Today I worked on some interesting applied exercises in the review of conics, as well as finishing a problem set in Analysis with an Introduction to Proof. I also spent some time thinking about a challenge problem that I found copied into one of my notebooks:
Problem of the Week #793 by Stan Wagon
A superprime is an integer (such s 7331) such that all of its left-to-right initial segments are prime. (For 7331, the segments are 7, 73, 733, and 7331, all prime.) There is largest superprime. Find it.1
I had done some work on the problem during one of my abortive stabs at doing math again. My approach was to try to prove that there is a largest superprime as a step toward constructing it. The work I did to that end is interesting, but I don’t know yet whether I can get beyond the place I got stuck before. Possibly finding the largest superprime empirically, then proving that it must be the largest would be more fruitful.
- To do. ↩︎
Go, Olly, go!
I love these! After you finished here, the Earlham Math Department had pencils made with such a prime printed on it, and we give them to graduating math majors. That way you start out with a prime, and however much you grind it down to sharpen it, you still have a prime. Send me an address, and I’ll send you come pencils.
You sent me some several years ago, actually, with the “congrats, math grad” tag. I keep them on my treasure shelf. It occurs to me now that the superprime printed there might actually be the largest.