Prime number generation is a fundamental concept in mathematics. It involves finding all the prime numbers up to a given limit. Prime numbers are numbers greater than 1 that are only divisible by 1 and themselves.

Prime Number Theorem

The Prime Number Theorem states that the number of prime numbers less than a given number ( n ) is approximately ( \frac{n}{\ln(n)} ).

Sieve of Eratosthenes

One of the most efficient algorithms for generating prime numbers is the Sieve of Eratosthenes. It works by iteratively marking the multiples of each prime number starting from 2.

  • Algorithm Steps:
    1. Create a list of numbers from 2 to the maximum number ( n ).
    2. Start with the first number (p) in the list.
    3. Remove all multiples of p from the list.
    4. Find the next number in the list and repeat steps 3 and 4 until all numbers have been processed.

Sieve of Eratosthenes

For more information on prime number generation and related algorithms, you can visit the Prime Number Theory page.