Bill Gosper wrote:

(People keep forgetting that Sin[π/5] is messier than Sin[π/10].)

Only people who paid (or are paid) for using Mathematica. Or didn't you mean that Mathematica command, but rather the value sin(π/5) ? Not that surprising, we all know that sin(π/3) is also messier than sin(π/6) ... Concerning 17, you can find through wikipedia.org/wiki/Trigonometric_constants_expressed_in_real_radicals that this is related to constructibility of the wikipedia.org/wiki/Heptadecagon . 17 is just the third (m=2) of the Fermat primes 2^2^m + 1, after 3 and 5. 257 and 65537 will tell you roughly the same thing as 17 (although more verbosely: Hermes spent 10 years to write it up in a 200 pages manuscript...). (Guess who proved that it can be done: Shares initial of last name with you! ;-)) For +1 they must be prime, but for 2^2^m - 1 you can use a²-1 = (a+1)(a-1) to go one further up to m=5 (i.e., n ~ 4.3e9). If you can do it (or show it can be done) for a larger odd n, people might be interested. (See also oeis.org/A045544.) - Maximilian