Properties of 2011

The number “2011” abounds with fun numerical and “visual-numerical” properties. Early into the new year, we experienced the time “1:11:11 on 1/1/11″. And this week, we had the even more auspicious “1:11:11 on 1/11/11″, at least with the date-writing convention we use in the United States. This week all the dates have been palindromes using the two-digit year convention, e.g., today is “1 14 11″, and if one uses the full four-digit year, this past Monday was “1 10 2011″, also a palindrome.

While text-based properties are fun, they are somewhat arbitrary and less interesting than mathematical properties of numbers. First, 2011 is a prime number, the first prime year since 2003. And from @mathematicsprof on twitter, we have this interesting coincidence:

“2011 is also the sum of 11 CONSECUTIVE prime numbers:
2011=157+163+167+173+179+181+191+193+197+199+211″
.

In other words, this is not just a series of prime numbers, but all the prime numbers between 157 and 211. I like that the last prime in the series happens to be 211!

The Republic of Math blog follows the consecutive-prime inquiry further, with the observation that 2011 can also be written as the sum of three consecutive primes “661 673 and 677″.

From The Power of Proofs, we have the property that 2011 is the sum of three squares:

2011 = 392 + 172 + 72

However, any number not congruent to 7 modulo 8 will have such a property. I.e., if you divide 2011 by 8, you have 3 left over. So really 7 out of 8 integers can be expressed this way. Finding the series of squares can take some time, though.

Please feel free to share any other mathematical or fun coincidental properties in the comments below.

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