2012

Today marks the start of a new year: 2012. I’d like to take this opportunity to say a few things about this number.

  • 2012 = 2 \cdot 2 \cdot 503
  • 2012, 2013, 2014, 2015 have the same number of primes in their prime factorizations (counting multiplicities). The smallest numbers n such that n, n+1, n+2, n+3 have the same number of primes in their prime factorizations are 602, 603, 1083, 2012, so this is actually fairly rare.

And some more really rare properties:

  • 2012 is not odd.
  • 2012 is not prime.
  • 2012 is not a square.
  • 2012 is not squarefree.
  • 2012 is not a perfect number.

I know I haven’t posted much recently. It’s a poor excuse, but I’ve been busy. I do have a number of things that I want to write about, however, and I’ll get to them eventually.

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