In this month’s episode of Wrong, But Useful, Colin and Dave are joined by @niveknosdunk, who is Professor Kevin Knudson in real life.

• Kevin, along with previous Special Guest Co-Host @evelynjlamb, has recently launched a podcast, My Favorite Theorem
• The number of the podcast is 12; Kevin introduces us to sublime numbers, highly composite numbers, and several other fascinating dozen-related facts.
• We rant about the whole 6÷2(1+2) thing hashtag fakemaths, and try to rescue it with a thread on the obelus. @divbyzero also has a post about the whole thing.
• “Obvious” things.
• Broken patterns:
  • Fermat primes, primes of the form $2^{2^n}+1$; up to $n=4$, all Fermat numbers are prime; no others are known.
  • $n^2 + n + 41$.
  • Digital sums
  • Borwein integrals
• Errors in nursery maths; posters and rainbows
• Caterpillars Choose an integer. If it’s even, halve it; if it’s odd, add one. What’s the longest chain? (Colin is wrong, but he’s not far off.)
• Colin enjoyed Talking Maths In Public
• @aap03102, who is Chris Smith in real life, has an excellent newsletter. Recent fact: quadratics $ax^2 + bx + c$ with odd $a,b,c$ can never factorise. Also, he’s been running Maths Wi’ Nae Borders and some politicians are outraged.
• Two different infinities turn out to be the same
• Plimpton 322 and @evelynjlamb’s take on it
• Shout out to @mikeandallie (Mike Lawler) for exploring the factors-of-a-million puzzle and the $\ln(2)$ fact from episode 47.
• Puzzle feedback: we missed @chrishazell72’s “elegant” spreadsheet solution to the passcode problem (0.9167…). He also wins a gold star for getting 72 as the answer to how many photo arrangements there are when the two brothers refuse to stand next to each other. Gold stars too for @jussumchick (Jo Sibley), @t23ty (Drew Barker), @schwartstack (Jon Schwartz) .
• This month’s puzzle: A number has exactly three prime factors, and can be written as $129 \times 141 \times 147 + 320$. What is the sum of the three prime factors?