Holy shit, it's 2018 2019 2020 2021 2022 2023 2024, and the US isn't a fascist country! What a time to be alive.
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Oh, and I probably should have clarified in my post of the problem that "composite" implies we're doing this over the natural numbers.
In other words, prove that there are strings of numbers as long as you like that haven't a single prime in them.