UPDATE: the sometimes triangular tables of values I have been building over the last several days have borne fruit, so to speak. I do not know where this will lead me, or how much easier it will make the task of integer factorization, but I have found a relationship between the product m of two distinct odd Primes p and q, with p<q, the number r which, if s is the least perfect square greater than m, equals s^{2}-m, and the quantity (q-p)^{2}/4. I have not teased out the exact relationship between those two quantities, but I have found that it relates to the function x x p – x where x is the number of times that q goes into r. I suspect x here has a relationship to c_{1} and c_{2} where they are s-p and q-s, respectively

## My Integer Factorization Study: Discouraged, but Then Renewed in Hope

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