VQC thread bake

The virtual quantum computer (VQC) is a grid made of constructably infinite elements that follow a known pattern. It is indexed using e, n, and t, where e is the column, n is the row, and t is the specific element in the cell.

The grid in its entirety serves as the superposition. The required input parameters to collapse the superposition are d and e, which are trivial to calculate for all c that is the difference of two squares. When the integers that are the difference of two squares are arranged into the grid and their corresponding properties are shown, a pattern emerges that shows a path to calculate the factors of c instead of searching for them. It can be understood using only the basic operations of arithmetic and sqrt. All currently-known patterns can be found within one thread here >>6506

C# VQC generator - ''pastebin.''com/XFtcAcrz
Java VQC generator - ''pastebin.''com/2MPYrJVe
Python VQC generator - ''pastebin.''com/NZkjtnZL


==Glossary==
''Look-up''
A pattern used to calculate the factors of c, like a value look-up table.

''Column''
All cells for a given e

''Row''
All cells for a given n

''Cell''
All entries for a given e,n (not to be confused with an entry itself.)

''Entry; record; element''
A set of variables corresponding to a factorization for a given c. The legend to read entries is {e:n:d:x:a:b} (e, n, t) = c
Example: {1:5:12:7:5:29} (1, 5, 4) = 145

''ab record; nontrivial factorization''
The element that contains the factorization of c that is not 1*c, hence, nontrivial.

''1c record; trivial factorization''
The element generated from setting a=1 and b=c

''Mirror element''
The element in -f corresponding to an element in e, in the context of a given c.


'''Variables'''
a and b are, to reiterate, the factors of c. a is the smaller factor of c, and b is the larger one.
d is the integer square root of c.
e is the remainder of taking the integer square root of c. Unless c is a perfect square, a remainder will be left over.
i is the root of the large square. It is equal to (d+n).
j is the root of the small square. it is equal to (x+n).
n is what you add to d to be exactly halfway between a and b, and it is the root of the large square, so it takes you from d to the large square.
x is what you add to a to make d. When added to n it makes the root of the small square.
f is what you add to c to make a square. (e is what you subtract from c to make the square below it, f adds to make the square above c.)
t is the third coordinate in the VQC, it is a function of x.
q is a product created by multiplying successive primes until the product is above d.
u is the triangle base of (x+n)^2. 8 times the triangle number of u plus one is (x+n)^2 for c with odd x+n.

ab = c
dd + e = c
(d + n)(d + n)-(x + n)(x + n) = c
a + 2x + 2n = b
a = d - x
d = a + x
d = floor_sqrt(c)
e = c - (dd)
b = c / a
n = ((a + b) / 2) - d
d + n = i
x = d - a
x = (floor_sqrt(( (d+n)*(d+n) - c))) - n
x + n = j
j^2 = 8*T(u) + 1
f = e - 2d + 1
u = (x+n) / 2
if (e is even) t = (x + 2) / 2
if (e is odd) t = (x + 1) / 2


'''Past threads'''

RSA #0 - ''archive.''fo/XmD7P
RSA #1 - ''archive.''fo/RgVko
RSA #2 - ''archive.''fo/fyzAu
RSA #3 - ''archive.''fo/uEgOb
RSA #4 - ''archive.''fo/eihrQ
RSA #5 - ''archive.''fo/Lr9fP
RSA #6 - ''archive.''fo/ykKYN
RSA #7 - ''archive.''fo/v3aKD
RSA #8 - ''archive.''fo/geYFp
RSA #9 - ''archive.''fo/jog81
RSA #10 - ''archive.''fo/xYpoQ
RSA #11 - ''archive.''fo/ccZXU
RSA #12 - ''archive.''fo/VqFge
RSA #13 - ''archive.''fo/Fblcs
RSA #14 - ''archive.''fo/HfxnM
RSA #15 - ''archive.''vn/59GwR
RSA #16 - ''archive.''vn/F49fw
RSA #17 - ''archive.''vn/u2Tu6
RSA #18 - ''archive.''is/FDVP9