We don't have to calculate g to determine whether g is closer to d or (d+1), we just have to see whether e or f is smaller. If f < e then α = (d+1), if f e then α = d
Kurwzeg has been treading on our territory since 2013 (most recent paper on factorization from what I've seen so far was in 2015).
I wouldn't consider it a miss. Using d+1 produces f.
Next paper from Kurzweg found:
Groundbreaking.
Also, a 2012 paper (much older than the rest) describing a method involving the "integer spiral."
A 2015 paper from Kurzweg on it as well.
He is quite the rising star.
Ulrich H Kurzweg factorization papers list (to eliminate confusion) (they are all describing different algorithms and approaches):
November 1, 2012 - (Factorizing-Semiprimes-with-the-Integer-Spiral.pdf)
August 2013 - the search for 2(x+n)^2 or 2(d+n)^2 paper (A-New-Method-for-Factoring-Large-Semiprimes.pdf)
Christmas (December?) 2013 - the search for 2(d+n) [N(f(N)] paper (A-Quick-Way-to-Factor-Large-Semiprimes.pdf)
January 2015 - d, e and f paper, (A-New-Approach-to-Factoring-Semiprimes.pdf) (hereby renamed the zeta search paper since it is a search for the value of a variable I've renamed to zeta ζ for our purposes)
August 2015 - Factorizing with Q primes (Factoring-Large-Semiprimes.pdf)
April 7, 2016 - (UNIVERSAL-CURVE.pdf)
Who knows where he's gotten by now.
ZetaSearch (UHK) —— https://pastebin.com/iUVg7q2u
It is not terrible.
I've got a new idea and it's simpler than what I was working on earlier. It's putting the remainder tree and the grid together and it also unifies the "the solution is recursive" and "the grid does all the work for you" hints.
The grid took me from (d+N) to (d+n)
you start at the odd column (it's either f or e), where t=-(d+N-1) then you take sqrt(2d) and it equals c, then you take sqrt d and it gives you another value and then you set that value as x and it will send you down the column, and then you take sqrt(d) again and use that as x, then keep doing that, sometimes it'll have you switch columns
Also, (d+N) - (d+n) is N-n because d is the same
It doesn't work for all semiprimes yet (need to look into how it works more, but here's a look so far
It can't factorize large semiprimes yet. I think it's missing something.
Interestingly it instantly terminates when you enter a prime, ie it takes one step to terminate on known rsa number factors. So if I can find the missing piece of this it could be a prime test too.
Here's the code.
https://pastebin.com/sEse8cxm
try exploring setting x = f or f-1 (depending on whether the column is even and odd), and try exploring setting x to root of f and root of e. Also, we should figure out what a diagonal is.
Also, I have no idea how to mix 0,n into this.