twin composite numbers

this comes from my friend Marty:

Three reminders:

(1) x^3 - 1 = (x - 1)(x^2 + x + 1)

(2) x^3 + 1 = (x + 1)(x^2 - x + 1)

(3) A number, other than one, which is not prime is called 'composite.'
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Interesting fact:

There exist infinitely many positive integers, n, such that
6n - 1 and 6n + 1 are composite.
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Interesting proof:

For any positive integer, k, let n = 6^(3k-1).

Then 6n = 6^(3k) = (6^k)^3.

Then 6n - 1 = (6^k)^3 - 1, and

6n + 1 = (6^k)^3 + 1, both of which can be factored

using equations (1) and (2) above.