Prime Number Checker
Find out whether a given number is Prime or not
Prime Number Checker
How to Identify Prime Numbers
What are Prime Numbers?
A prime number is a natural number greater than 1 that has exactly two distinct positive divisors: 1 and itself. This fundamental concept in number theory plays a crucial role in mathematics, cryptography, and computer science.
Key Properties of Prime Numbers
- Fundamental Theorem of Arithmetic - every integer can be uniquely factored into prime numbers
- Infinite Set - there are infinitely many prime numbers (proven by Euclid)
- Unpredictable Distribution - no simple formula exists to generate all prime numbers
- Cryptographic Importance - essential for RSA encryption algorithms
Prime Number Testing Methods
Several algorithms exist for determining if a number is prime:
- Trial Division - testing divisibility by all numbers up to the square root
- Sieve of Eratosthenes - efficient method for finding all primes up to a given limit
- Miller-Rabin Test - probabilistic algorithm for large numbers
- AKS Primality Test - deterministic polynomial-time algorithm
Real-World Applications
Prime numbers are actively used in modern technology:
- Cryptography - foundation of RSA, DSA, and elliptic curve algorithms
- Hash Functions - for uniform data distribution
- Random Number Generators - in pseudorandom sequences
- Mathematical Research - in number theory and abstract algebra
Fascinating Facts About Primes
The largest known prime number contains over 24 million digits and was discovered through the GIMPS (Great Internet Mersenne Prime Search) project.
Twin primes (like 11 and 13, 17 and 19) are pairs of prime numbers that differ by 2. It's still unknown whether there are infinitely many such pairs - this is called the Twin Prime Conjecture.
Prime Numbers from 1 to 20
See Also
- Factors of a Number - List all Factors and Factor Pairs of a Number
- Prime Factorization - Prime Factorization Calculator
- Prime Numbers List - List of all Prime Numbers - how many Prime numbers are between
Prime Number Checker
This calculator will help you find out if a given number is Prime. For example, it can help you find out is 17 a prime or composite number? (The answer is: Yes). Enter number (e.g. '17') and hit the 'Check' button.
Prime numbers are the positive integers having only two factors - 1 and the number itself
FAQ
What makes a number prime?
A prime is a whole number greater than 1 with exactly two divisors: 1 and itself. 17 is prime because nothing between 2 and 16 divides it, while 16 is not, since 2, 4 and 8 do. 2 is the only even prime — every other even number is divisible by 2.
How can you check a number for primality by hand?
Trial division: test the primes up to the square root of the number and stop there, because a composite number always has a factor at or below its square root. For 97 the square root is about 9.85, so 2, 3, 5 and 7 are the only candidates — none of them divides 97, so it is prime.
Is 1 a prime number?
No. 1 has only one divisor, not two, so it is neither prime nor composite. Excluding it is what makes factorization unique: if 1 counted as a prime, 6 could be written as 2 × 3, 1 × 2 × 3, 1 × 1 × 2 × 3 and so on without end.