Vérificateur de nombres premiers
A prime number is divisible only by 1 and itself — the building blocks of all integers via the Fundamental Theorem of Arithmetic. Our prime checker not only tells you if a number is prime but shows the complete trial-division proof, lists nearby primes, and provides prime factorization for composite numbers.
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À propos de Prime Number Checker
A prime number is divisible only by 1 and itself — the building blocks of all integers via the Fundamental Theorem of Arithmetic. Our prime checker not only tells you if a number is prime but shows the complete trial-division proof, lists nearby primes, and provides prime factorization for composite numbers.
Comment l'utiliser
- Enter any positive integer.
- Instantly see whether it is prime or composite.
- For composites, see the complete prime factorization.
- View the nearest prime numbers above and below.
- Generate a list of all primes up to a given limit using the Sieve of Eratosthenes.
Formule et méthodologie
Trial division: test divisibility by all primes up to √n. If none divide n, n is prime. Prime factorization: repeatedly divide by the smallest prime factor. Example: 360 = 2³ × 3² × 5. Number of primes below n ≈ n / ln(n) (Prime Number Theorem).
Cas d'usage courants
- RSA encryption relies on the difficulty of factoring large primes
- Hash table sizing (prime-sized tables reduce collision clustering)
- Verifying primality for number theory homework
- Competitive programming: sieve algorithms
- Generating cryptographically strong random numbers
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