Recently, I have made a series of blog posts about Redheffer matrices and the Mertens conjecture. After each of the posts, readers and colleagues offered suggestions to speed up the calculations. Here is a summary of what I have learned.... 続きを読む >>

Shortly after I published the second post about the Mertens conjecture, a reader's comment suggested a new approach to computing Redheffer determinants and the Mertens function. It is now possible to compute a half-million values of the Mertens function in about five hours.... 続きを読む >>

Shortly after I posted Redheffer, Mertens and One-Million Dollars a few days ago, Mathworks' Pat Quillen made an important observation about computing the Mertens function.... 続きを読む >>

I didn't know anything about these topics until a couple of weeks ago. Now I can't stop thinking about them.... 続きを読む >>

Today's post was inspired by a YouTube video, Why do prime numbers make these spirals?, on the channel 3Blue1Brown, created by Grant Sanderson. In my opinion this is the best math channel on YouTube. He has beautiful graphics and superb exposition. I recommend you take a look, if you haven't already.... 続きを読む >>