Thread: Number Theory and Physics. View Single Post 2019-08-07, 09:54   #3
jwaltos

Apr 2012
Oh oh.

7208 Posts Regarding the integer factorization method I developed and which I believe is new, here are some equations, working
programs and preliminaries:
The syntax is Maple and the material dates from 2005, just copy the text into a Maple worksheet, make sure to remove
the leading ">" greater-than symbols and reformat certain execution blocks otherwise the program will not work as intended.
If you don't have Maple then you should be able to easily translate the text for your preferred software. The equations
and the program which generates equations from two factors are the end points of an integer factorization
spectrum. There exists a transformation which I call "progressive duality" that creates all of the intermediate
factorization forms within this spectrum that I am cleaning up for later inclusion but I have provided an
example.
The coordinates used: n1->references the location of the parabola along the x-axis (+ve to the right)
m1->references the location of the parabola along the y-axis (+ve downward)
[interchangeably] xa/xb->references a point on the parabola

The equation, V=L*27000+K: V->number to be factored
L-> the [linear] "location" value of V
K-> V mod 30^3
Considering a two factor product, take mod 30 of each factor (ie. 01,29) and is labelled as a type.
There exist exactly 8 groups consisting of 4 or 6 "types" as noted within the "equations" textfile.
Exclusive of 2,3 and 5 each group references one of the following primes: 1,7,11,13,17,19,23 and 29.
As an observation note that with the exception of 3, the digit sum of every prime is: 1,4,2,8,5 and 7..lucky 7.

RSA1->RSA8 in the equation sheet references the eight challenge numbers of the defunct [as of 2007] RSA Challenge,eg. RSA7=RSA-1536. From each set of equations,
one of the equations either has factored or will factor the corresponding RSA number.

@Nick- no it's not the best but it works where it should.
Attached Files Equations.txt (18.9 KB, 137 views) EQN_generation.txt (3.0 KB, 134 views) RSA-232_pgm.txt (21.4 KB, 133 views)  