Prime Numbers Explained

A prime number is a whole number greater than 1 that has only two divisors: 1 and itself. For example, 5 is a prime number because it can only be divided evenly by 1 and 5. Numbers like 4 (divisible by 1, 2, and 4) are not prime.

Finding the First 10 Prime Numbers

To find the average of the first 10 prime numbers, we first need to list them:

• The first prime number is 2.
• The next prime number is 3.
• The next is 5.
• The next is 7.
• The next is 11.
• The next is 13.
• The next is 17.
• The next is 19.
• The next is 23.
• The tenth prime number is 29.

So, the first 10 prime numbers are: 2, 3, 5, 7, 11, 13, 17, 19, 23, 29.

Calculating the Sum of Primes

Next, we sum these numbers:

Sum = 2 + 3 + 5 + 7 + 11 + 13 + 17 + 19 + 23 + 29

Sum = 129

Average Calculation Step-by-Step

The average (or arithmetic mean) is calculated by dividing the sum of the numbers by the count of the numbers.

The formula for the average is:

Average = \(\frac{\text{Sum of numbers}}{\text{Count of numbers}}\)

In this case:

• Sum of the first 10 prime numbers = 129
• Count of the numbers = 10

Now, we plug these values into the formula:

Average = \(\frac{129}{10}\)

Average = 12.9

Final Result

The average of the first 10 prime numbers is 12.9.