Goodbye to 2017, a Prime, Sexy, Odious Year

The year 2017 has had its ups and downs. Mathematically, however, one thing is certain: The entire year has been prime time.

For a math geek like me, the properties of numbers are a source of excitement and fun. In that spirit, it’s a joy to point out that 2,017 is a prime number — that is, an integer only divisible by 1 and by itself. 1

And it’s not just any prime. It’s half of what mathematicians call a “sexy prime pair.” Before you get any abnormal impressions of mathematicians, I should clarify: Here, “sexy” comes from “sexa,” the Latin root for “six.” The term means that 2,017 is separated from another prime, in this case 2,011, by exactly 6. 2

That’s not all. If we multiply 2,017 by pi — the ancient constant that equals the circumference of a circle divided by its diameter — and then round to the nearest integer, we get another prime number: 6,337. We also get a prime if we start with 2,017 and tack on every decimal digit at the end to get 20,170,123,456,789.

It’s possible to cut a pizza into 2,017 slices using only 63 straight cuts across the whole pie. And if we convert 2,017 to its binary equivalent made up only of zeros and ones — 11111100001 — it becomes what mathematicians call odious. 3

So what should we expect from 2018? Next year isn't a prime number, but it’s about as close as you can get: 2,018 only has two factors — it’s 2 times 1,009. That makes it semiprime, not to be confused with subprime (a type of loan). And 2,018 is also a prime-part-partition number, but that’s a story for next December.

In the meantime, I hope you enjoyed your prime time while you had it. The next prime year after 2017 is 2027, a decade away. Hmm, now add 2 + 0 + 1 + 7 to 2,017 and see what you get.

Happy New Year x 10!

1. I’m not the only one who thinks this way – check out this post by TJ Wei from earlier this year, and this one from the Mathematical Association of America, which for some reason was posted in 2014.

2. And indeed, 2,011 = 2,017 + (2 - 0 - 1 - 7).

3. That’s not mathematical social commentary – it just means that the binary expansion has an odd number of ones.

To contact the author of this story:
Scott Duke Kominers at kominers@fas.harvard.edu

To contact the editor responsible for this story:
Jonathan Landman at jlandman4@bloomberg.net