input: Write a function to find all prime numbers from 1 to 100 using the Sieve of Eratosthenes algorithm. The function should take an integer n as input and return a list of all prime numbers up to n. If the input n is less than 2, return an empty list.
  
  assert sieve_eratosthenes(100) == [2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47, 53, 59, 61, 67, 71, 73, 79, 83, 89, 97]
  assert sieve_eratosthenes(10) == [2, 3, 5, 7]
  assert sieve_eratosthenes(1) == []
output: 
  if n < 2:
      return []
  sieve = [True] * (n + 1)
  sieve[0] = sieve[1] = False
  for start in range(2, int(n**0.5) + 1):
      if sieve[start]:
          for multiple in range(start*start, n + 1, start):
              sieve[multiple] = False
  return [num for num, is_prime in enumerate(sieve) if is_prime]
  