Prime Number Checker
The Prime Checker determines whether a whole number is prime or composite. Prime numbers are positive integers greater than 1 that have exactly two positive divisors: 1 and the number itself.
How to use this calculator
- Enter the whole number you want to test.
- Run the calculation.
- Review whether the number is identified as prime or not prime.
- For larger numbers, remember that the calculation concerns mathematical divisibility rather than whether a number merely looks unusual or random.
Prime number definition
A prime number n > 1 has no positive divisors other than 1 and n.
- A number is composite if it has at least one additional positive divisor besides 1 and itself.
- Testing divisibility only needs to consider possible factors up to the square root of the number. If no divisor is found by that point, a number greater than 1 is prime.
- The number 1 is neither prime nor composite because it has only one positive divisor.
Worked examples
Example: 13
The number 13 is greater than 1 and is not divisible by 2, 3, or any other integer up to its square root.
13 is a prime number.
Example: 15
The number 15 can be divided by 3 and 5 in addition to 1 and 15.
15 = 3 × 5
15 is composite, not prime.
Understanding the result
Every integer greater than 1 is either prime or composite.
The number 2 is the only even prime number because every other even number has 2 as a divisor.
Prime numbers are fundamental to number theory and are also important in areas of computer science such as cryptography.
Important notes
The input should be a whole number for a standard prime-number test.
The number 1 is not prime.
A prime check for very large integers can require more sophisticated algorithms than a basic divisibility test.
Frequently asked questions
What is a prime number?
A prime number is an integer greater than 1 that has exactly two positive divisors: 1 and itself.
Is 1 a prime number?
No. The number 1 has only one positive divisor, so it is neither prime nor composite.
What is the only even prime number?
2 is the only even prime number. Every other even integer greater than 2 is divisible by 2.
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This page provides a calculation tool plus explanatory information so you can understand what the result means and when the underlying method may not fit your situation.