Prime Number Checker - Free Online Prime Number Calculator
Check if a number is prime, find previous and next prime numbers, or list all primes up to N. Fast and accurate prime number calculations.
Results are estimates. Not professional advice.
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 can only be divided evenly by 1 and itself. Prime numbers are fundamental in mathematics and have many applications in cryptography, number theory, and computer science.
How to Use the Prime Number Checker
- Enter a Number: Enter the number you want to check or find primes up to.
- Select Mode: Choose between "Check if Prime" or "List all primes up to N".
- Click Calculate: Get the result instantly.
- Use Navigation Buttons: Click "Prev Prime" or "Next Prime" to find the previous or next prime number from your input.
What is a Prime Number?
A prime number (or a prime) is a natural number greater than 1 that cannot be formed by multiplying two smaller natural numbers. The first few prime numbers are 2, 3, 5, 7, 11, 13, 17, 19, 23, and so on.
Properties of Prime Numbers
- Only Two Divisors: A prime number has exactly two positive divisors: 1 and itself.
- Even Prime: 2 is the only even prime number. All other even numbers are divisible by 2 and are therefore not prime.
- Odd Primes: All prime numbers greater than 2 are odd.
- Infinite: There are infinitely many prime numbers (proven by Euclid around 300 BCE).
- No Pattern: There is no simple pattern to predict prime numbers, though they appear to become less frequent as numbers get larger.
Examples of Prime Numbers
- Small Primes: 2, 3, 5, 7, 11, 13, 17, 19, 23, 29
- Medium Primes: 101, 103, 107, 109, 113, 127, 131, 137, 139, 149
- Large Primes: 997, 1009, 1013, 1019, 1021, 1031, 1033, 1039, 1049, 1051
Non-Prime Numbers
Numbers that are not prime are called composite numbers. Composite numbers have more than two positive divisors. Examples include 4 (divisible by 1, 2, 4), 6 (divisible by 1, 2, 3, 6), 8 (divisible by 1, 2, 4, 8), and 9 (divisible by 1, 3, 9).
Special Cases
- 0: Not a prime number (has infinite divisors)
- 1: Not a prime number (only has one divisor: 1)
- 2: The smallest and only even prime number
Applications of Prime Numbers
- Cryptography: Used in RSA encryption and other cryptographic algorithms
- Number Theory: Fundamental building blocks in mathematical proofs
- Computer Science: Used in hashing algorithms and random number generation
- Prime Factorization: Every composite number can be uniquely expressed as a product of prime numbers
Frequently Asked Questions
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, 2, 3, 5, 7, 11, and 13 are prime numbers.
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 (1 itself), it does not meet the criteria for a prime number.
Is 2 a prime number?
Yes, 2 is a prime number. It is the smallest and only even prime number. All other even numbers are divisible by 2 and are therefore not prime.
How do you check if a number is prime?
To check if a number is prime, you need to test if it has any divisors other than 1 and itself. For efficiency, you only need to check divisors up to the square root of the number. If no divisors are found, the number is prime.
Are there infinitely many prime numbers?
Yes, there are infinitely many prime numbers. This was proven by the ancient Greek mathematician Euclid around 300 BCE using a proof by contradiction.
What is the largest known prime number?
The largest known prime number changes as new discoveries are made. As of recent years, the largest known primes are Mersenne primes (primes of the form 2^p - 1 where p is also prime), which have millions of digits.