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. For example, 5 is prime because only 1 and 5 divide it evenly.

No, 1 is not a prime number. By definition, a prime number must be greater than 1. The number 1 is neither prime nor composite.

Yes, 2 is a prime number. It is the only even prime number, as all other even numbers are divisible by 2.

What are composite numbers?

Composite numbers are natural numbers greater than 1 that are not prime. They have at least one divisor other than 1 and themselves.

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Reviewed by Dr. Alex M., Ph.D.

Mathematics Professor & Data Scientist | Last Updated: November 2025

Understanding Prime Numbers

A prime number is a whole number greater than 1 whose only factors are 1 and itself. A factor is a whole number that can be divided evenly into another number.

The First Few Prime Numbers

Here are the prime numbers less than 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
            

How to Check if a Number is Prime

To check if a number n is prime, you can try dividing it by all prime numbers less than or equal to the square root of n. If none of them divide n evenly, then n is prime.

For example, to check 29:

Square root of 29 is approx 5.38.
Primes less than 5.38 are 2, 3, 5.
29 is not divisible by 2 (it's odd).
29 is not divisible by 3 (2+9=11, not divisible by 3).
29 is not divisible by 5 (doesn't end in 0 or 5).
Therefore, 29 is prime.

💡 Expert Tip: The Number 2

The number 2 is the only even prime number. All other even numbers can be divided by 2, so they cannot be prime. This makes 2 a very special number in mathematics!

⚠️ Common Mistake: Is 1 Prime?

Many people mistakenly believe that 1 is a prime number. However, by mathematical definition, a prime number must have exactly two distinct positive divisors: 1 and itself. The number 1 has only one divisor (1), so it is not prime.

Frequently Asked Questions

What is the largest known prime number?

As of 2025, the largest known prime number is a Mersenne prime with millions of digits. There is no "largest" prime number, as Euclid proved that there are infinitely many primes.

What are twin primes?

Twin primes are pairs of prime numbers that differ by 2. Examples include (3, 5), (5, 7), (11, 13), and (17, 19).

Why are prime numbers important?

Prime numbers are the "building blocks" of all numbers (Fundamental Theorem of Arithmetic). They are also crucial for modern cryptography, which keeps your credit card information safe online.

References

1. "Prime number." Wikipedia. https://en.wikipedia.org/wiki/Prime_number
2. "Prime Numbers." Math is Fun. https://www.mathsisfun.com