I'm not going to explain now all the reasons why the decimal system is wrong.
You do not have to explain, just post a link (or more) is enough
in base 60 and 64
base 64 is a power of 2, and 2 is a fundamental base as it is the first integer base that allows for shorter representation of natural numbers. However 64 is 2^6 and 6 is not so fundamental. hexadecimal bas 16 is much more elementary as it is 2^2^2 = 2^4 = 16, 256 is the next in this line 256 = 2^2^2^2 and 65536 is 2^2^2^2^2 .
The only special thing of 60 is that it has many (12) dividers (1,2,3,4,5,6,10,12,15,20,30,60) That makes it easy to divide numbers and stay in the integer domain.
And yes that makes some things easy (like splitting an hour)
Base 60 or base 10 or base 12 or ... whatever is just a (human) representation of the number. Numbers and their properties do not change by presenting it in another base. A number which is prime in base 10 will also be prime in base 2,3,4,5,6 until a zillion and more. numbers that are each other dividers are that in any base.
I am not familiar with any basic numeric property that changes (pos/neg) due to different base except for the letter=digit puzzles like:
OK what does wikipedia say :
look at how in the Babylonian mathematics base 60 was represented: looks quite decimal to me ...
the number pops up several times in some corners of the math universe but so does PI ...
so still not convinced that base 60 is better than base 10 There are 10 types of people in the world: Those who understand binary, and those who don't...