Klapaucius, uh um, I mean Ghideon,
You act as there is noting of value in this tread. Sure, breaking RSA would be quite a feat. But you must admit there is no other method that does it. There is no guarantee the Pappy Craylar Method works. And I have moved on to other projects. However, we had an active discussion that may lead to something that might find a different approach.
You see, The Pappy Craylar Method is based on the fact that if you increase the size of one factor you must decrease the other. And since there is only one way the Semi-Prime factors go together, the equation to find the factors eliminates possibilities. Sure, the number of possibilities isn’t only one and sometimes the possibilities are further or closer to zero. But until a solution exists, the method leads to the ability to guess the factors by trial and error.
See my construction of the 2 graphs that intersect at 5. Of course, I already new the answer, but don’t you find the PC method simple yet interesting?
In[89]:= pnp = 85
x = 5
Show[{Plot[(x^4/(pnp^2 + x)), {x, 0, 10}],
Plot[(pnp - (x*Sqrt[(pnp^3/(pnp* x^2 + x))])), {x, 0, 10}]}]
Out[89]= 85
Out[90]= 5
In[109]:=
Clear[pnp, x]
pnp = 8637
{Plot[(x^4/(pnp^2 + x)), {x, 0, 3}]
Plot[(pnp - (x*Sqrt[(pnp^3/(pnp* x^2 + x))])), {x, 0, 3}]}
Out[110]= 8637
Does this work for every Semi-Prime? Maybe, maybe not. This is all I have to share. I am moving on to other projects. So, unless some idea comes along, I will not post. Is my last message Simple, yet interesting?