Prime Number Calculator
What is Prime Number Calculator?
A prime number calculator determines whether a given number is prime or composite. A prime number is a natural number greater than 1 that has exactly two distinct positive divisors: 1 and itself. Numbers with more than two factors are called composite numbers.
This calculator uses optimized algorithms including trial division for single numbers and the Sieve of Eratosthenes for finding all primes in a range. It provides detailed analysis including all factors, next/previous primes, and step-by-step explanations.
Key Concepts:
Prime: A number with exactly 2 factors (1 and itself)
Composite: A number with more than 2 factors
Examples: 2, 3, 5, 7, 11, 13, 17, 19, 23, 29...
How It Works
Enter Number/Range
Input single number or range to check
Apply Algorithm
Uses trial division or Sieve of Eratosthenes
Get Analysis
Receive prime status with detailed factors
Common Examples
Small Prime Numbers
2 (only even prime), 3, 5, 7, 11, 13
Each has exactly 2 factors: 1 and itself
Composite Numbers
4 (factors: 1, 2, 4), 6 (factors: 1, 2, 3, 6)
9 (factors: 1, 3, 9), 10 (factors: 1, 2, 5, 10)
Large Prime Numbers
97, 101, 103, 107, 109, 113
Require checking divisors up to √n
Special Cases
1 is neither prime nor composite
2 is the only even prime number
Calculation Table
| Number | Prime? | Factors | Factor Count |
|---|---|---|---|
| 2 | Yes | 1, 2 | 2 |
| 4 | No | 1, 2, 4 | 3 |
| 7 | Yes | 1, 7 | 2 |
| 12 | No | 1, 2, 3, 4, 6, 12 | 6 |
| 17 | Yes | 1, 17 | 2 |
Frequently Asked Questions
What is a prime number?
A prime number is a natural number greater than 1 that has exactly two distinct positive divisors: 1 and itself. Examples include 2, 3, 5, 7, 11, 13, 17, 19, 23, and 29. The number 1 is not considered prime.
How does the calculator check for primes?
For single numbers, it uses trial division, checking divisibility by numbers up to √n. For ranges, it uses the Sieve of Eratosthenes algorithm, which efficiently finds all primes up to a given limit by eliminating multiples of each prime.
Why is 2 the only even prime number?
All even numbers greater than 2 are divisible by 2, which means they have at least three factors: 1, 2, and themselves. Since prime numbers can only have exactly two factors, no even number except 2 can be prime.
What are the limitations of this calculator?
For single numbers, the maximum is 1,000,000 to ensure reasonable computation time. For ranges, the maximum span is 10,000 numbers. These limits balance accuracy with performance for practical use.
What are prime numbers used for?
Prime numbers are fundamental in mathematics and have practical applications in cryptography (RSA encryption), computer science (hash functions), and number theory. They're also used in algorithms, random number generation, and mathematical proofs.