Prime Numbers List

List of all Prime Numbers - how many Prime numbers are between

Prime Numbers List

Find all prime numbers between
and

Prime Numbers Calculator - Generate List of Prime Numbers

What are Prime Numbers?

Prime numbers are natural numbers greater than 1 that have no positive divisors other than 1 and themselves. For example, 2, 3, 5, 7, 11, 13 are prime numbers because they cannot be divided evenly by any other numbers except 1 and the number itself.

How does the Prime Number Generator work?

Our prime number calculator allows you to:

  • Find all prime numbers in a range — enter the starting and ending values
  • Count prime numbers — get the exact count of prime numbers in a given interval
  • Display list of prime numbers — for ranges up to 100,000 numbers

Prime Number Calculator Use Cases

The prime number calculator is useful in various scenarios:

  • Studying number theory and mathematical patterns
  • Solving cryptography and information security problems
  • Programming algorithms and computational optimization
  • Preparing for mathematical competitions and exams

Properties and Patterns of Prime Numbers

Prime numbers have unique properties:

  • Only even prime number — the number 2 is the only even prime
  • All other primes are odd — except for 2, all prime numbers are odd
  • Infinite set — there are infinitely many prime numbers
  • Fundamental theorem of arithmetic — every natural number can be factored into primes uniquely
Prime numbers are the "atoms" of arithmetic — all other natural numbers are built from them through multiplication.

Prime Number Algorithms

There are many methods for finding prime numbers:

  • Sieve of Eratosthenes — classic algorithm for finding all primes up to a given number
  • Primality testing — checking divisibility by numbers up to the square root
  • Probabilistic tests — fast algorithms for large numbers

See Also

Prime Numbers List

This calculator will show a list of primes between the given numbers. For example, it can help you find out what are Prime numbers between 20 and 30? (The answer is: 2). Select the starting number (e.g. '20') and the ending number (e.g. '30'). After that hit the 'Show' button.
Prime numbers are the positive integers having only two factors - 1 and the number itself

FAQ

What is a prime number?

A whole number greater than 1 that is divisible only by 1 and by itself: 2, 3, 5, 7, 11, 13. The number 1 is not prime, because it has a single divisor, and 2 is the only even prime.

How many prime numbers are there between 1 and 100?

Exactly 25: 2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47, 53, 59, 61, 67, 71, 73, 79, 83, 89 and 97. Between 1 and 1000 there are already 168 of them.

Is the list of prime numbers infinite?

Yes. Euclid proved it around 300 BC: multiply all the primes of any finite list and add 1, and the number you get is divisible by none of them, so the list was never complete.