# Notation of numbers in numbers with high bases

Evening all, I'm looking at a problem that looks like there may be a pattern dependant upon the base of a number, and that a value I'm looking for within that pattern improves as the base (or more specifically, the number of unique prime factors of the base) increases. I'm familiar with Binary, Decimal, Hex, etc but I can't seem to find if there is a standardised way to notate values with very high base values - how would one write 1999 in base 1000 or 19999 in base 10000? Thanks in advance, Ben

• As you wrote them. they are digits. Anything less than the base is a digit. You can set any code representations of them. Commented Dec 14, 2019 at 19:04
• Ah, my bad. I have edited the question so that it actually makes sense, I hope. Commented Dec 14, 2019 at 19:05

There is no standard.

Say "If we let $$K$$ be the digit representing $$999_{10}$$ then $$1999_{10}$$ will be represent as $$1K_{1000}$$."

Or you could say "For the purpose of this problem I will refer to the digit represent a value $$K: 10 \le K \le b-1$$ as $$[K]$$"

or you could say "For the purpose of this problem I will refer to the digit represent a value $$K: 10 \le K \le b-1$$ as $$a_K$$"

Make up your solution and stick to it.

If it were may I'd so $${1a_{999}}_{1000} = 1\times 1000^1 + 999\times 1000^0 = 1999_{10}$$

Or $${a_{32}7a_{528}}_{1000} = 32\times 1000^2 + 7\times 1000 + 528$$ but

"$$[32][7][528]_{1000}$$ or $$A7B; A=32, B=528;$$"

All acceptable.