How does the primality test work?

This tool uses the deterministic Miller-Rabin primality test with specific witness bases that are provably correct for all 64-bit integers. For numbers larger than 64 bits (BigInt), it uses a probabilistic Miller-Rabin test with high confidence.

What is the Sieve of Eratosthenes?

The Sieve of Eratosthenes is an ancient algorithm for finding all primes up to a given limit. It works by iteratively marking the multiples of each prime starting from 2. For range queries (primes between A and B), this tool uses a segmented sieve variant.

How large can the numbers be?

For primality checking and factorization, the tool supports arbitrarily large integers using JavaScript BigInt. For prime generation (sieve), the recommended limit is 2 million for best performance since the sieve runs entirely in your browser.

How does factorization work?

The tool uses trial division with the 6k plus or minus 1 optimization. It divides by 2 and 3 first, then checks divisors of the form 6k-1 and 6k+1. This is efficient for numbers with small prime factors.

Prime Number Calculator — Check, Fact...

Check if any number is prime (BigInt Miller-Rabin), generate primes via Sieve of Eratosthenes, factorize into prime factors, find the Nth prime, locate the nearest prime, test Goldbach’s conjecture, check coprimality, highlight twin primes, and visualize prime gaps and density. All runs in your browser.

Prime Number Tools

Check / Factorize

Generate primes ≤ N

Range A – B

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Nth prime

Nearest prime

Goldbach (even N > 2)

GCD / Coprime

Algorithms ▼

Primality: Deterministic Miller-Rabin for 64-bit; probabilistic for BigInt.
Sieve: Eratosthenes up-to-N; segmented for ranges.
Factorization: Trial division, 6k±1 optimization.
Nth prime: PNT upper bound n(ln n + ln ln n).
Goldbach: Sieve-based scan.
GCD: Euclidean algorithm (BigInt).

Result

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