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Maybe not as naive as I thought but still incomplete

A project log for Factoring using waveforms

Waveform sweep superposition to help factor large product of prime numbers.

macrofaradMacrofarad 02/22/2018 at 16:440 Comments

So, without mincing words, the approach I originally proposed is certainly incomplete, however I was unknowingly  stumbling into some interesting concepts.

Here's the core of what I found out through this: 

All factors of numbers are harmonic with the composites made of them.
When graphed in XY mode on an Oscilloscope, a number and its harmonics will not rotate, regardless of relative phase between them
Wave-wise, This rotation is also akin to the beats one would hear if two notes were out of tune

What I was working with was part of the baby steps needed to understand shor's algorithm.  The core concept that all numbers can be represented as frequencies, constructive and destructive interference, as well as other important things.

Something that I learned later:

Shor's algorithm operates based on periodicity.  For a given semi-prime, If we take the length of the periodic cycle of ((2^X)mod N), where x is the step number, we can learn about the P and Q that N is made of (assuming N is an integer not divisible by 2).  Specifically, (P-1)*(Q-1) = the length of the periodic cycle of ((2^X)mod N) * an integer.

To put it another way, if the length of that periodic cycle is known as W, we can say ((P-1)*(Q-1))mod w = 0.  Which is really pretty cool seeing as right there we now know that any given factor of N has to fit this pattern and has to be between 3 and N/3.  Factoring the number becomes more like tuning a guitar than doing hard math.

It doesn't sound like much, but by using some cool tricks with phase analysis on a quantum machine (assuming there's one capable of doing so), we can actually get results.  Without a quantum machine, you can (and I did) actually even use this information to factor things on paper.  Note: for doing it on paper, unless you hate your life, don't go above 4 digit semi-primes.  Even a 4 digit semi required the use of wolfram as my tiny calculator did not appreciate trying to modulus through a periodic sequence of 48.

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