2013

An item in the Sydney Morning Herald's Column 8 mentioned the following interesting mathematical tidbit - 2013 is the start of a uncommon triplet of years which are all the products of three distinct primes - 2013 = 3 x 11 x 61,  2014 = 2 x 19 x 53, and 2015 = 5 x 13 x 31.

When did this last happen? In 1885 (5 x 13 x 29),  1886 (2 x 23 x 41), 1887 (3 x 17 x 37), and before that, only in the years 1309 (7 x 11 x 17), 1310 (2 x 5 x 131), 1311 (3 x 19 x 23). It won't happen again until 2665 (5 x 13 x 41), 2666 (2 x 31 x 43), 2667 (3 x 7 x 127).

After that, the next such triplets are 3729-3731 and 5133-5135, but then it happens 5 times in the 7th millenium (6061-6063, 6213-6215, 6477-6479, 6853-6855 and 6985-6987).

So if you want to stimulate a discussion about factors and/or prime numbers, 2013 is a great year.