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Kordu Tools
Math & Numbers Runs in browser Updated 30 Mar 2026

Prime Number Tools

Check if a number is prime, find prime factorization, list all primes in a range using the Sieve of Eratosthenes, or find the Nth prime.

Enter any positive integer to test whether it is prime. Results include the nearest prime and smallest factor for composite numbers.

All calculations run in your browser. No data is sent to any server. Primality testing uses trial division up to the square root. Prime listing uses the sieve of Eratosthenes.
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How to use Prime Number Tools

  1. Choose a mode

    Select Primality Test, Prime Factorization, List Primes in Range, or Find Nth Prime using the tabs.

  2. Enter a number or range

    Type a positive integer. For range mode, enter a start and end value. For Nth prime, enter the position.

  3. View the result

    Results appear instantly. Factorization shows the prime factor decomposition as a product of powers.

  4. Expand the factor tree

    For factorization mode, expand the step-by-step working to trace how each factor was extracted.

  5. Explore the prime list

    In range mode, the full list of primes is displayed in a grid — useful for spotting patterns.

Prime Number Tools FAQ

What is a prime number?
A prime number is a positive integer greater than 1 that has no divisors other than 1 and itself. Examples: 2, 3, 5, 7, 11, 13, 17, 19, 23.

How do I test if a number is prime?
Trial divide by every integer from 2 to √n. If none divide evenly, the number is prime. This tool does it instantly for any input.

What is prime factorization?
Writing a number as a product of its prime factors. Example: 60 = 2² × 3 × 5. Every integer greater than 1 has a unique prime factorization (Fundamental Theorem of Arithmetic).

What is the Sieve of Eratosthenes?
An ancient algorithm to find all primes up to n. Start with numbers 2 to n, then repeatedly strike out multiples of each prime found. Remaining numbers are prime.

What is 1 — is it prime?
No. 1 is neither prime nor composite. By definition, primes must be greater than 1 and have exactly two distinct factors.

What is 2 — is it prime?
Yes. 2 is the only even prime number. All other even numbers are divisible by 2 and therefore composite.

How large a number can I test for primality?
Trial division works well up to about 10^12. Larger numbers need probabilistic algorithms like Miller-Rabin.

What is prime factorization used for?
It underlies GCD and LCM calculation, simplifying fractions, and forms the basis of RSA encryption in cryptography.

What are twin primes?
Prime pairs that differ by 2, such as (3,5), (5,7), (11,13), (17,19). They are infinitely conjectured but not proven.

Is any data sent to a server?
No. All calculations run entirely in your browser. Nothing is uploaded or stored.

Background

A complete suite of prime number tools in one place. Primality test instantly checks whether a number is prime using trial division up to its square root. Prime factorization decomposes any number into its prime factor product — displayed as both a factor tree and a product of powers (e.g. 360 = 2³ × 3² × 5). The prime listing mode uses the Sieve of Eratosthenes to generate all primes in a given range efficiently. The Nth prime finder returns the exact prime at any position in the sequence. Results appear instantly and step-by-step factorization working is shown. Useful for number theory coursework, cryptography students learning RSA fundamentals, competitive math, and anyone who needs to quickly verify whether a number is prime. All processing runs in your browser with no software or account needed.

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