Prime Number Checker
Check if a number is prime and understand prime number concepts
Prime Number Results
Number Type
Factors
Next Prime
Common Prime Numbers
| Range | Prime Numbers | Count |
|---|---|---|
| 1-10 | 2, 3, 5, 7 | 4 |
| 1-50 | 2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47 | 15 |
| 1-100 | 25 primes including 2, 3, 5, 7, 11, …, 97 | 25 |
| Famous Primes | 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 | 25 |
Prime Number Facts
- 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 the building blocks of all integers
- There are infinitely many prime numbers
Understanding Prime Numbers
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 is a whole number that cannot be exactly divided by any whole number other than itself and 1.
For example, 5 is a prime number because it can only be divided evenly by 1 and 5. In contrast, 6 is not a prime number (it’s composite) because it can be divided evenly by 1, 2, 3, and 6.
Applications of Prime Numbers
Cryptography
Essential for encryption algorithms like RSA
Computer Science
Used in hashing algorithms and random number generation
Mathematics
Fundamental in number theory and mathematical proofs
Internet Security
Critical for secure online transactions and communications
Key Properties of Prime Numbers
Prime numbers have several important mathematical properties:
- Infinite Quantity: There are infinitely many prime numbers (proved by Euclid)
- Fundamental Theorem: Every integer greater than 1 is either prime or can be factored into primes
- Distribution: Primes become less frequent as numbers get larger, but never disappear
- Twin Primes: Pairs of primes that differ by 2 (like 3 and 5, or 11 and 13)
- Mersenne Primes: Primes of the form 2^p – 1 where p is also prime
How to Use Our Prime Number Checker
Enter Your Number
Input a positive integer greater than 1
Click Check
Press the check button to verify if it’s prime
View Results
See if the number is prime, its factors, and next prime
Explore Properties
Learn about prime number characteristics and applications
Types of Prime Numbers
There are several special categories of prime numbers:
Twin Primes
Pairs of primes that differ by 2 (e.g., 3 and 5, 11 and 13)
Palindromic Primes
Primes that read the same forwards and backwards (e.g., 101)
Mersenne Primes
Primes of form 2^p – 1 where p is prime (e.g., 3, 7, 31)
Sophie Germain
Primes where 2p + 1 is also prime (e.g., 2, 3, 5, 11)
Frequently Asked Questions
1 is not considered a prime number because it doesn’t meet the definition that requires exactly two distinct positive divisors. Prime numbers must have exactly two divisors (1 and itself), but 1 has only one divisor (1 itself). This exclusion preserves the uniqueness of prime factorization.
Yes, there are infinitely many prime numbers. This was first proved by the ancient Greek mathematician Euclid around 300 BCE. His proof shows that if you assume there are only finitely many primes, you can always construct a new prime not in your list, creating a contradiction.
As of 2023, the largest known prime number is 2^82,589,933 − 1, a number with 24,862,048 digits. It was discovered in December 2018 as part of the Great Internet Mersenne Prime Search (GIMPS). This is a Mersenne prime, which are primes of the form 2^p – 1 where p is also prime.
Prime numbers are fundamental to modern cryptography, especially in public-key cryptosystems like RSA. The security of RSA relies on the difficulty of factoring the product of two large prime numbers. While multiplication is easy, factoring the product back into the original primes is computationally intensive, making encryption secure.
The prime number checker theorem describes the asymptotic distribution of prime numbers. It states that the number of primes less than or equal to a large number x is approximately x/ln(x), where ln(x) is the natural logarithm of x. This means primes become less frequent as numbers get larger, but they never completely disappear.