BYTETOOLS

Prime Number Generator

Generate all prime numbers up to a limit, or the first N primes, using a fast sieve. See the full list and the total count, computed instantly in your browser.

25
Primes found

Prime numbers

2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47, 53, 59, 61, 67, 71, 73, 79, 83, 89, 97

What is the Prime Number Generator?

The ByteTools Prime Number Generator lists prime numbers using the Sieve of Eratosthenes, one of the oldest and fastest ways to find primes.

  • Uses the fast Sieve of Eratosthenes
  • List primes up to a limit or the first N primes
  • Shows the total count of primes found
  • Sensible cap keeps your browser responsive
  • Copy the entire list in one click
  • 100% private — runs entirely in your browser

How to use the Prime Number Generator

  1. 1

    Choose a mode: primes up to a limit, or the first N primes.

  2. 2

    Enter your value of N.

  3. 3

    Read the count of primes found.

  4. 4

    Browse or copy the full list of prime numbers.

  5. 5

    Click Copy to grab the list.

About the Prime Number Generator

The ByteTools Prime Number Generator lists prime numbers using the Sieve of Eratosthenes, one of the oldest and fastest ways to find primes. Choose to list every prime up to a limit N, or the first N primes, and the tool shows the full list together with how many it found.

It is built for students learning number theory, programmers needing test data and anyone curious about the distribution of primes. The sieve is efficient enough to handle limits into the hundreds of thousands quickly.

All generation happens in your browser with JavaScript — no numbers are uploaded and there is no server round trip. Copy the whole list with one click.

Frequently asked questions

What is a prime number?

A prime number is a whole number greater than 1 that has no divisors other than 1 and itself. The first primes are 2, 3, 5, 7, 11 and 13. Numbers with additional factors, like 6 or 9, are composite.

How does the Sieve of Eratosthenes work?

Write out the numbers up to your limit, then repeatedly cross off the multiples of each prime, starting with 2. Whatever remains uncrossed is prime. It is far faster than testing each number individually.

What is the largest prime this tool can find?

The generator caps the limit to keep your browser responsive, typically at 100,000. Within that range it lists every prime instantly. If you exceed the cap, it shows a message asking for a smaller value.

Is 2 a prime number?

Yes. 2 is the smallest prime and the only even prime, because every other even number is divisible by 2. All primes after 2 are odd. The generator always includes it in the list.

How many primes are there below 100?

There are 25 prime numbers below 100. Primes thin out as numbers get larger, but they never run out — there are infinitely many, a fact proven by Euclid over two thousand years ago.

Guides for Prime Number Generator

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