Crivo de Eratóstenes — contagem

The Sieve of Eratosthenes is a classical algorithm to identify all prime numbers up to a given number N. It works by iteratively removing multiples of each prime starting from 2. The calculator implements this method to count primes ≤ N, useful in number theory studies or programming. Its simplicity makes it ideal for educational purposes.

The algorithm doesn’t have a single formula but follows these steps: 1) Create a list from 2 to N. 2) Mark the first number (2) as prime. 3) Eliminate all its multiples. 4) Repeat with the next unmarked number. The final count is the number of remaining primes. This method is efficient for N up to ~10,000 due to computational limits.

Use this tool to solve math exercises, test prime distribution hypotheses, or optimize code requiring primality checks. For example, in cryptography or numerical algorithm design. It also helps visualize how primes become sparser in larger sequences.

Important notes: performance degrades for N > 100,000 due to high computational load. Results are exact only for integers N ≥ 2. Avoid excessively large inputs that may cause memory errors. For N ≥ 10^6, consider analytical methods like the prime-counting function π(x).