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

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  4.3- nested Primitive Pythagorean Triples// AP wants to do one better on Ulam's Prime Spiral Archimedes Plutonium <plutonium.archimedes@gmail.com> - 2018-09-30 23:31 -0700
    Re: 4.3- nested Primitive Pythagorean Triples// AP wants to do one better on Ulam's Prime Spiral Archimedes Plutonium <plutonium.archimedes@gmail.com> - 2018-10-01 00:02 -0700
      research taken a new turn-- Heavily Dense Composites predicting future primes//nested Primitive Pythagorean Triples// AP wants to do one better on Ulam's Prime Spiral Archimedes Plutonium <plutonium.archimedes@gmail.com> - 2018-10-01 15:31 -0700
      stuck on 67// nested Primitive Pythagorean Triples// AP wants to do one better on Ulam's Prime Spiral Archimedes Plutonium <plutonium.archimedes@gmail.com> - 2018-10-01 23:45 -0700
        forced primes Re: stuck on 67// nested Primitive Pythagorean Triples// AP wants to do one better on Ulam's Prime Spiral Archimedes Plutonium <plutonium.archimedes@gmail.com> - 2018-10-02 23:57 -0700
          Perhaps found a pattern//forced primes Re: stuck on 67// AP wants to do one better on Ulam's Prime Spiral Archimedes Plutonium <plutonium.archimedes@gmail.com> - 2018-10-03 00:36 -0700
            Perhaps found a pattern//forced primes Re: stuck on 67// AP wants to do one better on Ulam's Prime Spiral Archimedes Plutonium <plutonium.archimedes@gmail.com> - 2018-10-03 00:44 -0700
              Perhaps found a pattern//forced primes Re: stuck on 67// AP wants to do one better on Ulam's Prime Spiral Archimedes Plutonium <plutonium.archimedes@gmail.com> - 2018-10-03 01:02 -0700
                Perhaps found a pattern//forced primes Re: stuck on 67// AP wants to do one better on Ulam's Prime Spiral Archimedes Plutonium <plutonium.archimedes@gmail.com> - 2018-10-03 01:27 -0700
                  Perhaps found a pattern//forced primes Re: stuck on 67// AP wants to do one better on Ulam's Prime Spiral Archimedes Plutonium <plutonium.archimedes@gmail.com> - 2018-10-03 01:34 -0700
                    Perhaps found a pattern//forced primes Re: stuck on 67// AP wants to do one better on Ulam's Prime Spiral Archimedes Plutonium <plutonium.archimedes@gmail.com> - 2018-10-03 01:41 -0700
                      Perhaps found a pattern//forced primes Re: stuck on 67// AP wants to do one better on Ulam's Prime Spiral Archimedes Plutonium <plutonium.archimedes@gmail.com> - 2018-10-03 01:51 -0700
                        Re: Perhaps found a pattern//forced primes Re: stuck on 67// AP wants to do one better on Ulam's Prime Spiral Archimedes Plutonium <plutonium.archimedes@gmail.com> - 2018-10-03 02:04 -0700
                          Re: Perhaps found a pattern//forced primes Re: stuck on 67// AP wants to do one better on Ulam's Prime Spiral Archimedes Plutonium <plutonium.archimedes@gmail.com> - 2018-10-03 02:11 -0700
                            Re: Perhaps found a pattern//forced primes Re: stuck on 67// AP wants to do one better on Ulam's Prime Spiral Archimedes Plutonium <plutonium.archimedes@gmail.com> - 2018-10-03 02:24 -0700
                            Re: Perhaps found a pattern//forced primes Re: stuck on 67// AP wants to do one better on Ulam's Prime Spiral Archimedes Plutonium <plutonium.archimedes@gmail.com> - 2018-10-03 02:31 -0700
                              Re: Perhaps found a pattern//forced primes Re: stuck on 67// AP wants to do one better on Ulam's Prime Spiral Archimedes Plutonium <plutonium.archimedes@gmail.com> - 2018-10-03 05:06 -0700
                                Re: Perhaps found a pattern//forced primes Re: stuck on 67// AP wants to do one better on Ulam's Prime Spiral Archimedes Plutonium <plutonium.archimedes@gmail.com> - 2018-10-03 10:17 -0700
                                  Formats to eliminate odd composites 9+6N // AP wants to do one better on Ulam's Prime Spiral Archimedes Plutonium <plutonium.archimedes@gmail.com> - 2018-10-03 10:41 -0700
                                    still think it all hinges on 2*a*b Re: Formats to eliminate odd composites 9+6N // AP wants to do one better on Ulam's Prime Spiral Archimedes Plutonium <plutonium.archimedes@gmail.com> - 2018-10-03 14:11 -0700
                                      summary at this point-- good-- but all depends on differentiation // AP wants to do one better on Ulam's Prime Spiral Archimedes Plutonium <plutonium.archimedes@gmail.com> - 2018-10-03 15:24 -0700
                                        the fingerprint of being prime // AP wants to do one better on Ulam's Prime Spiral Archimedes Plutonium <plutonium.archimedes@gmail.com> - 2018-10-03 19:16 -0700
                                          One of AP's most beautiful proofs to date-- the entire Pattern of Primes Re: the fingerprint of being prime // AP wants to do one better on Ulam's Prime Spiral Archimedes Plutonium <plutonium.archimedes@gmail.com> - 2018-10-03 23:32 -0700
                                            Re: Archimedes "Village Idiot" Plutonium flunked the Math Test of a lifetime-generation test moroney@world.std.spaamtrap.com (Michael Moroney) - 2018-10-07 03:31 +0000
                                            Re: One of AP's most beautiful proofs to date-- and a waste. eastside.erik@gmail.com - 2018-10-06 21:31 -0700
                                              Re: One of AP's most beautiful proofs to date-- and a waste. James Waldby <not@valid.invalid> - 2018-10-08 04:32 +0000
                                                Re: One of AP's most beautiful proofs to date-- and a waste. Archimedes Plutonium <plutonium.archimedes@gmail.com> - 2018-10-07 21:59 -0700
                                                concept of prime should include concept of coprime Re: One of AP's most beautiful proofs to date-- Archimedes Plutonium <plutonium.archimedes@gmail.com> - 2018-10-07 22:35 -0700
                                                  Re: concept of prime should include concept of coprime Re: One of AP's most beautiful proofs to date-- Archimedes Plutonium <plutonium.archimedes@gmail.com> - 2018-10-07 22:41 -0700
                                            Re: One of AP's most beautiful proofs to date-- the entire Pattern of Primes Re: the fingerprint of being prime // AP wants to do one better on Ulam's Prime Spiral qbwrfmlx@gmail.com - 2018-10-06 22:40 -0700
                                              bean counter gives a test Re: One of AP's most beautiful proofs to date-- the entire Pattern of Primes Archimedes Plutonium <plutonium.archimedes@gmail.com> - 2018-10-07 22:28 -0700
                                                Re: bean counter gives a test Re: One of AP's most beautiful proofs to date-- the entire Pattern of Primes qbwrfmlx@gmail.com - 2018-10-07 22:43 -0700
                                                  Re: Archimedes "Village Idiot" Plutonium flunked the Math Test of a lifetime-generation test moroney@world.std.spaamtrap.com (Michael Moroney) - 2018-10-08 13:58 +0000
                                              AP's tool to determine if prime or composite-- Odd Rectangles Re: the fingerprint of being prime // AP wants to do one better on Ulam's Prime Spiral Archimedes Plutonium <plutonium.archimedes@gmail.com> - 2018-10-08 14:12 -0700
                                                Re: Archimedes "Village Idiot" Plutonium flunked the Math Test of a lifetime-generation test moroney@world.std.spaamtrap.com (Michael Moroney) - 2018-10-09 06:58 +0000

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#424890 — summary at this point-- good-- but all depends on differentiation // AP wants to do one better on Ulam's Prime Spiral

Summary so far. Excellent progress, for I can take any odd number I wish and develop for you almost instantaneously what its PPT is. For example, the coding is 

2 x 3 is 6 so for 3,4,5

3 x 5 is 15 so for 5,12,13

4 x 7 is 28 so for 7,24,25

Call the first number the code increment, thus, give me any large odd number and I evaluate its code increment by adding 1 to the number then divide by 2 to obtain code increment.

So you hand me 27, I add 1 = 28, divide by 2 is 14 thus 14 x 27 = 378 and thus I easily find 27,364,365 bearing in mind that the B,C of A,B,C when added is the 27^2 364+365 = 729

So, hand me any odd number, and almost instantly I fetch its PPT where B,C are separated by 1 unit.

So, I have all the odd numbers but more importantly I have all the PRIMES.

Now comes the rub, the petal to the metal so to speak, the mountain to climb. All of that is good information and data, but what we want is to predict future primes, and the only way we have of that, is whether that PPT, can tell us if the odd number is prime or composite.

Is there something in that PPT of 27,364,365 that indicates to us, that 27 is composite, not prime.

Of course we can use quadrapole 27,364,365,391 and even quinapole 27,364,365,391,729

We can even do subtract or divide or multiply those A,B,C,D,E

Something, something that tells us A is prime or composite. What I call differentiation of A.

If there is nothing to differentiate, then this journey was not a success.

I have one advantage over all that have searched this problem, for I have the PPT. In the past, mathematicians had just the number itself, the odd number such as 27 to look at and seek a differential. What I have, is the PPT, that 27 is associated with 364,365,391,729. So I have other numbers to play with.

AP

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#424898 — the fingerprint of being prime // AP wants to do one better on Ulam's Prime Spiral

On Wednesday, October 3, 2018 at 5:24:40 PM UTC-5, Archimedes Plutonium wrote:
> Summary so far. Excellent progress, for I can take any odd number I wish and develop for you almost instantaneously what its PPT is. For example, the coding is 
> 
> 2 x 3 is 6 so for 3,4,5
> 
> 3 x 5 is 15 so for 5,12,13
> 
> 4 x 7 is 28 so for 7,24,25
> 
> Call the first number the code increment, thus, give me any large odd number and I evaluate its code increment by adding 1 to the number then divide by 2 to obtain code increment.
> 
> So you hand me 27, I add 1 = 28, divide by 2 is 14 thus 14 x 27 = 378 and thus I easily find 27,364,365 bearing in mind that the B,C of A,B,C when added is the 27^2 364+365 = 729
> 
> So, hand me any odd number, and almost instantly I fetch its PPT where B,C are separated by 1 unit.
> 
> So, I have all the odd numbers but more importantly I have all the PRIMES.
> 
> Now comes the rub, the petal to the metal so to speak, the mountain to climb. All of that is good information and data, but what we want is to predict future primes, and the only way we have of that, is whether that PPT, can tell us if the odd number is prime or composite.
> 
> Is there something in that PPT of 27,364,365 that indicates to us, that 27 is composite, not prime.
> 
> Of course we can use quadrapole 27,364,365,391 and even quinapole 27,364,365,391,729
> 
> We can even do subtract or divide or multiply those A,B,C,D,E
> 
> Something, something that tells us A is prime or composite. What I call differentiation of A.
> 
> If there is nothing to differentiate, then this journey was not a success.
> 
> I have one advantage over all that have searched this problem, for I have the PPT. In the past, mathematicians had just the number itself, the odd number such as 27 to look at and seek a differential. What I have, is the PPT, that 27 is associated with 364,365,391,729. So I have other numbers to play with.
> 

All I need to do is show some fingerprint in any odd composite that it is composite, not prime, using PPT, and then I am done, for then, we have a perfect pattern of all primes, and a 100% perfect predictor. Telling whether a number is prime will be made simple, and remember in True Math, numbers only go out to 1*10^604, and thereafter you no longer care or worry or can use those numbers beyond for math ends at this borderline.

AP

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#424911 — One of AP's most beautiful proofs to date-- the entire Pattern of Primes Re: the fingerprint of being prime // AP wants to do one better on Ulam's Prime Spiral

On Wednesday, October 3, 2018 at 9:16:41 PM UTC-5, Archimedes Plutonium wrote:
> On Wednesday, October 3, 2018 at 5:24:40 PM UTC-5, Archimedes Plutonium wrote:
> > Summary so far. Excellent progress, for I can take any odd number I wish and develop for you almost instantaneously what its PPT is. For example, the coding is 
> > 
> > 2 x 3 is 6 so for 3,4,5
> > 
> > 3 x 5 is 15 so for 5,12,13
> > 
> > 4 x 7 is 28 so for 7,24,25
> > 
> > Call the first number the code increment, thus, give me any large odd number and I evaluate its code increment by adding 1 to the number then divide by 2 to obtain code increment.
> > 
> > So you hand me 27, I add 1 = 28, divide by 2 is 14 thus 14 x 27 = 378 and thus I easily find 27,364,365 bearing in mind that the B,C of A,B,C when added is the 27^2 364+365 = 729
> > 
> > So, hand me any odd number, and almost instantly I fetch its PPT where B,C are separated by 1 unit.
> > 
> > So, I have all the odd numbers but more importantly I have all the PRIMES.
> > 
> > Now comes the rub, the petal to the metal so to speak, the mountain to climb. All of that is good information and data, but what we want is to predict future primes, and the only way we have of that, is whether that PPT, can tell us if the odd number is prime or composite.
> > 
> > Is there something in that PPT of 27,364,365 that indicates to us, that 27 is composite, not prime.
> > 
> > Of course we can use quadrapole 27,364,365,391 and even quinapole 27,364,365,391,729
> > 
> > We can even do subtract or divide or multiply those A,B,C,D,E
> > 
> > Something, something that tells us A is prime or composite. What I call differentiation of A.
> > 
> > If there is nothing to differentiate, then this journey was not a success.
> > 
> > I have one advantage over all that have searched this problem, for I have the PPT. In the past, mathematicians had just the number itself, the odd number such as 27 to look at and seek a differential. What I have, is the PPT, that 27 is associated with 364,365,391,729. So I have other numbers to play with.
> > 
> 
> All I need to do is show some fingerprint in any odd composite that it is composite, not prime, using PPT, and then I am done, for then, we have a perfect pattern of all primes, and a 100% perfect predictor. Telling whether a number is prime will be made simple, and remember in True Math, numbers only go out to 1*10^604, and thereafter you no longer care or worry or can use those numbers beyond for math ends at this borderline.
> 

Stunning beautiful, one of my most loveliest of all proofs, ever. Yes, I have successfully conquered primes, with not only a prime pattern, but the ability to tell you whether any odd number is prime or not prime, with an extraordinary simple test.

But before I tell you the discovery, I want to review what had happened.

This adventure of mine started 21September a few weeks ago.


Newsgroups: sci.math
Date: Fri, 21 Sep 2018 19:50:20 -0700 (PDT)

Subject: AP wants to do one better on Ulam's Prime Spiral
From: Archimedes Plutonium <plutonium....@gmail.com>
Injection-Date: Sat, 22 Sep 2018 02:50:21 +0000

AP wants to do one better on Ulam's Prime Spiral
So far in math history, Ulam has the best patterning of primes with his spiral. 

What I want to do is, one better than Ulam, so that primes have a pattern that you can use to predict future primes. 

And so I am looking at this convergence of division by consecutive primes. 

3/2 = 1.5 
5/3 = 1.666.... 
7/5 = 1.4 
11/7 = 1.5714.... 
13/11 = 1.1818..... 
17/13 = 1.3076.... 
19/17 = 1.1176.... 
23/19 = 1.2105...... 
29/23 = 1.2608..... 
31/29 = 1.0689...... 
37/31 = 1.1935..... 
41/37 = 1.1081..... 
43/41 = 1.04878...... 
47/43 = 1.09302..... 
53/47 = 1.12765...... 
59/53 = 1.1132...... 
61/59 = 1.03389..... 
67/61 = 1.09836...... 
71/67 = 1.0597........ 
73/71 = 1.02816....... 
79/73 = 1.08219........ 
83/79 = 1.05063......
89/83 = 1.072289......
97/89 = 1.0898..... 
101/97 = 1.04123......
103/101 = 1.0198......
107/103 = 1.0388.......
109/107 =  1.01869.....
113/109 = 1.03669......
127/113 = 1.12389......

What I am hoping to do is end up with a sequence that is a function and graphable. 

AP


So in September I wanted to do a geometry or algebra work which is far better than the Ulam Prime Spiral.

And so I embarked on that mission.

I recounted some of my prior years trips and forays into predicting primes, even instilling the idea and attitude that primes are Patterned, even though it is extremely difficult to see any pattern. And the best pattern so far was Ulam showing a long string of primes forming a straight line in a spiral.

So, in September, now is October 4, in September I recalled my earlier attempts such as the idea that primes are borne when the surrounding composite numbers are heavily dense composites such as 12 which is 2*2*3 so you have 11 nearby and 13 nearby. So I suggested looking at the heavily dense composite sequence, and even recently the heavily dense factorials sequence for nearby primes. But such hunting for prime truth is just a mere hunting engagement with hardly any theory to go with it, and no overall general pattern.

So in the excitement, I wanted a general theory a overall pattern and my hope for success was all tied to Primitive Pythagorean Triples, all tied to that because I knew that each triple bears many numbers-- three, but you can make quadrapoles, quinapoles of the three numbers. And I knew PPT had all the odd numbers and thus all the primes. That if I were to find a pattern and theory and be able to predict primes-- my very best chance was to look into PPT. And so from September to today 4OCT, it was mostly all about PPT. I had a few exciting moments there of making PPT triangles into like a Ulam spiral, only of PPT triangles, but that grounded to a halt with no fruition. And even blob-rectangles of assembling two PPT triangles into a blob rectangle, which also, went nowhere fast.

Then last night I realized that give me all the odd numbers in order that a PPT exists where the A,B,C the A is the odd number and B,C are separated by just 1 unit.

3, 4, 5
5, 12,13
7,24,25
9, 40,41
11,60,61
13,84,85
. .
. .
. .

And these have a beatiful pattern because if you use a increment, you can calculate the next numbers

2 x 3 forms the boundaries of 3,4,5
3 x 5 forms boundaries of 5, 12, 13
So if I did not know the next triple with 7, I multiply 4 x 7 = 28 and know it is the boundary so that around 28 I need a B,C separated by 1 and which when added together equals 7^2 = 49, so it is 24,25

And the same goes for all the odd numbers.

Let me call these separated by 1 Triples as the unit Triple. Highly highly patterned.

So, there I was last night, having found a PATTERNED Odd Numbers from PPT. Only, one thing remaining to do, be able to distinguish or differentiate whether an Odd Number is prime or Composite.

I had nothing, unless I can differentiate whether an odd number is prime or composite.  

So, I spent the whole thinking and thinking. Trying everything with especially 9,40,41 for it is the first odd composite, to see if _How in the World can I tell if 9 is prime or odd composite by PPT_ (so that if dished up a odd number with 500 digits, how would I know it is prime or composite. I cannot out-do Ulam, if I cannot tell if the number is prime or composite. So with 9,40,41, all day long I looked to see if something of a "fingerprint exists in 9" to recognize it as composite which its neighbors 7 and 11 have fingerprints in PPT saying they are prime.

No use in PPT if they cannot differentiate odd composite from odd prime. 

So all day long I was looking and comparing, going through the trouble of triple 9,40,41, then the quadrapole A+B  9, 40, 41, 49, then the quinapole of B+C 9, 40, 41, 49, 81, and recognizing that 9^2 was 40+41 = 81.

Then what I did, seeing no fingerprint, of composite, I subtracted those numbers, divided those numbers, multiplied those numbers all the while comparing to 7 and 11 and even 21 and 27. Nothing nothing appeared. Often if I found something interesting, the same thing appeared in the primes.

Finally, as nighttime came, I resorted back to the definition of PPT, 2*a*b, b^2-a^2, b^2+a^2 and I noticed that the a,b were equal to the odd number as additions, so that 5,12,13 was a=2, b=3 and 9,40,41 was a=4, b=5, where we have 4+5=9 and amazingly in all these UNIT PPT, the a+b= the A odd number in question.

Then a little bell started ringing in my mind-- this reminds me of my Goldbach proof that every even number is the sum of two primes (I count 1 as prime in Goldbach so that we have 2 = 1+1, 4= 2+2, 6 = 3+3, 8= 3+5, etc etc. 

Some readers will recall AP's Goldbach proof. We set up Algebra Columns of add and multiply simultaneously.

2  0
1   1

then

4   0
3   1
2   2

then

6   0
5   1
4   2
3   3

Notice that horizontally the sums add to the starting even number like 6, and the proof mechanism of Goldbach is that if there exists an even number that is not the sum of two primes, then what happens is that mathematics does not have a Two Prime Composite number.

We see this especially clearly in 8

8   0
7   1
6   2
5   3
4   4

So, for Goldbach 8 is 5 + 3, the sum of two primes, and the proof that Goldbach is true in all even numbers is that if a even number Column has no two matching primes, and because those matching numbers are also multiplication as well as addition, and Unique matching, that mathematics would not have the number 5X3 = 15, if math never had 5+3= 8. Of course my proof has much more details, but I am just glossing over the main issues.

So, tonight, I was looking at PPT of the a,b in forming 9,40,41 and the a,b were 4,5 added together is 9, and quickly that sent my mind back in time to adventures of proving Goldbach.

And then, after doing several Columns for Odd Numbers (mind you not even numbers but Odd Numbers) I realized that all odd numbers can be instantly recognized as composite or prime.

5   0
4   1
3   2

examine horizontals and do division where we discount the division by 1 or 0

7  0
6  1
5  2
4  3

no divisions possible, because well, 7 is prime

9   0
8   1
7   2
6   3
5   4

Notice we have 6 divided by 3, hence 9 is composite

11  0
10  1
9    2
8    3
7    4
6    5

No division possible, because 11 is prime

now skip down to 21 because the other primes show the same -- unable to divide

21    0
20   1
19    2
18    3
17    4
16   5
15   6
14   7
13   8
12   9
11   10

Now we have several divisions by factors possible we have 18/3 outright, but also factoring division to lowest terms 15/6, and 12/9

Now let us test this theory on the nearby prime 23, to see that there are no outright divisions and no factoring to lowest terms division

23   0
22   1
21   2
20   3
19   4
18   5
17   6
16   7
15   8
14   9
13   10
12   11

So, I see absolutely no outright divisions nor any factoring division into lowest terms, and that is because 23 is prime.

NOW QUESTION TO COMPUTERS around the world, how easy is it for them to Engineer a computer to scan through a 604 digit odd number and see if there is no-factoring-division and no outright division.

I mean, how amenable is it to engineer computers to code them to scan through a 604 Digit Number to check for division?

So, what I discovered is not only a bettering of Ulam Prime Spiral, but I discovered that it is an easy task to tell if a number is PRIME or Composite, by just a column algebra.

Now, what I discovered is in a sense a different version of Goldbach. For Goldbach was just a question of an even number being the sum of two primes. And the AP Primes, is a division question to separate the odd composite from the prime. Goldbach and AP Primes are two proofs dealing with a Column Algebra. The Columns are unique to numbers. 

Why does the column work? Good question. It is easy to see why it works for Goldbach because you tear a hole into the fabric of math if you do not have a number like 3*5=15 because 3+5 = 8. Math would dissolve if you had missing a number 3*5=15. But why does the Column Algebra be able to differentiate between a Odd Composite and a Prime ? Why?

I do not know at this moment, because Column Algebra is again addition, and why should division be involved with addition? We normally see division involved with multiplication and addition involved with subtraction.

But there has to be a link, because in PPT of 9, 40, 41, where a=4 and b=5 and so 4+5=9, that is what drove me over here to the Column Algebra. So in the next several days, as I digest this magnificient beautiful proof, I will try to answer the WHY, thereof.

Thank you dear lord god almighty 231PU, thank you graciously dear lord for letting me see the light of day. Atom.

AP

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#425105 — Re: Archimedes "Village Idiot" Plutonium flunked the Math Test of a lifetime-generation test

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

>Proofs ellipse is never a conic, always a cylinder section by
>Archimedes Plutonium
>--------------------
>AP's proof the ellipse is never a Conic Section, always a Cylinder 
>section, and how the proof works


You need to see Franz's proof yet again?  You should save his proof on
your computer so you can look at it at any time without asking me to post
it for you again each time!


Some preliminaries:

Top view of the conic section and depiction of the coordinate system used 
in the proof:

              ^ x
              |
             -+- <= x=h
         .'   |   `.
        .     |     .
        |     |     |
        '     |     '      
         `.   |   .'
 y <----------+ <= x=0
             
Cone (side view):
                 .
                /|\
               / | \
              /b |  \
             /---+---' <= x = h
            /    |'   \
           /   ' |     \
          / '    |      \
x = 0 => '-------+-------\
        /    a   |        \

Proof:

r(x) = a - ((a-b)/h)x  and  d(x) = a - ((a+b)/h)x,  hence

y(x)^2 = r(x)^2 - d(x)^2 = ab - ab(2x/h - 1)^2 = ab(1 - 4(x - h/2)^2/h^2.

Hence (1/ab)y(x)^2 + (4/h^2)(x - h/2)^2 = 1  ...equation of an ellipse

qed

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#425106 — Re: One of AP's most beautiful proofs to date-- and a waste.

On Wednesday, October 3, 2018 at 11:32:48 PM UTC-7, Archimedes Plutonium wrote:
> On Wednesday, October 3, 2018 at 9:16:41 PM UTC-5, Archimedes Plutonium wrote:
> > On Wednesday, October 3, 2018 at 5:24:40 PM UTC-5, Archimedes Plutonium wrote:
> > > Summary so far. Excellent progress, for I can take any odd number I wish and develop for you almost instantaneously what its PPT is. For example, the coding is 
> > > 
> > > 2 x 3 is 6 so for 3,4,5
> > > 
> > > 3 x 5 is 15 so for 5,12,13
> > > 
> > > 4 x 7 is 28 so for 7,24,25
> > > 
> > > Call the first number the code increment, thus, give me any large odd number and I evaluate its code increment by adding 1 to the number then divide by 2 to obtain code increment.
> > > 
> > > So you hand me 27, I add 1 = 28, divide by 2 is 14 thus 14 x 27 = 378 and thus I easily find 27,364,365 bearing in mind that the B,C of A,B,C when added is the 27^2 364+365 = 729
> > > 
> > > So, hand me any odd number, and almost instantly I fetch its PPT where B,C are separated by 1 unit.
> > > 
> > > So, I have all the odd numbers but more importantly I have all the PRIMES.
> > > 
> > > Now comes the rub, the petal to the metal so to speak, the mountain to climb. All of that is good information and data, but what we want is to predict future primes, and the only way we have of that, is whether that PPT, can tell us if the odd number is prime or composite.
> > > 
> > > Is there something in that PPT of 27,364,365 that indicates to us, that 27 is composite, not prime.
> > > 
> > > Of course we can use quadrapole 27,364,365,391 and even quinapole 27,364,365,391,729
> > > 
> > > We can even do subtract or divide or multiply those A,B,C,D,E
> > > 
> > > Something, something that tells us A is prime or composite. What I call differentiation of A.
> > > 
> > > If there is nothing to differentiate, then this journey was not a success.
> > > 
> > > I have one advantage over all that have searched this problem, for I have the PPT. In the past, mathematicians had just the number itself, the odd number such as 27 to look at and seek a differential. What I have, is the PPT, that 27 is associated with 364,365,391,729. So I have other numbers to play with.
> > > 
> > 
> > All I need to do is show some fingerprint in any odd composite that it is composite, not prime, using PPT, and then I am done, for then, we have a perfect pattern of all primes, and a 100% perfect predictor. Telling whether a number is prime will be made simple, and remember in True Math, numbers only go out to 1*10^604, and thereafter you no longer care or worry or can use those numbers beyond for math ends at this borderline.
> > 
> 
> Stunning beautiful, one of my most loveliest of all proofs, ever. Yes, I have successfully conquered primes, with not only a prime pattern, but the ability to tell you whether any odd number is prime or not prime, with an extraordinary simple test.
> 
> But before I tell you the discovery, I want to review what had happened.
> 
> This adventure of mine started 21September a few weeks ago.
> 
> 
> Newsgroups: sci.math
> Date: Fri, 21 Sep 2018 19:50:20 -0700 (PDT)
> 
> Subject: AP wants to do one better on Ulam's Prime Spiral
> From: Archimedes Plutonium <plutonium....@gmail.com>
> Injection-Date: Sat, 22 Sep 2018 02:50:21 +0000
> 
> AP wants to do one better on Ulam's Prime Spiral
> So far in math history, Ulam has the best patterning of primes with his spiral. 
> 
> What I want to do is, one better than Ulam, so that primes have a pattern that you can use to predict future primes. 
> 
> And so I am looking at this convergence of division by consecutive primes. 
> 
> 3/2 = 1.5 
> 5/3 = 1.666.... 
> 7/5 = 1.4 
> 11/7 = 1.5714.... 
> 13/11 = 1.1818..... 
> 17/13 = 1.3076.... 
> 19/17 = 1.1176.... 
> 23/19 = 1.2105...... 
> 29/23 = 1.2608..... 
> 31/29 = 1.0689...... 
> 37/31 = 1.1935..... 
> 41/37 = 1.1081..... 
> 43/41 = 1.04878...... 
> 47/43 = 1.09302..... 
> 53/47 = 1.12765...... 
> 59/53 = 1.1132...... 
> 61/59 = 1.03389..... 
> 67/61 = 1.09836...... 
> 71/67 = 1.0597........ 
> 73/71 = 1.02816....... 
> 79/73 = 1.08219........ 
> 83/79 = 1.05063......
> 89/83 = 1.072289......
> 97/89 = 1.0898..... 
> 101/97 = 1.04123......
> 103/101 = 1.0198......
> 107/103 = 1.0388.......
> 109/107 =  1.01869.....
> 113/109 = 1.03669......
> 127/113 = 1.12389......
> 
> What I am hoping to do is end up with a sequence that is a function and graphable. 
> 
> AP
> 
> 
> So in September I wanted to do a geometry or algebra work which is far better than the Ulam Prime Spiral.
> 
> And so I embarked on that mission.
> 
> I recounted some of my prior years trips and forays into predicting primes, even instilling the idea and attitude that primes are Patterned, even though it is extremely difficult to see any pattern. And the best pattern so far was Ulam showing a long string of primes forming a straight line in a spiral.
> 
> So, in September, now is October 4, in September I recalled my earlier attempts such as the idea that primes are borne when the surrounding composite numbers are heavily dense composites such as 12 which is 2*2*3 so you have 11 nearby and 13 nearby. So I suggested looking at the heavily dense composite sequence, and even recently the heavily dense factorials sequence for nearby primes. But such hunting for prime truth is just a mere hunting engagement with hardly any theory to go with it, and no overall general pattern.
> 
> So in the excitement, I wanted a general theory a overall pattern and my hope for success was all tied to Primitive Pythagorean Triples, all tied to that because I knew that each triple bears many numbers-- three, but you can make quadrapoles, quinapoles of the three numbers. And I knew PPT had all the odd numbers and thus all the primes. That if I were to find a pattern and theory and be able to predict primes-- my very best chance was to look into PPT. And so from September to today 4OCT, it was mostly all about PPT. I had a few exciting moments there of making PPT triangles into like a Ulam spiral, only of PPT triangles, but that grounded to a halt with no fruition. And even blob-rectangles of assembling two PPT triangles into a blob rectangle, which also, went nowhere fast.
> 
> Then last night I realized that give me all the odd numbers in order that a PPT exists where the A,B,C the A is the odd number and B,C are separated by just 1 unit.
> 
> 3, 4, 5
> 5, 12,13
> 7,24,25
> 9, 40,41
> 11,60,61
> 13,84,85
> . .
> . .
> . .
> 
> And these have a beatiful pattern because if you use a increment, you can calculate the next numbers
> 
> 2 x 3 forms the boundaries of 3,4,5
> 3 x 5 forms boundaries of 5, 12, 13
> So if I did not know the next triple with 7, I multiply 4 x 7 = 28 and know it is the boundary so that around 28 I need a B,C separated by 1 and which when added together equals 7^2 = 49, so it is 24,25
> 
> And the same goes for all the odd numbers.
> 
> Let me call these separated by 1 Triples as the unit Triple. Highly highly patterned.
> 
> So, there I was last night, having found a PATTERNED Odd Numbers from PPT. Only, one thing remaining to do, be able to distinguish or differentiate whether an Odd Number is prime or Composite.
> 
> I had nothing, unless I can differentiate whether an odd number is prime or composite.  
> 
> So, I spent the whole thinking and thinking. Trying everything with especially 9,40,41 for it is the first odd composite, to see if _How in the World can I tell if 9 is prime or odd composite by PPT_ (so that if dished up a odd number with 500 digits, how would I know it is prime or composite. I cannot out-do Ulam, if I cannot tell if the number is prime or composite. So with 9,40,41, all day long I looked to see if something of a "fingerprint exists in 9" to recognize it as composite which its neighbors 7 and 11 have fingerprints in PPT saying they are prime.
> 
> No use in PPT if they cannot differentiate odd composite from odd prime. 
> 
> So all day long I was looking and comparing, going through the trouble of triple 9,40,41, then the quadrapole A+B  9, 40, 41, 49, then the quinapole of B+C 9, 40, 41, 49, 81, and recognizing that 9^2 was 40+41 = 81.
> 
> Then what I did, seeing no fingerprint, of composite, I subtracted those numbers, divided those numbers, multiplied those numbers all the while comparing to 7 and 11 and even 21 and 27. Nothing nothing appeared. Often if I found something interesting, the same thing appeared in the primes.
> 
> Finally, as nighttime came, I resorted back to the definition of PPT, 2*a*b, b^2-a^2, b^2+a^2 and I noticed that the a,b were equal to the odd number as additions, so that 5,12,13 was a=2, b=3 and 9,40,41 was a=4, b=5, where we have 4+5=9 and amazingly in all these UNIT PPT, the a+b= the A odd number in question.
> 
> Then a little bell started ringing in my mind-- this reminds me of my Goldbach proof that every even number is the sum of two primes (I count 1 as prime in Goldbach so that we have 2 = 1+1, 4= 2+2, 6 = 3+3, 8= 3+5, etc etc. 
> 
> Some readers will recall AP's Goldbach proof. We set up Algebra Columns of add and multiply simultaneously.
> 
> 2  0
> 1   1
> 
> then
> 
> 4   0
> 3   1
> 2   2
> 
> then
> 
> 6   0
> 5   1
> 4   2
> 3   3
> 
> Notice that horizontally the sums add to the starting even number like 6, and the proof mechanism of Goldbach is that if there exists an even number that is not the sum of two primes, then what happens is that mathematics does not have a Two Prime Composite number.
> 
> We see this especially clearly in 8
> 
> 8   0
> 7   1
> 6   2
> 5   3
> 4   4
> 
> So, for Goldbach 8 is 5 + 3, the sum of two primes, and the proof that Goldbach is true in all even numbers is that if a even number Column has no two matching primes, and because those matching numbers are also multiplication as well as addition, and Unique matching, that mathematics would not have the number 5X3 = 15, if math never had 5+3= 8. Of course my proof has much more details, but I am just glossing over the main issues.
> 
> So, tonight, I was looking at PPT of the a,b in forming 9,40,41 and the a,b were 4,5 added together is 9, and quickly that sent my mind back in time to adventures of proving Goldbach.
> 
> And then, after doing several Columns for Odd Numbers (mind you not even numbers but Odd Numbers) I realized that all odd numbers can be instantly recognized as composite or prime.
> 
> 5   0
> 4   1
> 3   2
> 
> examine horizontals and do division where we discount the division by 1 or 0
> 
> 7  0
> 6  1
> 5  2
> 4  3
> 
> no divisions possible, because well, 7 is prime
> 
> 9   0
> 8   1
> 7   2
> 6   3
> 5   4
> 
> Notice we have 6 divided by 3, hence 9 is composite
> 
> 11  0
> 10  1
> 9    2
> 8    3
> 7    4
> 6    5
> 
> No division possible, because 11 is prime
> 
> now skip down to 21 because the other primes show the same -- unable to divide
> 
> 21    0
> 20   1
> 19    2
> 18    3
> 17    4
> 16   5
> 15   6
> 14   7
> 13   8
> 12   9
> 11   10
> 
> Now we have several divisions by factors possible we have 18/3 outright, but also factoring division to lowest terms 15/6, and 12/9
> 
> Now let us test this theory on the nearby prime 23, to see that there are no outright divisions and no factoring to lowest terms division
> 
> 23   0
> 22   1
> 21   2
> 20   3
> 19   4
> 18   5
> 17   6
> 16   7
> 15   8
> 14   9
> 13   10
> 12   11
> 
> So, I see absolutely no outright divisions nor any factoring division into lowest terms, and that is because 23 is prime.
> 
> NOW QUESTION TO COMPUTERS around the world, how easy is it for them to Engineer a computer to scan through a 604 digit odd number and see if there is no-factoring-division and no outright division.
> 
> I mean, how amenable is it to engineer computers to code them to scan through a 604 Digit Number to check for division?
> 
> So, what I discovered is not only a bettering of Ulam Prime Spiral, but I discovered that it is an easy task to tell if a number is PRIME or Composite, by just a column algebra.
> 
> Now, what I discovered is in a sense a different version of Goldbach. For Goldbach was just a question of an even number being the sum of two primes. And the AP Primes, is a division question to separate the odd composite from the prime. Goldbach and AP Primes are two proofs dealing with a Column Algebra. The Columns are unique to numbers. 
> 
> Why does the column work? Good question. It is easy to see why it works for Goldbach because you tear a hole into the fabric of math if you do not have a number like 3*5=15 because 3+5 = 8. Math would dissolve if you had missing a number 3*5=15. But why does the Column Algebra be able to differentiate between a Odd Composite and a Prime ? Why?
> 
> I do not know at this moment, because Column Algebra is again addition, and why should division be involved with addition? We normally see division involved with multiplication and addition involved with subtraction.
> 
> But there has to be a link, because in PPT of 9, 40, 41, where a=4 and b=5 and so 4+5=9, that is what drove me over here to the Column Algebra. So in the next several days, as I digest this magnificient beautiful proof, I will try to answer the WHY, thereof.
> 
> Thank you dear lord god almighty 231PU, thank you graciously dear lord for letting me see the light of day. Atom.
> 
> AP

Mathematicians don't do this because it is probably THE most inefficient way to
test for primes.

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#425161 — Re: One of AP's most beautiful proofs to date-- and a waste.

On Sat, 06 Oct 2018 21:31:52 -0700, eastside.erik wrote:
> On Wednesday, October 3, 2018 at 11:32:48 PM UTC-7, Archimedes Plutonium
> wrote:
...[snip 252 lines]
>> And then, after doing several Columns for Odd Numbers (mind you not
>> even numbers but Odd Numbers) I realized that all odd numbers can be
>> instantly recognized as composite or prime.
>> 
>> 5   0 4   1 3   2
>> 
>> examine horizontals and do division where we discount the division by 1
>> or 0
>> 
>> 7  0 6  1 5  2 4  3
>> 
>> no divisions possible, because well, 7 is prime
>> 
>> 9   0 8   1 7   2 6   3 5   4
>> 
>> Notice we have 6 divided by 3, hence 9 is composite
>> 
>> 11  0 10  1 9    2 8    3 7    4 6    5
>> 
>> No division possible, because 11 is prime
>> 
>> now skip down to 21 because the other primes show the same -- unable to
>> divide
>> 
>> 21    0 20   1 19    2 18    3 17    4 16   5 15   6 14   7 13   8 12  
>> 9 11   10
>> 
>> Now we have several divisions by factors possible we have 18/3
>> outright, but also factoring division to lowest terms 15/6, and 12/9
>> 
>> Now let us test this theory on the nearby prime 23, to see that there
>> are no outright divisions and no factoring to lowest terms division
>> 
>> 23   0 22   1 21   2 20   3 19   4 18   5 17   6 16   7 15   8 14   9
>> 13   10 12   11
>> 
>> So, I see absolutely no outright divisions nor any factoring division
>> into lowest terms, and that is because 23 is prime.
...[snip 37 lines]
> 
> Mathematicians don't do this because it is probably THE most inefficient
> way to test for primes.

In real life, the method AP demos is inefficient [it is an O(n) method]
but in AP-life, where "instantly" is the cost of writing out 2n numbers
in a row and then seeing if two consecutive numbers in the row have a
common divisor > 1, efficiency is perfect.

What I find more surprising than the inefficiency of the method is that
it actually is a method that will work.  To see this, note that AP's
examples imply the claim that if n is composite, there exists an 
integer j giving us two pairs of numbers (j-1, n-j), (j, n-j-1) such 
that gcd(n-j, j) > 1, while if n is prime, there does not exist such j.

To prove 'if' case: Let d>1 be a divisor of n. (d exists because n is
composite.)  Set j=d.  As d|n, we have d|(n-d), QED.

To prove other case:  If n is prime, we have gcd(n, j) = 1 for all j<n, 
j>1.  Now gcd(n-j, j) = gcd(n, j) = 1 for all j<n, j>1. QED.
[Or: In pairs (h,i),(j,k), if gcd(i,j) = d > 1, write i=f*d, j=g*d;
as n = i+j = (f+g)*d, n is composite, contradicting that n is prime.]

-- 
jiw

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#425163 — Re: One of AP's most beautiful proofs to date-- and a waste.

Thanks James Waldby, will use your i j notation

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#425165 — concept of prime should include concept of coprime Re: One of AP's most beautiful proofs to date--

On Sunday, October 7, 2018 at 11:32:27 PM UTC-5, James Waldby wrote:

> 
> In real life, the method AP demos is inefficient [it is an O(n) method]
> but in AP-life, where "instantly" is the cost of writing out 2n numbers
> in a row and then seeing if two consecutive numbers in the row have a
> common divisor > 1, efficiency is perfect.
> 
> What I find more surprising than the inefficiency of the method is that
> it actually is a method that will work.  To see this, note that AP's
> examples imply the claim that if n is composite, there exists an 
> integer j giving us two pairs of numbers (j-1, n-j), (j, n-j-1) such 
> that gcd(n-j, j) > 1, while if n is prime, there does not exist such j.
> 
> To prove 'if' case: Let d>1 be a divisor of n. (d exists because n is
> composite.)  Set j=d.  As d|n, we have d|(n-d), QED.
> 
> To prove other case:  If n is prime, we have gcd(n, j) = 1 for all j<n, 
> j>1.  Now gcd(n-j, j) = gcd(n, j) = 1 for all j<n, j>1. QED.
> [Or: In pairs (h,i),(j,k), if gcd(i,j) = d > 1, write i=f*d, j=g*d;
> as n = i+j = (f+g)*d, n is composite, contradicting that n is prime.]
> 
> -- 
> jiw

The above is not a proof of the AP Conjecture on columns. That conjecture involves the idea that Outright Division is different from NonCoprime Reduce to Lowest Terms.

Perhaps there is no difference between say 18/3 in 21 and 15/10 in 21. But I tend to see a difference between a Outright division and a Reduce to Lower Terms. This means the concept of prime has more to it than the Old Math notion of raw division.

AP

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#425166 — Re: concept of prime should include concept of coprime Re: One of AP's most beautiful proofs to date--

On Monday, October 8, 2018 at 12:35:48 AM UTC-5, Archimedes Plutonium wrote:
> On Sunday, October 7, 2018 at 11:32:27 PM UTC-5, James Waldby wrote:
> 
> > 
> > In real life, the method AP demos is inefficient [it is an O(n) method]
> > but in AP-life, where "instantly" is the cost of writing out 2n numbers
> > in a row and then seeing if two consecutive numbers in the row have a
> > common divisor > 1, efficiency is perfect.
> > 
> > What I find more surprising than the inefficiency of the method is that
> > it actually is a method that will work.  To see this, note that AP's
> > examples imply the claim that if n is composite, there exists an 
> > integer j giving us two pairs of numbers (j-1, n-j), (j, n-j-1) such 
> > that gcd(n-j, j) > 1, while if n is prime, there does not exist such j.
> > 
> > To prove 'if' case: Let d>1 be a divisor of n. (d exists because n is
> > composite.)  Set j=d.  As d|n, we have d|(n-d), QED.
> > 
> > To prove other case:  If n is prime, we have gcd(n, j) = 1 for all j<n, 
> > j>1.  Now gcd(n-j, j) = gcd(n, j) = 1 for all j<n, j>1. QED.
> > [Or: In pairs (h,i),(j,k), if gcd(i,j) = d > 1, write i=f*d, j=g*d;
> > as n = i+j = (f+g)*d, n is composite, contradicting that n is prime.]
> > 
> > -- 
> > jiw
> 
> The above is not a proof of the AP Conjecture on columns. That conjecture involves the idea that Outright Division is different from NonCoprime Reduce to Lowest Terms.
> 
> Perhaps there is no difference between say 18/3 in 21 and 15/10 in 21. But I tend to see a difference 

Correction 15/6 in 21

between a Outright division and a Reduce to Lower Terms. This means the concept of prime has more to it than the Old Math notion of raw division.
> 
> AP

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#425108 — Re: One of AP's most beautiful proofs to date-- the entire Pattern of Primes Re: the fingerprint of being prime // AP wants to do one better on Ulam's Prime Spiral

On Wednesday, October 3, 2018 at 11:32:48 PM UTC-7, Archimedes Plutonium wrote:
> NOW QUESTION TO COMPUTERS around the world, how easy is it for them to Engineer a computer to scan through a 604 digit odd number and see if there is no-factoring-division and no outright division.
> 
> I mean, how amenable is it to engineer computers to code them to scan through a 604 Digit Number to check for division?

The computer needs to check (10^604)/2 rows in your table.

It is far too optimistic to think a computer could check a billion rows a second, but let's be generous and assume it could.

That takes (10^604)/2 / 10^9 seconds = 1.6*10^587 years.

Too long to wait, have a billion computers working on it at the same time.
That takes 1.6*10^578 years.

Too long to wait, have a billion solar systems each with a billion computers.
That takes 1.6*10^569 years.

Too long to wait, have a billion universes each with a billion solar systems
each with a billion computers.
That takes 1.6*10^560 years.

That is roughly 10^550 times the expected life of the universe.

And that is just to check ONE number near 10^604.
And you still have to wait for the time to send the results.
And you have to figure out how and where you are going to store that.
And you need to check all the other 10^604-1 numbers to build your list of primes.

If you want to begin to try it yourself then you can work on

9999999999999999999999999999999999999999999999999999999999999999999999\
9999999999999999999999999999999999999999999999999999999999999999999999\
9999999999999999999999999999999999999999999999999999999999820999999999\
9999999999999999999999999999999999999999999999999999999999999999999999\
9999999999999999999999999999999999999999999999999999999999999999999999\
9999999999999999999999999999999999999999999999999379000000000000000000\
0000000000000000000000000000000000000000000000000000000000000000000000\
0000000000000000000000000000000000000000000000000000000000000000000000\
0000000000000000000000000000000000000111159

which is just a tiny bit less than 10^604.
If you can find the factors of that then you will probably astonish everyone.

It is good that you have seen the light.
Once you've gone crank you'll never go back.

Bean Counter

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#425164 — bean counter gives a test Re: One of AP's most beautiful proofs to date-- the entire Pattern of Primes

On Sunday, October 7, 2018 at 12:40:40 AM UTC-5, qbwr...@gmail.com wrote:

> 
> 9999999999999999999999999999999999999999999999999999999999999999999999\
> 9999999999999999999999999999999999999999999999999999999999999999999999\
> 9999999999999999999999999999999999999999999999999999999999820999999999\
> 9999999999999999999999999999999999999999999999999999999999999999999999\
> 9999999999999999999999999999999999999999999999999999999999999999999999\
> 9999999999999999999999999999999999999999999999999379000000000000000000\
> 0000000000000000000000000000000000000000000000000000000000000000000000\
> 0000000000000000000000000000000000000000000000000000000000000000000000\
> 0000000000000000000000000000000000000111159
> 
> which is just a tiny bit less than 10^604.
> If you can find the factors of that then you will probably astonish everyone.

I do not need to astonish anyone after having shown that everyone was wrong on the ellipse. The Ellipse is never a conic, always a cylinder section, and you are just a side show bean counter.

In your number above, I am not going to eyestrain myself with the full number but if you examine just the end piece, assuming 3 divides evenly up to that point

55581  55578 then 3 is a factor
55580  55579 

As for the beginning 111159 is factorable by 3 provided the rest of string is factorable.

AP

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#425167 — Re: bean counter gives a test Re: One of AP's most beautiful proofs to date-- the entire Pattern of Primes

On Sunday, October 7, 2018 at 10:28:52 PM UTC-7, Archimedes Plutonium wrote:
> On Sunday, October 7, 2018 at 12:40:40 AM UTC-5, qbwr...@gmail.com wrote:
> > 9999999999999999999999999999999999999999999999999999999999999999999999\
> > 9999999999999999999999999999999999999999999999999999999999999999999999\
> > 9999999999999999999999999999999999999999999999999999999999820999999999\
> > 9999999999999999999999999999999999999999999999999999999999999999999999\
> > 9999999999999999999999999999999999999999999999999999999999999999999999\
> > 9999999999999999999999999999999999999999999999999379000000000000000000\
> > 0000000000000000000000000000000000000000000000000000000000000000000000\
> > 0000000000000000000000000000000000000000000000000000000000000000000000\
> > 0000000000000000000000000000000000000111159
> > 
> > which is just a tiny bit less than 10^604.
> > If you can find the factors of that then you will probably astonish everyone.
> 
> I do not need to astonish anyone after having shown that everyone was wrong on the ellipse. The Ellipse is never a conic, always a cylinder section, and you are just a side show bean counter.
> 
> In your number above, I am not going to eyestrain myself with the full number but if you examine just the end piece, assuming 3 divides evenly up to that point
> 
> 55581  55578 then 3 is a factor
> 55580  55579 
> 
> As for the beginning 111159 is factorable by 3 provided the rest of string is factorable.

I'll guarantee you that that number is not divisible by 3 or by any other
small factor that you might be able to come up with, but it is the product
of two large integers.

If any competent working mathematician, who hasn't lost his or her mind,
has been convinced by your claim about ovals then you should certainly
get them to announce this. I don't believe that anyone except you has
been convinced by your years of saying it is because you peered down
your tube and imagine what you see.

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#425191 — Re: Archimedes "Village Idiot" Plutonium flunked the Math Test of a lifetime-generation test

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

> Moroney must be autistic to call everyone else such

Pluto, you _demonstrate_ your autism by REPEATEDLY reposting the same old
crap with stalker lists, poor ascii art and non-proofs. Why else would you
be so illogical? Your autism (plus maybe OCD) OWNS you!

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#425208 — AP's tool to determine if prime or composite-- Odd Rectangles Re: the fingerprint of being prime // AP wants to do one better on Ulam's Prime Spiral

On Sunday, October 7, 2018 at 12:40:40 AM UTC-5, qbwr...@gmail.com wrote:

> If you want to begin to try it yourself then you can work on
> 
> 9999999999999999999999999999999999999999999999999999999999999999999999\
> 9999999999999999999999999999999999999999999999999999999999999999999999\
> 9999999999999999999999999999999999999999999999999999999999820999999999\
> 9999999999999999999999999999999999999999999999999999999999999999999999\
> 9999999999999999999999999999999999999999999999999999999999999999999999\
> 9999999999999999999999999999999999999999999999999379000000000000000000\
> 0000000000000000000000000000000000000000000000000000000000000000000000\
> 0000000000000000000000000000000000000000000000000000000000000000000000\
> 0000000000000000000000000000000000000111159
> 
> which is just a tiny bit less than 10^604.

Alright, I need a really fast prime to composite tool.

Let me try the AP Geometry Rectangle Method, newly invented for this purpose.

Let me try the Rectangle method on a small prime first-- say 67.

The idea is that if a odd number is prime, it cannot form a rectangle with length x width as odd numbers, and remain a straight line segment such as 67, whereas 69 can be 3*23

So, give me a odd number, say 67. The first immediate thing I do is divide by 3, which if evenly divided, then it is odd composite, if not, then further testing.

67/3 = 22+1/3

Next, take square root of 67 which is 8.18.... and although it is not a rectangle, but a square, like 7*7 eliminates 67 as a odd square.

Now the division by 3 tells us one more important fact, that 23 is the highest odd number that can make 67 a odd composite rectangle. So we need to go with 21, 19, 17, ... , 3 in pairs to see if they form a odd rectangle. Sounds tedious, but now we do 67/5

67/5 = 13 + 2/5

This tells us that we now only need look at 7, 9, 11 to form a odd rectangle and those cannot work. Hence 67 is prime.

Now let us try that out on 121 just to be sure. We want an odd rectangle, and if we cannot get one we know it is prime.

first divide by 3

121/3 = 40+1/3
next, take square root and is 11, so is a square
next, divide by 5
121/5 = 24+1/5 and this tells us, only the odd 7,11,13,17,19,23 can form a rectangle and 7*17 comes close with 119
So, the next step would have been
121/7 = 17+ 2/7 which tells me the only solutions are 11,13 and we already know 11 square

Let us try this out on 127
First divide by 3
127/3 = 42+1/3
Next take square root 127 = 11.26... so to not be a square, for we need a odd rectangle
Next divide by 5
127/5 = 25+2/5 this narrows our search to that of 23 to 7
Next divide by 7
127/7 = 18+1/7 this narrows our search to 17 to 11 and now it ends because 11*13= 143

So, let me try a version of this on the above huge number.

AP

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#425244 — Re: Archimedes "Village Idiot" Plutonium flunked the Math Test of a lifetime-generation test

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

>A few clowns short of a circus.

>     A few clues shy of a solution.

>     A few brains short of a mind.

>     A few centimeters short of a meter.

>     A few kernels short of an ear.

>     A few links shy of a chain.

>     A few open splices.

>     A few peas short of a casserole.

>     A few pickles short of a jar.

>     A few pies short of a holiday.

>     99 short of 100

>     A few points short of a polygon.

Once again, Archie, you describe yourself perfectly!

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