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Prime Number Checker & Factorizer (BigInt Support)

Professional mathematical tool to check prime numbers with BigInt precision. Features visual Sieve of Eratosthenes, prime factorization, and nearest prime locator for crypto and CS.

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About

This Prime Number Checker is an enterprise-grade mathematical utility designed for students, developers, and cryptography enthusiasts. Unlike standard calculators, this tool utilizes JavaScript BigInt primitives to handle integers beyond the 16-digit safe limit, ensuring zero precision loss for large numbers.

Key capabilities include Full Prime Factorization (breaking down composite numbers into their building blocks), a Nearest Prime Locator for optimizing hash table sizes, and an interactive Visual Sieve for numbers under 1,000 to demonstrate primality testing in real-time.

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Formulas

The distribution of prime numbers up to a value x can be approximated using the Prime Number Theorem:

π(x) ≈ xln(x)

To check for primality n using trial division, we test divisors d up to:

d ≤ √n

Reference Data

CategoryDescriptionExample
Prime NumberA number greater than 1 with exactly two factors: 1 and itself.2, 3, 17, 104729
Composite NumberA number that has more than two factors.4 (2×2), 15 (3×5)
Mersenne PrimeA prime number of the form 2n − 1.3, 7, 31, 127
Twin PrimesTwo primes that differ by exactly 2.(3, 5), (11, 13)
CoprimeTwo numbers whose greatest common divisor (GCD) is 1.8 and 15

Frequently Asked Questions

By definition, a prime number must have exactly two distinct positive divisors: 1 and itself. The number 1 has only one divisor (1), so it fails this criterion. Excluding 1 is essential for the Fundamental Theorem of Arithmetic to hold unique factorization.
This tool uses BigInt, meaning it is limited only by your browser's memory and CPU time. However, factorization of numbers with more than 15-20 digits may take significant time as it involves computationally intensive trial division.
Primes are fundamental in Cryptography (RSA encryption relies on the difficulty of factoring large semiprimes), Hash Tables (using prime sizes reduces collisions), and Random Number Generators.