Category: My Math Studies

My Mathematical/Number Study: What Got Me Up Early This Morning
Advertisements Consider the positive integer m which is the product of distinct primes p and q. Consider s, the smallest integer greater than the square root of m, and the difference r = s^2 – m. p will be less than s, and q will be greater than s. Thus p = s – c1…

My Number Study: Possible Breakthrough?
Advertisements This is a continuation of progress reports on a number study of the integer factorization problem I have been conducting this Spring. Last night, in working through my calculations to see which quantities involved I could express in terms of other quantities, I came upon one that surprised me, and I wonder if the…

My Mathematical Study: A Brief Revelation/Realization
Advertisements When m is the product of two odd primes p and q, with p < q, and m is also equal to s^2 – r where s is the integer ceiling of the square root of m, the polynomial x^2 + n*x – (r + s*n) for the positive integer n that allows it…

My Mathematical Study: The Current Integer Factorization Tree Up Which I’m Barking
Advertisements Let m = p * q denote the positive integer that is the product of prime numbers p and q. Determine s as the integer ceiling of the square root of m. If s is a perfect square, then p = q = s. Otherwise, perform the following steps: Determine r = s^2 –…

My Number Study: A Short Perl Script for Integer Factorization
Advertisements This is no great revelation post, merely a progress report. See the script below, which is an automation of the procedure I am using and analyzing so far. It’s not nearly the quickest – I expect extreme slowness for anything remotely near the RSA challenge number! – but it’s a starting point which I…

[Image Post] The number study so far…
Advertisements I will periodically put updates to the above image here, so that the progress shown is more or less current. I updated it on Sat Apr 23 10:30 AM.

Hairy Math Stuff (my number study, April 2022)
Advertisements Let positive integer m = p*q where p, q are prime numbers and p is not equal to q. Let s be the smallest positive integer such that s^2 > m, and let r be the difference between them so that: m = s^2 – r. Consider x^2 – r to be a quadratic…