A new type of equation to meet several equation descriptions. Can you solve this using known techniques?

[Trurl]

y = (((pnp^2/ x ) + x^2) / pnp)

 

pnp = x * y

 

(((((pnp^2 / x) + x^2)) / x) / pnp) where y = 0

 

 

If all of these are true in the factors we wish to find, x and y, is there a limit; a range; that could be computed that said if x is this big then y is that big? It wouldn’t be a differential equation that solves a spring. But how do I find and x that is true by testing if y is also true in these 4 constraints?

 

It is a simple idea, but what is the math that completes it? I know that where y on the graph equals zero x has the value approximate to the smaller factor. I have an equation that will tell me y factor knowing x. If you move x larger y gets smaller. Move x smaller y gets larger. There is only a certain range that will prove this true. Combine that with all the other constraints you have and equation that solves a polynomial.

[Trurl]

Clear[x, y, g, pnp]

pnp = 2211282552952966643528108525502623092761208950247001539441374831\
912882294140\
   2001986512729726569746599085900330031400051170742204560859276357953\
757185954\
   2988389587092292384910067030341246205457845664136645406842143612930\
176940208\
   46391065875914794251435144458199;

x = 1.13056560621865239372901234269585839625544`15.653559774527023*^100

y = (((pnp^2/x) + x^2)/pnp)

g = x*y

N[y]



Out[75]= 1.130565606218652*10^100

Out[76]= 1.955908211597676*10^159

Out[77]= 2.211282552952967*10^259

Out[78]= 1.95591*10^159

 

 

This is my estimate of RSA-206. Not yet factored. Crunch away!

 

Trying to quit number crushing. Just wanted to see if this is significant.

 

 

 

[Trurl]

On 12/20/2024 at 7:19 PM, Trurl said:

Out[75]= 1.130565606218652*10^100

Out[76]= 1.955908211597676*10^159

Out[77]= 2.211282552952967*10^259

Out[78]= 1.95591*10^159

So Out [77] is the semiPrime. The RSA-260 number not factored.

Out [76] is the larger Prime factor.

Out [75] is the smaller Prime factor. It was found by finding what the x-value of the graph is while the y-value of the graph equals zero.

So we know that this x-value of the graph can be no larger than where the y-value equals zero. And we plug that x-value into the equation y = (((pnp^2/x) + x^2)/pnp) to find that y in the equation is smaller than the x value in the equation. So we switch x and y of the equation. To find Out [75].

So we know that the SemiPrime factor x is no less than Out [75]. And the larger we test for x of the equation, y of the equation must be smaller then Out [76].

So now we crunch numbers by division, increasing in incrementation and test those numbers from Out [75] until we find the smaller Prime factor, x.