Prime Number Calculator — Primality Test & Factorization
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Understanding Prime Numbers
A prime is a natural number > 1 with no divisors other than 1 and itself. The first primes are 2, 3, 5, 7, 11, 13. The number 2 is the only even prime. There are infinitely many primes.
Every integer > 1 has a unique prime factorization. This is used in RSA cryptography, which relies on the difficulty of factoring large numbers.
This tool uses trial division for testing and factoring, and the Sieve of Eratosthenes for listing primes up to a given limit efficiently.
Frequently Asked Questions
Is 1 a prime number?
No. A prime must be > 1 with exactly two distinct divisors.
Why is 2 the only even prime?
Every other even number is divisible by 2, so it has more than two factors.
How does the Sieve of Eratosthenes work?
It marks multiples of each prime starting from 2. Remaining numbers are prime.
What are primes used for?
RSA encryption, hash functions, random number generators, error-correcting codes.