Find the arithmetic mean of the prime numbers in this list:      21, 23, 25, 27, 29
The prime numbers are $23$ and $29$. Since $29-23=6$, the mean is $\frac62=3$ numbers away from $23$ and from $29$. The mean is $\boxed{26}$. We can also find the mean of $23$ and $29$ with $\frac{29+23}{2}=\frac{52}{2}=26$ or just by noticing that the number in the middle of $23$ and $29$ is $26$.
26
Level 2
Number Theory
Problem: Find the arithmetic mean of the prime numbers in this list:      21, 23, 25, 27, 29
Solution:<|START_OF_LATENT|><|PRIOR_PREFIX|>To find the arithmetic mean, first identify the prime numbers in the list. A prime number is defined as a natural number greater than 1 that has no positive divisors other than 1 and itself. 

Examine each number in the list: 
- 21 is not prime (divisible by 3 and 7).
- 23 is prime (only divisible by 1 and 23).
- 25 is not prime (divisible by 5).
- 27 is not prime (divisible by 3 and 9).
- 29 is prime (only divisible by 1 and 29).

The prime numbers identified are 23 and 29. 

Next, calculate the arithmetic mean of these prime numbers. The arithmetic mean is calculated by summing the numbers and dividing by the count of the numbers. 

Sum the prime numbers: 
23 + 29 = 52.

Count the prime numbers: 
There are 2 prime numbers.

Now, divide the sum by the count: 
52 / 2 = 26.

Thus, the final answer is 26.<|END_OF_LATENT|> The final answer is $26$.