Senary

Senary (also known as seximal or base 6) is a positional number system structured around the number 6 and its powers. It has been independently adopted by a few cultures. Like a decimal, it is a semiprime, but it is unique as the product of two consecutive numbers, both of which are primes (2 and 3).

The website https://seximal.net advocates senary.

Usage
Six is considered one of the best bases for human usage. It is the smallest base that has seriously been proposed as an alternative to decimal. Many dozenalists list the base as second best, after dozenal.

Among the biggest proponents of Senary (or Seximal, the Misalian name for the base) is the YouTuber jan Misali.

Advantages
Base six is compact; it has just six digits; its multiplication table has only 21 unique products; each digit has a simple pattern and a small number of products to know. Even children would find learning base six math to be simple. The numerous intuitive divisibility principles allow one to know if any number is divisible by the ten smallest integers and more than two-thirds of the integers less than the square of six.

Six is positioned extremely conveniently, as the product of two smallest primes surrounded by the two next primes. This produces very easy divisibility tests and either terminating or brief peridoic fractional expansions for all four of the initial primes {2, 3, 5, 7}. The first "psuedoprime" expressed in senary (it does not pass any of the easy divisibility tests, but isn't actually prime) is 3216, which is the result of 15*156. This number is equivalent to 11*11=12110.

Disadvantages
The biggest disadvantage of base 6 is the fact that it lies on the lower end of the human scale (or is sometimes excluded from it altogether). This results in numbers getting long really quickly - for example, 36 is already three digits (1006), and 216 is four (10006). It also suffers from a low amount of digit diversity. Dozenalists also sometimes point out the lack of a second binary factor (4), which results in the loss of clean fourths and quicker descent into more digits in the radix point expansions of powers of two.