It has been a slow crawl to the end of 2016, with many losses and disappointments for me along the way.  It always make me feel better to think numerically about a situation and let my mind wander into the lovely forest of numbers.  The year 2016 was not only even (ends in 6 which is even), it was also divisible by 4 (last two digits divisible by 4, therefore entire number is divisible by 4) which meant it was a leap year.  Most interestingly 2016 is a triangle number.  [You can read last year’s blog post about triangle numbers here.]  2016 seemed to have so much going for it!  And then there were all of the celebrity deaths, issues with math test items, local tragedies, and the presidential election.  Bye bye 2016.

Hello 2017.  You are an odd, which makes me wonder if you are prime.  Every prime number is odd except for 2, the first prime number.  Prime numbers by definition have exactly two factors, 1 and itself.  This rules out 1 as a prime number (it only has 1 factor) and makes 2 the first prime number.  I was thinking about this as I was walking my dogs the other day and I mentally started dividing 2017 by numbers to see if I could find any factors other than 1 and 2017.  This really took my mind off Carrie Fisher’s death for about 20 minutes.  By the time I got back home, I was pretty convinced that 2017 was prime and so I looked it up on line.  2017 is prime!  2011 was the most recent prime year before 2017 and 2027 will be the next prime year after 2017.  This made me remember a theorem which suggests that if n is a prime number, then the distance to the next prime number is, on average, approximately ln(n), the natural log of n.

Ln(2011), ln (2017), and ln(2027) are all approximately 7.6.  Since prime numbers are all positive integers and would thus have a whole number distance to the next prime number, we could consider 8 to be a better approximation than 7.6.  So, on average the next closest prime number should be about that far away.  2017-2011 = 6 and 2027-2017=10.  The average of six and ten is 8.  Voilà!  You can try the exercise yourself with three prime numbers of your choosing.  It is easy to find prime number charts on line.

And with that I must go pick up my 14-year old from a party.  How else do you think I could stay up this late on New Year’s Eve?