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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

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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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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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