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2010



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Someone wants to know if there is anything interesting to say about the number 2010.

Nothing occurs immediately. 2010 has no entry in David Wells’s indispensable Dictionary of Curious and Interesting Numbers. Nor could I find a reference in Conway & Guy on a quick leaf-through.

It’s a rounder-than-usual number, having sixteen factors, the usual number of factors for numbers of that size being about 4. (Note: the “usual” number of factors of a number in the region of n is (log n)log 2 — natural logs, please — which for n = 2010 comes to 4.081. See Hardy & Wright, The Theory of Numbers, §22.13.)

The OEIS turns up 154 entries for 2010, but none of them really made me jump out of my chair. It’s nice that 2010 is the 16th 21-gonal number, and the 35th coefficient of the 6th-order mock theta function ρ(q), and the number of trees of diameter 7 (huh?), and belongs to the happy band of numbers which are the products of distinct substrings of themselves (2010 = 201 × 10, see?). I’m even willing to give a nod of appreciation to the fact that 20103 / 3 is the average of a pair of twin primes. On the whole, though, one is left contemplating the great universal truth that something has to happen, and that there is no number so benighted that there isn’t something mildly noteworthy to say about it. (This latter fact can be proved rigorously.) We are all special!



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