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# 1. Initialize a compact bytearray where 1 byte represents
   8 numbers sieve = bytearray([0xFF]) * ((limit // 8) + 1)
   sieve[0] &= ~3 # Clear bits for 0 and 1 (not prime)

   # 2. Iterate up to the square root of the limit
   for i in range(2, int(limit**0.5) + 1):
          if sieve[i // 8] & (1 << (i % 8)): # Check if 'i' is prime # 3.
                      Fast bit-clearing for all multiples of 'i' for j in range(i * i, limit + 1, i):
                      sieve[j // 8] &= ~(1 << (j % 8)) # 4. Extract and return the actual
          prime numbers return [p for p in range(limit + 1) if sieve[p // 8] &
          (1 << (p % 8))]
    # Example usage: Find all primes up to 1,000,000
     in a flash print(len(hardcore_sieve(1000000)))

# 1. Initialize a compact bytearray where 1 byte represents
   8 numbers sieve = bytearray([0xFF]) * ((limit // 8) + 1)
   sieve[0] &= ~3 # Clear bits for 0 and 1 (not prime)

   # 2. Iterate up to the square root of the limit
   for i in range(2, int(limit**0.5) + 1):
          if sieve[i // 8] & (1 << (i % 8)): # Check if 'i' is prime # 3.
                      Fast bit-clearing for all multiples of 'i' for j in range(i * i, limit + 1, i):
                      sieve[j // 8] &= ~(1 << (j % 8)) # 4. Extract and return the actual
          prime numbers return [p for p in range(limit + 1) if sieve[p // 8] &
          (1 << (p % 8))]
    # Example usage: Find all primes up to 1,000,000
     in a flash print(len(hardcore_sieve(1000000)))