An Ode to the Number 2015

December 31, 2014

We have to live with the number 2015 for the next twelve months. And anything that happens next year will be forever linked with those digits. We’ll talk about the 2015 World Series, the 2015 UN Summit, the 2015 heat wave. Decades from now someone will say, “Remember when they found that giant zucchini growing on the side of the Hubble telescope? What year was that?” You’ll look wistfully into the distance and say, “2015.”

Happy New Year
Happy New Year! “New Year” is licensed by Sally Mahoney under CC by 2.0.

Let’s take a closer look at the number 2015 to see what we’re getting into. 2015 is the product of three prime factors: 5, 13, and 31. According to the Erdos-Kac Theorem, a typical four-digit number only has 2 prime factors, making 2015 slightly above average.

You might have heard of perfect numbers: numbers whose divisors add up to the number itself.  The sum of 2015’s divisors falls woefully short at 673, earning the label “Deficient.” (The next perfect year isn’t until 8128.) But things get more exciting when we look at 2015 in binary. Written in base 2, 2015 is a palindrome: 11111011111. We haven’t had a binary palindromic year since 1967 (11110101111), and the next one isn’t until 2047. There’s also a nice pattern when 2015 is written in base 4: 133133. And written in base 8, it’s 3737.

But the most exciting numerical event of the New Year? Mark your calendars for March 14, “Pi Day.” This year, the date will match even more digits of pi than usual: 3/14/15.

So here’s to a year of numerical exploration and problem-solving! What other properties of 2015 can you uncover? Let us know on Facebook, TwitterPinterest, or Google+.

Post by Maisie Wiltshire-Gordon, Educational Media Writer

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