Prime Number Checker

Enter any number to instantly determine if it's a prime number. Learn about the properties that make a number prime.

Quick Facts

Smallest Prime
2
The only even prime number
Primes under 100
25 primes
2, 3, 5, 7, 11... up to 97
Prime Discovery
Infinite
Proven by Euclid ~300 BC
Largest Known Prime
2^82,589,933 - 1
Over 24 million digits!
0
is a prime number

Key Takeaways

  • A prime number is only divisible by 1 and itself
  • 2 is the only even prime number
  • 1 is NOT considered a prime number
  • Prime numbers are infinite - there's no largest prime
  • Prime numbers are fundamental to modern cryptography and security

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. In other words, a prime number cannot be formed by multiplying two smaller natural numbers together (other than 1 and the number itself).

For example, 7 is a prime number because the only ways to express 7 as a product of two positive integers are 1 x 7 or 7 x 1. However, 6 is not prime because it can be written as 2 x 3.

First 25 Prime Numbers

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

1

Check if the number is greater than 1

By definition, prime numbers must be greater than 1. The number 1 is not considered prime.

2

Check divisibility by 2

If the number is even and greater than 2, it's not prime. Only 2 is both even and prime.

3

Test divisibility up to the square root

You only need to check divisors up to the square root of the number. If no divisor is found, the number is prime.

4

Skip even divisors after 2

After checking 2, you only need to check odd numbers (3, 5, 7, 9...) as any even divisor would have been caught by the check for 2.

Example: Is 37 Prime?

To check if 37 is prime:

  • 37 > 1 (passes first check)
  • 37 is odd (not divisible by 2)
  • Square root of 37 is approximately 6.08
  • Check divisibility by 3, 5: 37/3 = 12.33..., 37/5 = 7.4...
  • No divisors found, so 37 is prime!

Why Are Prime Numbers Important?

Prime numbers are considered the "building blocks" of mathematics because every positive integer greater than 1 can be uniquely expressed as a product of prime numbers (this is called the Fundamental Theorem of Arithmetic).

Cryptography

RSA encryption relies on the difficulty of factoring large prime numbers to secure online transactions.

Hash Tables

Prime numbers are used in hash functions to minimize collisions and improve performance.

Random Number Generation

Many pseudorandom number generators use prime numbers in their algorithms.

Digital Security

SSL/TLS certificates, secure passwords, and blockchain technology all use prime numbers.

Fun Fact: Twin Primes

Twin primes are pairs of prime numbers that differ by exactly 2 (like 11 and 13, or 17 and 19). It's still an unsolved problem in mathematics whether there are infinitely many twin primes!

Common Prime Number Questions

Is 1 a prime number?

No, 1 is not a prime number. By definition, a prime number must have exactly two distinct positive divisors: 1 and itself. Since 1 only has one divisor (itself), it doesn't meet this criterion.

Is 2 the only even prime number?

Yes! 2 is the only even prime number. All other even numbers are divisible by 2, which means they have at least three divisors (1, 2, and themselves), disqualifying them from being prime.

How many prime numbers are there?

There are infinitely many prime numbers. This was proven by the ancient Greek mathematician Euclid around 300 BC. His elegant proof shows that no matter how many primes you know, you can always find another one.

What is the largest known prime number?

As of 2024, the largest known prime number is 2^82,589,933 - 1, a Mersenne prime with over 24 million digits. Finding new large primes is an ongoing effort, with projects like GIMPS (Great Internet Mersenne Prime Search) using distributed computing to search for new record-breaking primes.