Prime Number Checker
Check whether a whole number is prime, with the trial-division method explained and worked examples for 97 and 91.
Results
Result
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Educational estimates · not financial advice · free, no signup
Formula / how it works
A prime has exactly two divisors, 1 and itself. To test n, check divisibility by every prime up to √n; if none divides n, it is prime. 1 is not prime.
Detailed guide
What it is, how to use it, how to read the numbers, common mistakes, a worked example, formulas, and FAQs.
What this calculator is
A prime number is a whole number greater than 1 whose only divisors are 1 and itself. 2, 3, 5, 7, 11 and 13 are primes; 9 and 15 are not. Primes are the building blocks of integers, since every whole number factors uniquely into primes, and they underpin modern cryptography. This tool tests a number using trial division. It is meant for classroom-size numbers, homework, puzzles and checking factors. It does not factorise very large numbers, which is a hard problem and the basis of security systems.
When to use / who it helps
- You are checking homework or a puzzle involving primes.
- You want to know if a number can be divided evenly by anything other than 1 and itself.
- You are simplifying fractions and need to find factors.
- You are exploring number patterns.
- You are testing small numbers in a program.
How to use
Steps
- Enter an integer greater than 1.
- Read whether it is prime.
- If not prime, find a divisor by hand using the factor tools.
- Check divisibility by 2, 3 and 5 using quick rules.
- Repeat for neighbouring numbers to see prime gaps.
- Use specialised software for very large numbers.
How to interpret results
- A prime result means the number has no divisors other than 1 and itself.
- Composite means it has at least one other factor.
- 2 is the only even prime.
- Testing divisors up to the square root is enough.
- 0, 1 and negative numbers are not prime.
Common mistakes & gotchas
- Calling 1 a prime.
- Assuming all odd numbers are prime.
- Forgetting to test 7 and 11 when checking by hand.
- Entering a decimal.
- Using the tool for numbers far beyond the classroom range.
Worked example
Worked example — 97 and 91
- √97 ≈ 9.85, so test the primes 2, 3, 5 and 7.
- 97 is odd, its digit sum 16 is not divisible by 3, it does not end in 0 or 5, and 97 ÷ 7 ≈ 13.86, so none divide it.
- Therefore 97 is prime.
- For 91: √91 ≈ 9.54; 91 ÷ 7 = 13 exactly, so 91 = 7 × 13 and is not prime.
Result: 97 is prime; 91 is composite.
To load the form's own demo values, tap Try example above the Calculate button.
How to calculate / formula
A prime has exactly two divisors, 1 and itself. To test n, check divisibility by every prime up to √n; if none divides n, it is prime. 1 is not prime.
Frequently asked questions
What is a prime number?
A whole number greater than 1 with exactly two divisors: 1 and itself.
Is 1 a prime number?
No, by convention, because primes have exactly two divisors.
Why check only up to the square root?
A composite number must have a factor no larger than its square root.
Is 2 prime?
Yes, and it is the only even prime.
How many primes are there?
Infinitely many, as Euclid proved.
Why are primes important?
They underpin number theory and cryptography.