Here is a numeral system I came up with (probably independently invented by someone else before). It can only represent positive integers.
There are two symbols: unary digit (1) and separator (,).
The numbers are represented as the exponents of its prime factors in unary numeral system (base one; 0 = nothing, 1 = 1, 2 = 11, etc.), separated by commas. A number never ends with a comma, except for one (",").
Examples:
Decimal | Prime factors | Prime factors (alt.) | My system |
---|---|---|---|
1 | – | 2^{0} | , |
2 | 2 | 2^{1} | 1 |
3 | 3 | 2^{0}×3^{1} | ,1 |
4 | 2^{2} | 2^{2} | 11 |
5 | 5 | 2^{0}×3^{0}×5^{1} | ,,1 |
6 | 2×3 | 2^{1}×3^{1} | 1,1 |
7 | 7 | 2^{0}×3^{0}×5^{0}×7^{1} | ,,,1 |
8 | 2^{3} | 2^{3} | 111 |
9 | 3^{2} | 3^{2} | ,11 |
10 | 2×5 | 2^{1}×3^{0}×5^{1} | 1,,1 |
13 | 13 | 2^{0}×3^{0}×5^{0}×7^{0}×11^{0}×13^{1} | ,,,,,1 |
30 | 2×3×5 | 2^{1}×3^{1}×5^{1} | 1,1,1 |
64 | 2^{6} | 2^{6} | 111111 |
Pros:
Cons:
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