December 31, 2016

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The Best Prime Numbers of 2016

Because prime numbers didn't let us down this year.

By Evelyn Lamb

Number Hill in Arco, Idaho. Can you see any primes?

Evelyn Lamb

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This article was published in Scientific American’s former blog network and reflects the views of the author, not necessarily those of Scientific American

I’m not saying 2016 was the worst year ever for politics or high-profile deaths, but the world does feel dark to me right now. But you know who didn’t let me down this year? Prime numbers. (If your last math class was a while ago, remember that a prime number is a whole number that’s larger than 1 and whose only factors are itself and 1. So 2 and 3 are prime, but 4 is not because it’s divisible by 2.) 

From new largest known examples in different categories of primes to the ever-faithful prime number tweetbot, prime numbers killed it this year. So instead of a math news roundup—you can find that on the American Mathematical Society’s Blog on Math Blogs—I bring you a list of the best primes of the year.

11. 221,453 This is the first prime number I retweeted this year from the @_primes_ tweetbot. Not too shabby. It has all the digits from 1-5, and it was a harbinger of more great primes to come.

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10. 274,207,281-1. This is still the largest known prime number, weighing in at over 22 million digits. Like many of the other largest known primes, it’s a Mersenne number, meaning it’s one less than a power of 2. I wrote an article for Slate about why so many of the largest known prime numbers are Mersennes. You can impress your friends by producing this number from memory if you write it in base 2: it’s just 74,207,281 copies of the digit 1.

9. 222,323 Now that’s pretty special! A prime that, when written in base 10, is made of just the digits 2 and 3, which are also the smallest prime numbers. High 2+3! 

8. 323,333 Second verse even better than the first. A double high 2+3 for this one!

7. 29 A nice, solid, workaday prime any year, but a leap year is an especially good time to appreciate it.

6 & 5 (tie): 2,996,863,034,895×21,290,000±1 These are the current world record largest known twin primes. (Twin primes are prime numbers that differ by just 2.) I wrote about the discovery for Science News for Students. Unlike the primes in general, which we know to be an infinite set, we still don’t know whether there are infinitely many twin primes. In theory, this could be the last pair of twins ever discovered. (That’s very, very unlikely. Mathematicians are quite confident that the twin primes are infinite, so I’d put my money on more being discovered.)

4. 314,159 A prime number that is almost exactly 100,000 times π? Be still, my heart!

3. 322,111 I eagerly anticipated this prime number for 50 minutes after seeing @_primes_ tweet 322,109. I was not disappointed. Even more exciting, the similar number 4,332,221,111 is also prime. We only have to wait 22,000 years (more or less, if my calculations are correct) for @_primes_ to get to that one.

2. 10,223×231172165+1 This number, discovered by Peter Szabolcs as part of the PrimeGrid distributed computing project in October, is the seventh largest known prime and the largest known prime that is not a Mersenne prime. It has 9,383,761 digits. Read more about it in this this press release by PrimeGrid (pdf).

1. 2017 Perhaps I am as foolish as Charlie Brown running at Lucy’s football, but 2017 is the prime number giving me the most hope right now. I’m holding out for more peace, less war, more happiness, and less oppression. Bring it, 2017.

Want more info on the biggest primes? Check out Chris Caldwell’s Prime Pages. Want more artisanally curated, gluten-free primes selected and hand-delivered to your timeline? Follow me on Twitter! Not into numbers but want to comfort yourself with tweeted mathematics? Check out the Symmetric Curve bot, another of my favorite sources of algorithmically-generated math. 

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