prime numbers — Python Fundamentals

Problem

The goal is to develop a Python program that identifies all prime numbers up to a specified limit $n$ . A prime number is a natural number greater than 1 that has no positive divisors other than 1 and itself.

Finding primes efficiently often involves the Sieve of Eratosthenes, an ancient algorithm that systematically “marks” multiples of each prime starting from 2.

Input

The program reads from standard input (stdin):

Limit ( $n$ ): A single positive integer representing the upper bound (inclusive).
- Constraint: $n \geq 2$ .

Output

The program writes to standard output (stdout):

Prime List: All prime numbers $p$ such that $2 \leq p \leq n$ , separated by spaces. No trailing space should exist after the last number.

Example with Input and Output

Input

Output

import sysdef generate_primes(n): """ TODO: Implement the Sieve of Eratosthenes logic. 1. Create a list of booleans of size n + 1. 2. Initialize all elements (except 0 and 1) to True. 3. Loop from 2 up to the square root of n (i * i <= n). 4. If a number is prime, mark all its multiples starting from i*i as False. 5. Collect and return the indices that remain True. """ primes = [] # --- YOUR CODE STARTS HERE --- # --- YOUR CODE ENDS HERE --- return primesdef main(): # Read input from stdin input_data = input() if not input_data: return try: n = int(input_data[0]) except ValueError: return if n < 2: return result = generate_primes(n) # Print output to stdout with space separation print(*(result))if __name__ == "__main__": main()

Problem

The goal is to develop a Python program that identifies all prime numbers up to a specified limit

n

. A prime number is a natural number greater than 1 that has no positive divisors other than 1 and itself.

Finding primes efficiently often involves the Sieve of Eratosthenes, an ancient algorithm that systematically “marks” multiples of each prime starting from 2.