Finding the Number of Prime Numbers Less Than 55

The question asks us to find the total count of prime numbers that are strictly less than 55. To solve this, we first need to understand what a prime number is and then identify all such numbers within the specified range.

What is a Prime Number?

A prime number is a natural number greater than 1 that has no positive divisors other than 1 and itself.

• Numbers like 2, 3, 5, 7 are prime because their only divisors are 1 and the number itself.
• Numbers like 4 (divisors are 1, 2, 4) or 6 (divisors are 1, 2, 3, 6) are not prime; they are called composite numbers.
• The number 1 is not considered a prime number.

Listing Prime Numbers Below 55

Let's list all the prime numbers starting from the smallest prime number (which is 2) and going up, ensuring they are less than 55. We check each number to see if it has any divisors other than 1 and itself.

Here are the prime numbers less than 55:

• 2 (only divisible by 1 and 2)
• 3 (only divisible by 1 and 3)
• 5 (only divisible by 1 and 5)
• 7 (only divisible by 1 and 7)
• 11 (only divisible by 1 and 11)
• 13 (only divisible by 1 and 13)
• 17 (only divisible by 1 and 17)
• 19 (only divisible by 1 and 19)
• 23 (only divisible by 1 and 23)
• 29 (only divisible by 1 and 29)
• 31 (only divisible by 1 and 31)
• 37 (only divisible by 1 and 37)
• 41 (only divisible by 1 and 41)
• 43 (only divisible by 1 and 43)
• 47 (only divisible by 1 and 47)
• 53 (only divisible by 1 and 53)

The next prime number after 53 is 59, which is greater than 55, so we stop at 53.

Counting the Prime Numbers Less Than 55

Now we count the numbers we listed above: 2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47, 53.

Counting these numbers one by one, we get:

1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16.

There are exactly 16 prime numbers less than 55.

Conclusion

By listing and counting all the prime numbers less than 55, we find that there are a total of 16 such numbers.

Revision Table: Prime Numbers Less Than 55

Additional Information: Properties of Prime Numbers

Prime numbers are fundamental building blocks in number theory. Here are some key points about them:

• The number 2 is the only even prime number. All other prime numbers are odd.
• There are infinitely many prime numbers. This was proven by the ancient Greek mathematician Euclid.
• The distribution of prime numbers is a complex topic studied in advanced mathematics.
• Identifying prime numbers can be done using methods like the Sieve of Eratosthenes for a given range.