You look radixing

I sure hope a math nerd sees this and helps me make sense of this stuff.

I do math in my head to get myself to sleep. One of my favorite methods has been converting numbers between different bases or radixes (radices?). I started wondering if there was a more purely mathematical way to represent numbers. Radix/ces seem arbitrary.
Since primes are the same regardless of base could they be a less arbitrary way to represent numbers? The math iself affords them special relevance. I thought about it for a couple weeks of bedtimes before breaking down and googling it. I found Mixed Radix Primary Notation.

Each place stands for a prime number and the digits stand in essence for powers of that number.
I think i have the hang of it as far as comverting to or from but it seems to be more radix-less or infinite-radix than mixed radix (radix is the number of symbols used to represent numbers – afaik there is no limit to the number of symbols one would eventually use in primary notation). Also, what is it for?

Just for fun, and in case anyone out there can check me, counting back:
twenty 102
Nineteen 10,000,000
Eighteen 21
Seventeen 1,000,000
Sixteen 4
Fifteen 110
Fourteen 1001
Thirteen 100,000
Twelve 12
Eleven 10,000
Ten 101
Nine 20
Eight 3
Seven 1000
Six 11
Five 100
Four 2
Three 10
Two 1
One (oops, no one bothered to make a one!)

So it probably is not for counting.It does make multiplication easy. eg fourteen times twenty looks like this: 1001×102=1103 It looks like addition without any carrying if i understand correctly.
1103 is two hundred eighty (seven times five times two cubed… i think)

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