I like this one: Let y Y =y T(y) = + - 1 a and a a a (1+Y ) a -(a+Y ) (1+Y ) a k k k Y =----------------- = --------- - 1 k+1 a a (a+Y ) (a+Y ) k k then ___oo 1/a | | (1+T(Y )) = (1+y) | |k=1 k Convergence is quadratic. The ansatz (T(y)="terms 1..(n-1) of Taylor series") also works for 1/\sqrt[a]{1+y} and gives products with n-th order of convergence. -- p=2^q-1 prime <== q>2, cosh(2^(q-2)*log(2+sqrt(3)))%p=0 Life is hard and then you die.