Enter an integer to check whether it is prime or composite
Result
Answer
Step-by-Step Derivation
Prime Number Test Formula
n is prime if no integer d divides n for 2 <= d <= sqrt(n)
If n mod d = 0, then n is composite
The square root test works because every composite number has a factor pair. If both factors were larger than sqrt(n), their product would exceed n, so checking possible divisors only up to sqrt(n) is enough.
⚠This checker is intended for ordinary integer inputs in the browser. Very large cryptographic-size numbers need specialized primality algorithms.
What Is a Prime Number?
A prime number is a whole number greater than 1 that can only be divided evenly by 1 and itself. Prime checking is one of the most common number theory tasks because it supports factorization, modular arithmetic, and many contest problems.
Prime Definition
A prime has exactly two positive divisors: 1 and itself.
Composite Case
A composite number has at least one divisor other than 1 and itself.
Square Root Limit
Testing to sqrt(n) is enough because every factor pair has a smaller factor.
Verification
The derivation shows the first divisor found or confirms none was found.
Example: For n = 97, test divisors up to sqrt(97), about 9.8. It is not divisible by 2, 3, 5, or 7, so 97 is prime.
Applications of Prime Number Checking
Prime TestingFactorizationCryptography BasicsMath ContestsNumber Theory
Frequently Asked Questions
What is a prime number checker?▼
A prime number checker tests whether an integer has exactly two positive divisors: 1 and itself. If it has another divisor, it is composite.
What formula does this prime checker use?▼
The tool tests divisibility up to the square root of n. If no divisor is found by sqrt(n), the number is prime.
How do I use the prime number checker?▼
Enter a positive integer and press Calculate. The result shows prime or composite and gives a short derivation with the divisor test.
Are 0 and 1 prime numbers?▼
No. Prime numbers are positive integers greater than 1 with exactly two positive divisors, so 0 and 1 are not prime.
Where are prime numbers used?▼
Prime numbers are used in factorization, fractions, modular arithmetic, cryptography, coding contests, and many number theory problems.
Free online calculators and tools covering mathematics, unit conversion, text processing, and daily life. Accurate, fast, mobile-friendly, and completely free to use.