Canonical Prime Tree Details
Integer (N)
64
Prime Power Tower Set
Leaf Node Paths
Factorization Walkthrough
Base-3 Ternary Encoding
Base-B Digit Paths
The paths highlighted in the tree correspond to the encoding of the active number.
How it works: Each path rank segment in the canonical representation is converted into a leading digit and a run of zeros. In Base 3:
How it works: Each path rank segment in the canonical representation is converted into a leading digit and a run of zeros. In Base 3:
Digit = N Mod 2 (if 0, then 2)
Zeros = (N-1) / 2
Hover over any node in the tree to dynamically decode its path and see its evaluated prime tree value!
Recombination Playground
Input paths (either canonical ranks like
/1/1, /1/2 or digits like 11, 12) to recombine them back to an integer in real-time.
Resulting Integer N
-
Binary String Length & Complexity
In the binary case (Base 2), a canonical path
/R1/R2/.../Rk has a binary representation length of:
Length L = R1 + R2 + ... + Rk
The number of bits reflects the sum of the ranks, serving as a measure of "complexity" or "navigational effort" to reach that specific prime tower.
Level 3 Binary Tower Partitions (L = 3)
| Partition | Tower Form | Value | Binary Path |
|---|---|---|---|
| 1 + 1 + 1 | 2^2^2 |
16 | 111 |
| 2 + 1 | 3^2 |
9 | 101 |
| 1 + 2 | 2^3 |
8 | 110 |
| 3 | 5 |
5 | 100 |