Trash, Training, and Triplets of Primes

In 2012, my family put 22 trash cans at the curb, getting us to an average of fewer than one-trash-can-per-fortnight.  [Our cans are the 33-gallon variety, so they're relatively small compared to most garbage cans.]  I had hoped that this year, we could reduce that to one-trash-can-per-three-weeks.  Did we?  

YES!  The trash total for this year was 17 cans!  

Cool Math Fact: 17 is the smallest number

that's a sum of 3 primes four different ways:

17 = 2+2+13.

17 = 3+7+7.

17 = 3+3+11.

17 = 5+5+7.

I'm not sure I can bring this number down any further without breaking my "don't drive them crazy" rule.  A bunch of the trash is from the four other people who live in this home -- fast food containers, packaging from toys etc, --  and I haven't figured out a way to compensate for this by trash-less acquisitions of my own.  As for areas where I do have some influence, the family has been bemused and mostly willing participants in the no-paper-towels, food-in-canning-jar aspects of this life.  (My step-daughter tells me that whenever she's in a group where the conversation flags, she starts telling people about me.  It's useful for her that I'm so odd).   So for 2014, I'm hoping to maintain this number. 

*****

And triathalon training?  How's that going? 

It was a year and a half ago that I came to my husband and said, "I'm terrified of riding a bike, but I want to do an Iron Man-length triathalon," and he replied, "I can't swim, but I'll join you!"   We each started preparing in our own ways.  I bought a bike and found some friends to ride with.  He hired a coach to teach him to swim and got a gym membership.  

The training number of the year is 80:  80 is the number of miles I rode on my longest ride of the year, and 80 is the number of miles my husband swam in 2013.

Cool Math Fact: 80 is the smallest number  

that's a sum of 3 distinct primes seven different ways:

80 = 2+5+73

80= 2+7+71

80= 2+11+67

80= 2+17+61

80= 2+19+59

80= 2+31+47

80= 2+37+41

Now, we've both still got a ways to go.  In the triathalon, I'll actually have to bike 112 miles (and that's after the swim and before the marathon).  And my husband's longest daily swim so far was a bit under 2 miles in the local pool:  he'll need to get up to 2.4 miles in open water.  But considering that we both started at 0, I'm pretty confident we'll be able to rock this out*.

* Late breaking update:  today my husband swam the full 2.4 miles.  Go, guy, go!