What is a prime number?

A prime number is a positive integer greater than 1 that has exactly two positive divisors: 1 and itself. The first few are 2, 3, 5, 7, 11, 13, …

What algorithm is used?

Trial division up to √n, with early checks for 2 and 3 and a 6k ± 1 wheel for efficiency. This is fast for numbers up to ~10¹⁵.

No. By modern definition, 1 is a unit, not a prime. The smallest prime is 2.

For numbers above 10¹⁵ the trial division can be slow. Use a Miller–Rabin probabilistic test for cryptographic-size inputs.

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Is a number prime? Instant yes/no with factor if composite.

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Everything you might want to know about prime number checker.

List the first N primes — or primes up to a limit.

Break any integer into its prime factors — 2² × 3 × 5, etc.

Greatest common factor and least common multiple of any integers.

Generate the first N Fibonacci numbers — arbitrary precision.