What is a prime number?

A prime number is a natural number greater than 1 that has no positive divisors other than 1 and itself. Examples: 2, 3, 5, 7, 11, 13.

No, 1 is not prime. By definition, a prime must have exactly two distinct divisors, but 1 only has one divisor (itself).

Is 2 the only even prime?

Yes! 2 is the only even prime number because all other even numbers are divisible by 2.

What is a composite number?

A composite number is a positive integer greater than 1 that has at least one divisor other than 1 and itself. Examples: 4, 6, 8, 9, 10.

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Prime Number Calculator

Check if any number is prime, find all factors, and explore prime number properties. Features instant primality testing, complete factorization, and educational insights about number theory and divisibility rules.

How to Use the Prime Number Calculator

Use the Prime Number Calculator to check if any number is prime, find all factors, and explore prime number properties. Features instant primality testing, complete factorization, and educational insights about number theory and divisibility rules.. Enter your values to get accurate, instant results tailored to your situation.

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Prime Numbers Guide

Primality testing

Expert Tips

Prime = Divisible Only by 1 and Itself: Primes: 2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31... Not prime: 1 (by definition), 4, 6, 8, 9, 10, 12... 2 is only even prime. All others are odd.
Check Divisibility Up to √n Only: Check if 97 is prime: √97 ≈ 9.8. Test divisibility by primes up to 9: 2, 3, 5, 7. None divide evenly → 97 is prime. No need to test beyond √n (if n = a×b and a > √n, then b < √n).
Sieve of Eratosthenes: Find All Primes Up to N: List numbers 2 to n. Cross out multiples of 2 (except 2), then 3, then 5, etc. Remaining numbers are prime. Efficient for finding many primes. Ancient algorithm still used today.
Primes Used in Cryptography (RSA): Internet security relies on difficulty of factoring large numbers into primes. RSA uses 2,048-bit primes (617 digits). Easy to multiply primes, hard to factor product. Fundamental to online security.

Essential Fundamentals — Prime concepts

Properties

Prime Definition: Natural number > 1 with exactly two divisors: 1 and itself. Fundamental building blocks—every number is prime or product of primes (Fundamental Theorem of Arithmetic). Infinite primes (proven by Euclid ~300 BC).
Composite Numbers: Non-prime numbers > 1. Have more than two divisors. Examples: 4 (1,2,4), 6 (1,2,3,6), 9 (1,3,9). Every composite number can be uniquely factored into primes: 12 = 2² × 3.

Advanced Strategies — Efficient testing

Optimization Methods

Divisibility Shortcuts: Even numbers (except 2) are composite. Sum of digits divisible by 3 → number divisible by 3. Last digit 5 or 0 → divisible by 5. Apply quick checks before systematic testing.
Prime Factorization Use: Factor composites into prime powers. 360 = 2³ × 3² × 5. Reveals divisibility, simplifies GCD/LCM, essential for fraction operations. Every composite has unique prime factorization.

Frequently Asked Questions

What is a prime number?: A prime number is a natural number greater than 1 that has no positive divisors other than 1 and itself. Examples: 2, 3, 5, 7, 11, 13.
Is 1 a prime number?: No, 1 is not prime. By definition, a prime must have exactly two distinct divisors, but 1 only has one divisor (itself).
Is 2 the only even prime?: Yes! 2 is the only even prime number because all other even numbers are divisible by 2.
What is a composite number?: A composite number is a positive integer greater than 1 that has at least one divisor other than 1 and itself. Examples: 4, 6, 8, 9, 10.