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Prime Number Checker

Check if a number is prime, find factors, list primes up to N, find nth prime, and generate primes in range

Updated

What is the Prime Number Checker?

Prime Number Checker instantly determines whether a number is prime, reveals its prime factors if composite, finds nearby primes, and generates comprehensive lists of primes.

Whether you're a student learning number theory, a developer needing quick primality tests, or simply curious about mathematics, this tool provides accurate, lightning-fast results entirely in your browser.

Key Features:

  • Check single numbers (supports large safe integers)
  • List all primes up to a limit
  • Find the nth prime number
  • Generate primes within custom ranges
  • Automatic prime factorization
  • Next/previous prime detection

Fast, private, and no sign-up required.

How it works

The tool combines several proven mathematical algorithms for optimal performance and accuracy:

Single Number Primality Test

For checking individual numbers, it uses an optimized trial division method:

  • Early rejection for even numbers and multiples of 3
  • Checks divisors only up to the square root of the number (using 6k ± 1 optimization)
  • Supports BigInt for numbers up to JavaScript's safe integer limit (~9 quadrillion)

Prime Factorization

When a number is composite, it efficiently finds all prime factors using trial division, handling the factor 2 separately before checking odd divisors.

Listing Primes (Sieve of Eratosthenes)

For "Primes ≤ N" and range queries within reasonable bounds, the classic Sieve of Eratosthenes is used — marking multiples of each prime starting from 2. This is highly efficient for limits up to 1 million.

Nth Prime & Range Generation

  • Uses the sieve for small-to-medium n
  • Incremental next-prime search for extension
  • Safe caps ensure responsive performance in the browser

All computations happen locally in your browser with pure JavaScript. No data is sent to any server, ensuring complete privacy.

Examples

Check if 17 is Prime

Verify primality of a small number

17
Prime ✓

List Primes Up To 50

Generate first primes in range

50
2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47

Find the 10th Prime

Discover the nth prime number

10
29

Primes Between 100 and 150

Range-based prime listing

100 to 150
101, 103, 107, 109, 113, 127, 131, 137, 139, 149

Frequently asked questions

What is a prime number?

A prime number is a natural number greater than 1 that has no positive divisors other than 1 and itself. The first few primes are 2, 3, 5, 7, 11, and 13.

How do you check if a large number is prime?

This tool uses an optimized trial division algorithm that checks divisibility only up to the square root of the number, making it efficient even for large numbers within JavaScript's safe integer range.

What is the largest number this tool can handle?

It reliably handles numbers up to approximately 9 quadrillion (JavaScript safe integer limit). For extremely large numbers, results may be approximate or limited by browser performance.

Does it list primes in a specific range?

Yes. Switch to "Range" mode and enter start and end values to generate all primes within that interval (up to a practical 1 million difference).

How accurate is the nth prime finder?

Very accurate for n up to 10,000 (and beyond with incremental search). The 10,000th prime is around 104,729.

Why is 2 the only even prime number?

Because every even number greater than 2 is divisible by 2, violating the definition of a prime (exactly two distinct positive divisors).

Can I copy the list of primes?

Yes. Every result section includes a convenient "Copy" button for easy export of results to clipboard.

Is this tool free and private?

Completely free, works offline after loading, and all calculations happen in your browser — no data is collected or sent to servers.

What algorithms power the prime generation?

Primarily the Sieve of Eratosthenes for bulk lists and optimized trial division for individual checks and factorization.

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