#### Fun with birthdays, and primes

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, May 16th, 2013 at 04:07 PM (632 Views)
Today was a birthday swim morning at Riverbank for one of my lanemates. Two friends and I put on our festive flowery swim caps and did the following set to celebrate:

800 lcm warmup (400s, 200k, 200p, photo op)

43 x 50 @ whenever-lane-space-permitted intervals (usually 5-10 sec. rest, with a few chat/calculation breaks), with all FR except prime numbers = non-free

[I did BK for the non-free lengths, and sprinted the triangular numbers and kicked the cubes just for good measure.

200 warmdown

This set really brought out my high-school-math-team-geek tendencies. Since all my sprints but one ended up being free, I wondered if 3 were the only prime triangular number. It seemed like that had to be so, but it took me a few 50s to work out a proof. After the set was over we noticed that our ages were all now prime—I wondered if this had happened before (the answer is yes, it was in fact the fourth time during our lifetimes). It would be nice to think we’ll be around to celebrate the next occurrence, but that's a ways off—I would be competing in the 105-109 age group by then!