Prime Cuts

Family dinners are sometimes full of eccentricity. I have a family which puns all the time; it drives non-members and honorary members crazy once in a while. Last night though, the announcement that my siblings and I would be observing a rare occasion – the fact that we'd all be having prime birthdays (i.e., birthdays celebrating a prime number of years lived) in the same year – met with silence as people either tried to work it out or failed.

I have a sister who is ten years younger and a brother who is four years younger. If I were x years old, you'd be looking for a set of positive integers {x, x-4, x-10} such that these three numbers were all prime. The interesting thing about this set, of course, is that it seems impossible to prove how many sets there are which will meet the requirement.

Fortunately (as some people would say, God being one of them), we are not immortal and hence there is a limited range of possible solutions in the real world. And the real world offers at least one other benefit; many of you already know approximately how old I am and are thus able to narrow the search down considerably.

This is an example of reducing complicated problems to simple ones, a useful (but not always applicable) skill. Sometimes, life favours us with problems that are obviously and/or immediately reducible; sometimes, it doesn't. All I know is that we're glad we're in the primes of our lives.