Integer Factorization: An Observation About jumpfactor.pl

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I’m taking the results from jumpfactor.pl, and its algorithm for making the “jumps” in order to try to figure out ways to combine the jumps into few or (I hope) one jump to the Zone that will permit factorization.

What I’ve observed is that the rational point where the Remainder Line hits each Zone has a numerator that increases quadratically while the denominator decreases linearly.

I will do some heavy thinking about when exactly this produces the condition that (numerator) modulo (denominator) equals zero.

The pattern is there, as always, and, as always also too, hidden in the pattern is the way to break it algorithmically.

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