Ok here is a new hypothesis. Not related to Prime numbers, but cryptography itself. I know it is a long shot. But it is just a thinking exercise.

I must thank my good friend Wyatt for explaining sesquation and quotation to me. Even though I am still trying to learn how to spell them. Yes I didn't make up sesquation or quotation. They are actually a thing in math. I have never encountered them before. So if anyone knows any links describing them please let me know.

I know my hypothesis is off the wall, but I am quite serious. I reiterate that I did not make up sesquation and quotation. This is the first I heard of them. I am only pointing out these simple methods have uses in cryptography and also multivariable equations. Yes I know it sounds like nonsense, but a one-way-function is not just solving an impossible pattern. Instead it can be approached as solving for more than one unknown variable.

Sesquation:

2+3 = 5

2*3 = 6

5+6 = 11

11/2 = 5.5

Quotation:

2+3

4+6 = 10

4*6 = 24

10+24=34

34/4 = 8.5

Patterns? Simple enough but does it describe slope, derivation, cryptography, or Trurl's Method?

Taking the values from the last tabulation of Quotation above:

34-8.5 = 25.5

25-10 = 15.5

______

10+18.5 = 18.5

34-18.5 = 15.5

The Hypothesis is that the methods of sesquation and quotation can solve equations of multiple unknowns, if we know the end values of these methods. It could also be used to solve polynomial equations if we treat the variable in the polynomial equation as separate variables as the variable of the equation is raised to different power.

For example for the polynomial method of the equation: (((pnp^2/ x ) + x^2) / pnp) = 1; replace x^2 with an unknown variable (say z) and plug it into quotation. Yes you have to know multiple answers of the quotation, but in cryptography the user is given many wrong tries compared to one right answer. There are many incorrect answers to work with. The goal is to see how the cypher effects the variables. This means if the user can find a pattern where the values produced randomness, then maybe the message could be solved. Yes I now that these patterns are hidden by cryptographic hash, but I am referring to pattern of the open source equation of the public key cryptography.

1 hour ago, Trurl said:

The Hypothesis is that the methods of sesquation and quotation can solve equations of multiple unknowns, if we know the end values of these methods. It could also be used to solve polynomial equations if we treat the variable in the polynomial equation as separate variables as the variable of the equation is raised to different power.

Well I have heard of 'sesqui...' in mathematics

Sesqui comes form the Latin 'sesqui ' meaning one and a half.

For instance you have sesquilinear forms and antilinear maps.

For two variables on a complex linear space, one can be linear and the other antilinear or sesquilinear.

These devices appear in quantum mechanics amongst other places.

The sesqui prefix is also used in Chemistry to descibe a mixture containing two kinds of radicals in the proportions 2 : 3

But I have never heard of quotation spaces.

Perhaps you mean quotient spaces in higher algebra ?

Edited 11 hours ago11 hr by studiot