User blog:WaxPlanck/Turing Machines and Prime Numbers

This is a program that factors prime numbers using Turing machines. This may seem like a silly project because it took me ~6 seconds to factor 21 (3*7) and it printed the number in unary. This project is studying the amount of time that it takes to factor each semiprime that is:

1. Greater than or equal to 21

2. The larger factor is less than 1.6 times the square root.

3. The semiprime is at least 3 integers away from the last prime being tested.

Why is this useful?
Because we are not testing the ability to factor, we are testing the number of steps required to factor and dividing it by the number. This function, so far, has not grown that fast. But, because of the way that busy beavers behave, I believe there is a possibility that it is an uncomputable one.

Steps
21: 2952

25: 4986

35: 9164

49: 22816

63:

Steps divided by Number (rounded down to the nearest integer)
21: 140

25: 199

35: 261

49: 465

63:

Function
By following the above rules, we could create a function with the rules above that is defined with any integer greater than 0. It is defined as the number of steps on the above machine on a number that fits the rules described above divided by the number that is being tested rounded down to the nearest integer, so P(1) = 140, P(2) = 199, P(3) = 261, etc. What I find fascinating that supports my case is, so far, the numbers logs have grown non-linerarly. log10(P(1)) ~ 2.15, log10(P(2)) ~ 2.30, log10(P(3)) ~ 2.42, and then log10(P(4)) ~ 2.67.

Note: the project was found at http://morphett.info/turing/turing.html?8cb3169e282f92da6d7c by LittlePeng9. I may "break" the rule