sieve of eratosthenes c

Explanation of the Sieve of Eratosthenes Algorithm in C

The Sieve of Eratosthenes is an algorithm used to find all prime numbers up to a given limit. Here is an explanation of each step of the algorithm:

1. Initialization: The algorithm begins by initializing a list of non-prime numbers called nonPrimes. The list starts with the number 1, as it is not a prime number. The algorithm also initializes an array called primes to store the prime numbers found.

2. Finding Primes: The algorithm enters a loop that continues until a break condition is met. Inside the loop, it uses the MissingNumbers.find() function to find prime numbers between 1 and a maximum value MAXN. The function takes a list of non-prime numbers as input and returns an array of prime numbers.

3. Selecting a Prime: The algorithm selects the last prime number found from the primes array using the lastPrimeIndex variable. This prime number is guaranteed to be prime.

4. Generating Non-Primes: The algorithm enters another loop that iterates over the remaining prime numbers in the primes array. It multiplies the selected prime number (p) with each subsequent prime number (q) and adds the result (pq) to the nonPrimes list. This generates a list of non-prime numbers.

5. Breaking the Loop: If the last prime number (q) is equal to the selected prime number (p), it means that no new prime numbers were found in the previous iteration. In this case, the algorithm breaks out of the loop.

6. Output: Finally, the algorithm outputs the number of prime numbers found (primes.length) and the maximum value used (MAXN).

The Sieve of Eratosthenes algorithm efficiently finds prime numbers by eliminating multiples of each prime number found. It is a simple and effective method for generating a list of prime numbers up to a given limit.