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nested Primitive Pythagorean Triples// AP wants to do one better on Ulam's Prime Spiral

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  nested Primitive Pythagorean Triples// AP wants to do one better on Ulam's Prime Spiral Archimedes Plutonium <plutonium.archimedes@gmail.com> - 2018-09-30 10:44 -0700
    Re: Archimedes "Village Idiot" Plutonium flunked the Math Test of a lifetime-generation test moroney@world.std.spaamtrap.com (Michael Moroney) - 2018-09-30 19:22 +0000

#424597 — nested Primitive Pythagorean Triples// AP wants to do one better on Ulam's Prime Spiral

Date: Sun, 30 Sep 2018 10:40:50 -0700 (PDT)
From: Archimedes Plutonium <plutonium.archimedes@gmail.com>
To: Plutonium Atom Universe <plutonium-atom-universe@googlegroups.com>
Message-Id: <8c028903-1597-4de0-9eb5-409b5645fb14@googlegroups.com>
Subject: nested Primitive Pythagorean Triples// AP wants to do one better on
 Ulam's Prime Spiral

nested Primitive Pythagorean Triples// AP wants to do one better on Ulam's Prime Spiral

Alright, so far I have investigated spiraling PPT

3,4,5 
5,12,13 
8,15,17 
7,24,25 
20,21,29 
12,35,37 
9,40,41 
28,45,53 
.  .
.  .
.  .

Trouble with this is the spirals get large fast and so we have to know too much in order to be practical, whereas in Ulam, all he did was count the counting numbers in a square spiral pattern. So I cannot outbest Ulam unless I make it as simple as Ulam, not something far more complex and complicated. I have to match Ulam on simplicity in order to beat him at a prime predictor.

My second attempt is this Blob Rectangle where I start by a "union" of 5,12,13 and 8,15,17 to put together as best as possible a rectangle and then reading off the primes. But trouble here again-- more complicated than Ulam.

So today, let me introduce something as simple as Ulam, and go from there. Now it is recognized that just listing and fetching the PPT is more complicated than Ulam counting numbers in a square spiral pattern. But then again Ulam's Prime Spiral has only a accuracy (I am guessing) at best 50% accuracy in general. So for me to outbest Ulam, I need something simple yet able to boost the accuracy to 90%.

So, for simplicity sake, let me try this.

We have a list of PPT and we nest, nest nest, the prior smaller PPT into the next larger PPT at its right angle.

So we nest 3,4,5 inside of 5,12,13


|            .
|5 .                    .13
|3      . 5                                   .
|____4_________12_______________

depiction of a 3,4,5 PPT nested inside a 5,12,13 PPT

Now, we just read off the primes and look for some sort of pattern

We get 3,5, from 3,4,5, and now need 7. The 7 comes from 3+4 in 3,4,5, or it comes from 12-5 = 7 in 5,12,13. Next we need 11. If we include all the numbers of a PPT so that 3,4,5 is actually a quinapole of 3,4,5,6,7 then we get 11 from 5+6, or 4+7. The quinapole of 5,12,13 is 5,12,13,30,17 and I see no 11 out of there.

Now we need 13 and it is immediate from 5,12,13, next I need 17 and it is 5+12 or is 17 from the quinapole of 5,12,13. Or a 17 from 8,15,17. Next I need 19 and apparently have to go to the next higher PPT of 8,15,17. The quinapole of 8,15,17 is 8,15,17,60,23.

So, I need a 19 desperately,,,,, more later

AP

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#424610 — Re: Archimedes "Village Idiot" Plutonium flunked the Math Test of a lifetime-generation test

Math Failure Archimedes Plutonium <plutonium.archimedes@gmail.com> fails:

>Texas Rangers ALERT please!!! Who is this Texan spewing violence?

Quit taking the brown acid!

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