dChan
Anonymous ID: 26ea67 March 16, 2019, 1:55 p.m. No.8844   🗄️.is 🔗kun   >>8847 >>8850 >>8869

Image description:

There are two sides to the image divided at the center. The green are factors existing in -f and the red are factors existing in e. Each pixel to the right of the center represents the occurrence of a factor (example center + 1 = gcd(a, 5) while center + 2 = gcd(a, 13)), same goes for the green (although moving in the opposite direction, ie center = gcd(a, 5), center - 1 = gcd(a, 13)).

 

What we see here are primes multiplied by RSA100 (primes from column 1). I got a bit lazy so we're talking about primes that exist in (1, 1) as a (that is a[t] = p).

 

Each frame is an INCREASE in the product. So the very first frame is RSA100 * 5, the second is RSA100 * 5 * 13, the third is RSA100 * 5 * 13 * 41 …

 

The height is represented by t-values. So we create RSA100 * 5, then calculate the e and -f for that record and generate the first 10000 t's and compute the gcd against each factor. Green and red colors represent the factors we multiply with (distinguished by their x-coordinate) and white cells are represented as RSA100a or RSA100b (Not sure if they actually occur).

Anonymous ID: 26ea67 March 16, 2019, 1:56 p.m. No.8847   🗄️.is 🔗kun   >>8848

>>8844

You can see in multiple of the frames what looks to be parabolas / waves. Not sure if this is what we're looking for. Maybe there is a specific parabola / wave that will yield a or b?

Anonymous ID: 26ea67 March 16, 2019, 2:04 p.m. No.8848   🗄️.is 🔗kun   >>8849

>>8847

I also trailed off a bit and found something very pretty, something similar to what we are generated before?

 

https://oeis.org/A051731/a051731_1.gif

 

Related to https://oeis.org/A051731 which is again related to http://oeis.org/A034729 which is related to phi, binary and divisors of a number.

Anonymous ID: 26ea67 March 16, 2019, 2:10 p.m. No.8851   🗄️.is 🔗kun   >>8852

>>8850

It wasn't as much skipping as it was being lazy. I only check if a[t] is a prime in (1, 1) instead of factorizing and creating a set of all primes in (1, 1). I'll probably redo it, though. Need to be thorough. I initially just wanted to generate that GIF to see how the patterns evolve.

Anonymous ID: 26ea67 March 16, 2019, 2:25 p.m. No.8853   🗄️.is 🔗kun   >>8855 >>8869

>>8852

The first 82 primes found in (1, 1) from the first 150 cells:

5, 13, 17, 29, 37, 41, 53, 61, 73, 89, 97, 101, 109, 113, 137, 149, 157, 173, 181, 193, 197, 229, 233, 241, 257, 269, 277, 281, 293, 313, 317, 337, 349, 373, 389, 397, 409, 421, 433, 449, 457, 521, 593, 601, 613, 653, 701, 757, 761, 797, 821, 857, 877, 941, 997, 1013, 1061, 1069, 1181, 1201, 1277, 1301, 1321, 1489, 1613, 1741, 1861, 1877, 1973, 2017, 2113, 2161, 2341, 2381, 2389, 2521, 2657, 2789, 3037, 3121, 3257, 3613

 

These were used to generate this new gif. So the first frame consists of RSA100 * 5, the second RSA100 * 5 * 13, third RSA100 * 5 * 13 * 17 …

 

Again, the (x, y) represent (factor, t).

 

What's neat is that it almost looks like some sort of cellular automata, each frame almost looks connected. Like you can see how it evolves / moves as the number of factors is increased.