Is 2013 prime? Obviously not, but can we make it prime by a trick?

A year ago I wrote a blog post claiming that 2012 is prime. The trick was that 2012 is prime when viewed as a number in base 3, base 5, base 13, etc.

I decided to revisit my base trick this year. Is 2013 prime in any base? No. In base n, 2013 represents 2n^3 + n + 3, and this number is composite for every positive n because it can be factored into (n + 1)(2n^2 - 2n + 3).
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