Isn’t it logical that if there are infinite base systems (base-2 binary, base 16 hexadecimal, etc.) then there ought to be infinite prime numbers?
Our base-10 numbers are just a coincidence that the Indians invented and was adopted worldwide. The Sumerians were doing base-12, but the Indians had the convenient zero.
Most ancient cultures used base-10 in one way or another. Many used different symbols for ones, tens, hundreds, etc. like Roman numerals, but the grouping of powers of ten was there. The Sumerians used base 60, with each place value of 60s, split as tens and ones.
Wikipedia, Babylonian numerals
Wikipedia, Egyptian numerals
Classic Greek numbers
There are infinite prime numbers (that is easy to prove).
What is harder to prove is whether there are infinite pairs of primes (say 11&13, 17&19, etc.) two apart. Of course they’d have to end in {1,3}, {7,9}, or {9,1).