It occurs to me that Apery's sensational and then-mysterious discovery of a proof that zeta(3) is irrational could have been found by computer by the following method for seeking numbers that are provably irrational. 1. consider all continued fractions of the form p1/(q1+p2/(q2+p3/(q3+...))) where pn is a polynomial of n with small-integer coefficients and low degree and qn is another, and we ignore continued fractions which do not converge fast enough. [Also, one can allow the pn to be sequences which are modular-cased polynomials, such as "n^2 if n odd, 3 if n even."] All such numbers should be provably irrational. 2. compute these numerically, and for each number you get, look it up in the Plouffe catalog of important real numbers. 3. if any number arises that was not previously known to be irrational then you have a proof it is irrational.* *Except you have to prove the continued fraction really does represent that number. But even if you cannot prove that you will have found a very cool conjectured identity. So... maybe you should try this.  It ought to be dead easy for Plouffe to try. [Of course if the irrational has a rational ratio with a Plouffe-catalog number, that also suffices.] -- Warren D. Smith http://RangeVoting.org  <-- add your endorsement (by clicking "endorse" as 1st step)