🎓 Mathematics • Number Theory
100% Client-Side Privacy
Prime Number Checker
Instant trial division and deterministic primality tester up to 100 trillion, listing divisors and factor trees.
Presets:
Classification
360 is a COMPOSITE Number
Prime Factorization:
360 = 2^3 × 3^2 × 5
All Divisors (24):
1234568910121518202430364045607290120180360
Previous Prime: 359
Next Prime: 367
What is a Prime Number?
A prime number is a positive integer strictly greater than 1 that has no positive divisors other than 1 and itself.
Formula & Step-by-Step Calculation
Tested by trial division up to √n
If n has no divisors up to √n, n is guaranteed to be prime.
Worked Step-by-Step Examples
Example 1
Check 97
Solution: Prime Number
• √97 ≈ 9.85. Divisors 2, 3, 5, 7 tested: none divide 97. 97 is prime.
Common Real-World & Academic Use Cases
- ✓ Cryptography key generation
- ✓ Mathematical proof verification
- ✓ Number theory research
How to Use the Prime Number Checker
1
Enter Number
Input integer.
2
Review Primality
Inspect Prime/Composite status and divisors.
Frequently Asked Questions
Q: Is 1 a prime number?
No, 1 is neither prime nor composite by modern mathematical definition.