My Integer Factorization Study: Woof?


The latest revelations, which came almost unbidden despite my expressed desire to take a break from this study, turned out to be exciting ones, and I am trying to remain calm.

I have found relationships between the value of r (which is the difference between the square of s (the integer ceiling of the square root of m) amd m, and the value of c1 (which is the difference between s and p, with p being the smaller of the two prime factors of m). I am looking at the small odd positive integers starting at 3, and charting out how they behave. There are factorization exceptions – short cuts – when either r=0 or r is a positive perfect square.

I have also seen that some of the trees hindering me from seeing the forest become more manageable if, instead of the r and s above, I look at a similar family of polynomials suggested by s2, the integer floor of the square root of m, and the difference m-s22.

It is all very exciting, but there are still strange kinks in the relationship between these quantities and n (or n2), the index, so to speak, of the polynomial in one family or the other that will factor.

Maybe this won’t have any more promise than the other trees up which I have barked, to belabor that tired metaphor of mine. But maybe it will. Stay tuned.

One response to “My Integer Factorization Study: Woof?”

  1. JCSBimp – Christian Zen Discordian. I act. I sing. I go on and on about stuff. I do math. I go on and on about stuff. Federal Civilian Retiree, Tenor Section Leader, Happy Father and Grandfather. In love with my wife Wendy.

    I truly, honestly feel I am on to something now, if only I can tease it out of the equations I am examining. The patterns feel like they are within my reach to master. This may be irrational hope, but it is what wakes me up early and brings me to more and more interesting discoveries so far. I hope it will take me all the way to Eureka.

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