Bracket Primes

A number system of primes and angle brackets. <><<>><<><>>

Numbers as Primes

A cool fact about prime numbers is that you can represent any number entirely using multiples of prime numbers, this is called the fundamental theorem of arithmetic.

If you think about these things too much (like I do) you'll realize that it's a logical necessity for this to be true due to a couple simple facts:

You cannot infinitely divide a whole number (and have it remain such).
The definition of a prime number is that it's a number that can't be factored (split into smaller whole numbers)

If you split up a number enough times you'll just be left with just prime numbers that multiply to make the original.

Try splitting some numbers into primes:

2

Lets Make This a Number System

to start lets just make a way to write a prime number.

<n> = nth prime number

ex:

<1> = 2
<2> = 3
<3> = 5
<4> = 7
<10> = 29

Using the angle brackets we can show primes now, but we still need a way to multiply them for numbers in between.

<x><y> = prime x multiplied by prime y

ex:

<1><1> = 2 × 2 = 4
<1><2> = 2 × 3 = 6
<1><1><2> = 2 × 2 × 3 = 12
<2><4> = 3 × 7 = 21

As cool as this is we cant just use decimal (Base 10) for the inside of our brand new number system, we don't want to have a joint system, just a single cohesive one.

Since angle brackets are numbers, we can use them inside of other numbers definitions.

ex:

< <1> > = <2> = 3
< <1><1> > = <2 × 2> = <4> = 7
<< <3> >> = < <5> > = <11> = 31

At this point the numbers inside are basically irrelavent since we can simplify all of them down to just brackets and 1s.

<> = 2

ex:

< <> > = < 2 > = 3
<<< <> >>> = <<< 2 >>> = << 3 >> = < 5 > = 11
< <><<>> > = < <><2> > = <2 × 3> = <6> = 13

Finally with only those 2 symbols we can represent any whole number above 1, it's in no way a readable/usable system, but it works and is pretty interesting.

Try converting some numbers

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