Segmented sieve of Eratosthenes can be used to evaluate prime numbers less than n, where n is large enough in pretty less time and memory.
Time complexity: O(n.log(log(n)))
Space complexity: O(sqrt(n))
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Codeforces (c) Copyright 2010-2024 Михаил Мирзаянов
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Auto comment: topic has been updated by matcoder (previous revision, new revision, compare).
If you had posted this 1 day earlier, I could've solved problem C at the NCTU camp :(. (the problem involved looking for minimum prime gaps in a given range, where the left and right bounds can be very big, but their difference is small).
Be it late or not, at least I learned something :).
If n is 1e9, then T.C. would be O( 1e9 * log( log( 1e9) ) ) ?