If you start to look for other primes that are also average primes, you may stumble into some fascinating conjectures related to various forms of the Goldbach conjecture.
Pat Ballew also blogs about fascinating properties of 2011:
Well, it's the first prime day (the 2nd day of the year 2011) of a prime year that is the sum of a prime number of consecutive primes. In fact, it can be written as the sum of a prime number of consecutive prime numbers in at least two ways. The easy one is 2011 = 661+673+677, the other one that I know takes eleven consecutive primes...find it..I have been told there is not a year that can be expressed as a sum of successive primes in more than two ways for over a thousand more years That, my mathematical readers, is a lot of primes.
2003 was the last prime year, and it had the special property that the sum of its digits was also prime... not true for 2011.
Both 2017 and 2027 will be prime, but only 2027 is expressible as the sum of consecutive primes, but not a prime number of them.2081 is the next year that will be, like 2011, a prime that is the sum of a prime number of consecutive primes. If you forget, I'll remind you on Jan 2nd of that year... guess I better start working on a healthier diet... let's see, that will make me .... WOW, that IS a big number....
So what is the next year that can be expressed as a sum of consecutive primes starting with two... 2 + 3 + 5 + 7 ...... ????