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...
