She was pleased and impressed when I noted that both before and after our recent birthdays (many thanks for your cards and gifts), both our ages were semiprime: which is to say all four numbers have precisely 2 prime factors (but you knew that already).
Which leads to the obvious questions:
- What is the density of semiprimes?
- What is the density of consecutive semiprimes: in particular is it asymptotically >0?
There does not seem to be a clear answer to the second question, which it need not surprise us pre-occupied the ubiquitous Paul Erdös (did I mention I once beat him at chess?). A simple computer program suggests there are many consecutives, and indeed triples (clearly, 4 in a row is no-go). Heath-Brown has shown there is an infinite number of such pairs  but I am unsure of their density.
Anyway, if I live to be 141-142, the pair of us can enjoy this happy numerological event again.
- D. R. Heath-Brown, The divisor function at consecutive integers, Mathematika 31, 141–149, 1984.