There was a bit of a Twitter storm earlier today. Someone decided it would be fun to extol the virtues of 2011 by proclaiming that the number 2011 was the sum of eleven consecutive primes: 157, 163, 167, 173, 179, 181, 191, 193, 197, 199 and 211. Oh, and there were further palpitations at the fact that 2011 is itself prime.
I was out on the street at the time. But the incredulity that this phenomenon was drawing from the Twitter crowd seemed in my head to be unwarranted. So when I got home, I did some analysis. Some lovely analysis.
First things first, the smallest number for which the above is true is 160—the sum of the first eleven primes. Not a prime itself though. The smallest prime that is the sum of eleven consecutive primes is 233.
Analysing all years from AD 1 to AD 3000 (to give us some room for giddiness in the years to come), 40.4% of them are the sum of two or more consecutive primes. (I ruled out those that are merely the sum of a single [consecutive] prime, as their names shouldn’t really be on the door.) That’s right: 1,213 are the sum of two or more consecutive primes.
Fifty-seven of them are sums of 30 or more consecutive primes, our stellar performer being 2914, the sum of 39 consecutive primes. If the number itself has to be prime (as 2011 is), then 2909 is the sum of 37 consecutive primes (all primes between five and 167 inclusive).
To more immediate times. The miraculous feat of 2011 will be surpassed in 2016 (18 consecutive primes), while Twitter will likely come crashing to its knees in 2027 as people retweet the fact that as well as the year itself being prime, it is the sum of a whopping 25 consecutive primes.
As for recent past, 1999 (prime) was the sum of nine. But wait for this: 1986 was the sum of 32, 1987 (prime) the sum of 19, and 1988 the sum of 33. Can you imagine if Twitter had been around then?