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Went with trial division first just to show I understood the basics, then mentioned a sieve as the cleaner option.
Start by clarifying requirements (e.g., input validation, return type) and then present a clean, efficient solution using a sieve-based approach for generating primes up to a limit, or trial division with optimizations. Explain the algorithm's time and space complexity and discuss potential improvements or edge cases.
Pro tip: Mention that for large n, a segmented sieve or incremental sieve can be more memory-efficient, and always test with small n (e.g., n=0,1,2) to catch off-by-one errors.
Ask about input constraints (e.g., n can be 0 or negative), expected return type (list or generator), and performance requirements. Confirm whether the function should handle large n efficiently.
Decide between trial division (simple but slower for large n) and sieve of Eratosthenes (faster but requires an upper bound). For unknown upper bound, use an incremental sieve or estimate the nth prime.
Write clean, readable code with meaningful variable names. For sieve, estimate an upper bound using the prime number theorem (n log n + n log log n for n >= 6) and generate primes up to that bound, then slice the first n.
Discuss time and space complexity (e.g., O(n log log n) for sieve, O(n sqrt(n)) for trial division). Handle edge cases: n <= 0 returns empty list, n=1 returns [2], etc.
Walk through test cases (small n, large n) and mention potential optimizations like using a bit array, skipping even numbers, or using a generator for memory efficiency.
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