# Rambling Thoughts

## 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.