2357

This number is a prime.

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The polynomial (-X^3 + 9*X^2 - 14*X + 18)/6 produces 2, 3, 5, 7 for x = 1, 2, 3, 4. [Gaydos]

The 7 in 2357 is the 666th 7 to appear in a positive integer. [Gaydos]

n! * n falls between a pair of prime twins for n = 2, 3, 5, and 7. Is this true for any other n? [Gaydos]