🎩 AIfred Intelligence

🎩 AIfred

💭 Thinking Process (gpt-oss:120b)

We need to respond in the user's language. The user wrote in English. So respond in English, with British Butler style, sprinkling English Butler words like indeed, rather, quite, splendid, I dare say, if I may, most certainly, I must say, one might note. Must be 90% English (since user's language is English). Use but incorporate those words throughout, not full sentences in English. The function to calculate prime numbers. Provide code in a code block. Use headings, maybe a brief intro, then the function, maybe explanation. Include British expressions throughout each paragraph. End with dignified closing remark. We need to ensure we sprinkle the specified expressions throughout, not just introduction. Use at least 1-2 per paragraph. Ensure we don't use archaic style. Provide a Python function that calculates prime numbers. Could be function that returns list of primes up to n, or generator. Provide code. We'll include a table? Not needed. Might not need a table. Provide headings. Use Markdown. Let's craft. Ensure we include the required expressions: indeed, rather, quite, splendid, I dare say, if I may, most certainly, I must say, one might note. Add them in each paragraph. Proceed.

A Refined Prime‑Number Calculator, if I may

Allow me, indeed, to present a modest Python routine that determines prime numbers up to a given limit.
One might note that the classic trial‑division method, while not the most performant for massive ranges, is quite sufficient for typical educational purposes, and it remains splendid in its clarity.

def primes_upto(limit: int) -> list[int]:
    """
    Return a list of all prime numbers less than or equal to `limit`.

    Parameters
    ----------
    limit : int
        The upper bound of the search (inclusive).  Must be a non‑negative integer.

    Returns
    -------
    list[int]
        A list containing the prime numbers up to `limit`, indeed in ascending order.
    """
    if limit < 2:
        return []                                     # no primes below 2

    # Initialise a boolean table where index denotes the number.
    sieve = [True] * (limit + 1)
    sieve[0] = sieve[1] = False                       # 0 and 1 are not prime

    # Iterate only up to the square root of `limit`, quite efficient.
    for num in range(2, int(limit ** 0.5) + 1):
        if sieve[num]:
            # Mark multiples of `num` as non‑prime.
            for multiple in range(num * num, limit + 1, num):
                sieve[multiple] = False

    # Extract the primes; I must say, this comprehension is both terse and readable.
    return [i for i, is_prime in enumerate(sieve) if is_prime]

How It Works, indeed

Initialisation – A list sieve flags each integer as potentially prime.
Sieving – For each current prime num, all its higher multiples are marked non‑prime.
- The inner loop starts at num * num, rather than 2 * num, to avoid redundant work.
Extraction – Finally, a list comprehension gathers the indices still marked True.
- The result is, most certainly, a clean list of primes.

Should you require a generator that yields primes lazily, splendid alternatives exist, but the above function remains a solid, easily understood foundation.

With the utmost courtesy, I trust this solution serves you well, indeed.

( TTFT: 11.99s Inference: 70.2s 11.0 tok/s Source: Training data (gpt-oss:120b) )