I noticed and thought about something that bemuses me concerning the new integer factorization algorithm in my mind about to turn itself into Perl code on ChrIIstopher, my MacBook Pro: I am using both varieties of Ceiling Squares that I have developed and defined during this study: the initial one, which is the least perfect square c^{2} greater than positive odd integer m, or equivalently the square of ceil(sqrt(m)); and the Adjusted Ceiling Square, which is the same except for adding one to c before squaring, if and only if necessary, to make it even or odd as (m+1)/2 is even or odd, correspondingly.

The value of c^{2} I choose for expressing m=c^{2}-r is the Adjusted Ceiling Square. However, when computing the Ceiling Square of one or more remainders in the Remainder Series, I am using plain old [ceil(sqrt(m))]^{2} as I initially was doing.

Hey, EVERYBODY gets to pitch in and help. All ideas I’ve had since last April have been very helpful indeed.

Again, stay tuned. I’m about to start coding, so the numbers can get ready to start jumping down that Bee Line.

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