2011 Is One Sexy Prime

This story was published by Boston Globe on January 25, 2010 (online edition) and February 10 (paper edition). Link.


2011 is a sexy prime. And not only in a Playboy calendar.

Like prime ministers and prime ribs, prime numbers are the elite of their kind. They are unbreakable.

Unlike other numbers that can be split into smaller factors (e.g. 6=2 x 3), prime numbers can only be divided by 1 and themselves. Three is prime, so are 5, 7, and 11. The only even prime is 2.

A lot of special numbers around us are primes. Emergency phone numbers 911 and (in some European countries) 101 are primes. The fearful 13 is a prime.

The world of primes is very colorful, especially when you look at their relationship with their neighboring primes. Those that differ by 2, like 3 and 5, are called twin primes. Those that differ by 4 are cousin primes. Two subsequent primes that differ by 6 are called sexy primes — because ‘‘sex’’ is Latin for ‘‘six.’’

2011 and 2017 are two sexy primes. There are also lucky primes, happy primes, Cuban primes, Titanic primes, and many more.

Primes have always been the most talked about numbers; even Pythagoras believed that these unbreakable numbers have some spiritual properties. It was discovered that you can create any number by multiplying or adding the primes together. Check it out: Every even number larger than 6 can be represented as a product of primes and as a sum of two primes. For example: 8 = 2 x 2 x 2 = 5 + 3

But about 40 years ago, primes became celebrities. Math paparazzi all around the world are now hunting for primes. Awards are offered for those who discover hundred-million-digit prime numbers and every new prime spotting is noted and celebrated.
Why? Because any bank transaction, any online purchase, any medical or military data exchange requires data encryption.

Cryptographers found a great encryption mechanism using the observation that when a number is created as a product of two large primes, guessing or computing those primes from the total number is almost impossible. Those primes are used to encrypt the message and serve as a secret digital key known only to the encrypting and decrypting parties.

The more unbreakable you want your code to be, the larger the primes you should use for encryption. Thus, the search for the ultra-large prime numbers.

Want to help search? The good news is that there are infinitely many prime numbers. Euclid proved that. But the bad news is that higher you climb in digits, the more rare these prime numbers are.

The probability of any random number being prime is inversely proportional to the number of its digits (roughly). So, for a hundred-million-digit number, the probability of it being prime is 1/100,000,000, or 0.00000001.

Also, for such large numbers it takes about a month — even for a computer — to check whether any given number is a prime or not.

In addition to helping scramble secret messages, primes can be used to help hide the messages inside an image or audio signal.

As appropriate for celebrities, primes are surrounded by some mysticism. They are not regularly positioned among other numbers, nor are they randomly spread.

Take the recent and future prime years: 2003, 2011, 2017, 2027, 2029. Some are 10 years apart and some only 2. Like fortune tellers, number theory scientists are trying to detect and predict patterns in prime number appearances. Turns out that if you arrange all the numbers in a spiral instead of a number line, and then connect all the primes, you will find some surprising diagonal patterns.

Back to our special year. The upside-down reflection of 2011 on a digital calculator or clock is 5011, which is also a prime. Parents who gave birth on the second Tuesday in January could just remember a bunch of 1s for their child’s birth date: 1/11/11. You can still make it for 11/1/11 or 11/11/11 if you plan ahead. There is also 9/10/11 for grabs.

Since prime is so hip and relevant this year, I suggest we should start using it more outside the context of mathematics, prime ministers, and ribs.

This year’s Oscar ceremony hosts — James Franco and Anne Hathaway — are undoubtedly two sexy primes, while the Oscars (and Superbowl) winners could be referred to as lucky primes. And who would argue that Leonardo DiCaprio and Kate Winslet are Titanic primes?

Tom Brady, what can we say about him? With a #12 and the recent devastating Patriots’ loss to the Jets, he is ‘‘almost prime’’— that, believe it or not, also happens to be a math term.

With 11 (also a prime number) out of the 12 months ahead of us, there is still plenty of time to make this year a very happy and important prime.

Top cartoon by Peter Mesnik.

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