not prime).
- **25**: Divisible by 5 (not prime).
- **26**: Divisible by 2 (not prime).
- **27**: Divisible by 3 (not prime).
- **28**: Divisible by 2 (not prime).
- **29**: Not divisible by any number other than 1 and 29 (prime).
- **30**: Divisible by 2 (not prime).
- **31**: Not divisible by any number other than 1 and 31 (prime).
- **32**: Divisible by 2 (not prime).
- **33**: Divisible by 3 (not prime).
- **34**: Divisible by 2 (not prime).
- **35**: Divisible by 5 (not prime).
- **36**: Divisible by 2 (not prime).
- **37**: Not divisible by any number other than 1 and 37 (prime).
- **38**: Divisible by 2 (not prime).
- **39**: Divisible by 3 (not prime).
- **40**: Divisible by 2 (not prime).
- **41**: Not divisible by any number other than 1 and 41 (prime).
- **42**: Divisible by 2 (not prime).
- **43**: Not divisible by any number other than 1 and 43 (prime).
- **44**: Divisible by 2 (not prime).
- **45**: Divisible by 5 (not prime).
- **46**: Divisible by 2 (not prime).
- **47**: Not divisible by any number other than 1 and 47 (prime).
- **48**: Divisible by 2 (not prime).
- **49**: Divisible by 7 (not prime).

3. **List the prime numbers found**: The prime numbers between 20 and 50 are:
- 23
- 29
- 31
- 37
- 41
- 43
- 47

### Final Answer:
The prime numbers between 20 and 50 are: **23, 29, 31, 37, 41, 43, 47**.