@ Mariano: I hadn't thought of that. Assuming that I could obtain his email address, do you think academics would be interested in answering emails from amateurs such as myself?

@Scott: 37 will always be prime, but it may be that someone in the future will find a better way to calculate homotopy groups. I see it as being similar to L-functions, no-one can determine their roots, but people are excited about L-functions because if their roots could be found then all sorts of excellent things would follow. But I don't know what excellent things would follow from improvements to homotopy theory.