The Fourth Carnival of Mathematics is up!

My web server, fano.ics.uci.edu, will be down temporarily while we move from one building to another.

All pairs of consecutive 47-smooth numbers, calculated by my Python code for Lehmer's improvement to Størmer's theorem. That is, this file lists pairs x, x+1 such that all prime factors of both x and x+1 are at most 47. There are 1502 such pairs, the largest of which is formed by 1109496723125 = 5⁴ × 7 × 17 × 19² × 31² × 43 and 1109496723126 = 2 × 3 × 11² × 23 × 29² × 41² × 47.

It took nearly two days on a dual-core Pentium, so the next prime 53 may be in reach but would likely take more computer time than I'm willing to devote to it. Judging by A002072, faster codes are out there.

Looking through the latest Society of Illustrators Annual, I found the perfect illustration of a visibility graph on the cover of a New Yorker from two years ago, by Richard McGuire.



(I have no connection to this site, but since I stole their image instead of taking the trouble to scan it myself, I'll give them a link: prints available for sale here.)