Hello and welcome to December 2025's Carnival of Mathematics!
We've reached Carnival number $246 = 2 \times 3 \times 41$, and that's special for a variety of reasons, not least of which is that its digits are, in order, the first three terms in one of the first sequences most of us were introduced to; the chicken soup of all integer progressions that is the two times table.
$246$ is also the current best-known upper-bound for the minimum size of gap that exists between an infinite number of pairs of consecutive primes. It's palindromic in (e.g.) bases 5, 9, and 40; it is untouchable (which means that it is not expressible as the sum of the proper factors of any other number); and if you had a bit of string and seven of each of two colours of bead, you could make one of $246$ different necklaces (using every bead).
And in maths history, Indiana House Bill No. $246$ was an 1897 foray into proof by legislation: it proposed to square the circle using a method that, among other things, implied that $ \pi =3.2 $.
You've taken your seats and loaded up on popcorn, so let's get started on the Carnival's...
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