Visual Prime Pattern identified

In summary,This person has been dreaming about the square roots of prime numbers and has a feeling that the square roots of smaller prime numbers exhibit more "chaotic" behavior in their decimal expansion than the square roots of larger prime numbers.
  • #106
well, since raphie seems to be restricted at the moment, i have to ask, is anyone else following this?
 
Physics news on Phys.org
  • #107
  • #108
dimension10 said:
Wow, but it is rather a hard method. Is it, by any chance, related to the sieve of erasothones?
dimension10 ,
It is a sieve and all prime sieves seem to smack of Eratosthenes to me. I'm approaching it in my head from a different angle though. My method relates to the fact that a square number added to a prime number only equals another square number when the square added to the prime is equal to ((n-1)/2)^2. Or basically:

n+((n-1)/2)^2 = ((n+1)/2)^2

Its true that all integers share this property despite their primality but composite numbers will have other square congruence, less than the ((n-1)/2)^2 ratio, according to their integer divisors.

These ratios form a lattice when you deal with integers at their square root the way I have. This lattice creates a parabolic coordinate system. This coordinate system is what I'm using to exploit the sieve.

jeremy
* http://en.wikipedia.org/wiki/Congruence_of_squares
* http://en.wikipedia.org/wiki/Parabolic_coordinates
 
  • #109
JeremyEbert said:
Here is a visual prime pattern:
http://plus.maths.org/content/catching-primes
I have developed one of my own based upon trig, square roots and the harmonic sequence.
Here is an animation/application that shows the formula visually:
http://tubeglow.com/test/Fourier.html
Thoughts? Questions?

Ok, maybe I'm the first that doesn't see it. In the first link, I see the primes. In the second link I don't see what identifies the primes. Clue me in.
 
  • #110
PAllen said:
Ok, maybe I'm the first that doesn't see it. In the first link, I see the primes. In the second link I don't see what identifies the primes. Clue me in.

PAllen,
As an intger n increases, the first blue horizontal line north (north/south = y axis) of the green line (east/west = x axis) increases by the square root of n. The intersections of the vertical lines and the concentric circles at the square root of n (blue horizontal line) equate to the divisors d of n by (n-d^2)/2d = 0 mod(.5). Does that help?

Jeremy
 
  • #111
a spherical version of my equation:
http://dl.dropbox.com/u/13155084/PL3D2SPHERE/P_Lattice_3D_Sphere.html [Broken]
 
Last edited by a moderator:
  • #112
Raphie (quoted below),

I'm probably late on this but when saying things like:
(11+13/((1+1)+(1+3)) = 4

You should see what mod9 (*notated by %9) gives you...

I.e.
((x+y)/(x%9+y%9))

It matches most of your numbers...
since mod9 is the infinite digital sum.. (digital sum taken as many times as possible until a single digit is reached)

I.e.
(11+13/((1+1)+(1+3)) == ((11+13)/(11%9+13%9))

Raphie said:
A POSSIBLY RELATED SEQUENCE
Suppose the sum of the digits of prime(n) and prime(n+1) divides prime(n) + prime(n+1). Sequence gives prime(n).
http://oeis.org/A127272
2, 3, 5, 7, 11, 17, 29, 41, 43, 71, 79, 97, 101, 107...

e.g.
(2 + 3)/(2+3) = 1
(3+5)/(3+5) = 1
(5+7)/(5+7) = 1
(7+11)/(7+(1+1)) = 2
(11+13/((1+1)+(1+3)) = 4
(17+19/((1+7)+(1+9)) = 2
(29+31/((2+9)+(3+1)) = 4
(41+43/((4+1) + (4+3)) = 7
(43+47/((4+3)+(4+7)) = 5
(71+73)/((7+1)+(7+3)) = 8
(79+83)/((7+9)+(9+7)) = 5
(97+101)/((9+7)+(1+0+1)) = 11
(101+103)/((1+0+1) + (1+0+3) = 34
(107+109)/((1+0+7)+(1+0+9) = 12

ALSO...
Numbers n such that 1 plus the sum of the first n primes is divisible by n+1.
http://oeis.org/A158682
2, 6, 224, 486, 734, 50046, 142834, 170208, 249654, 316585342, 374788042, 2460457826, 2803329304, 6860334656, 65397031524, 78658228038

002 - 002 = 000 = K_00
012 - 006 = 006 = K_02 (Max)
600 - 224 = 336 = K_10 (Lattice Max known)
924 - 486 = 438 = K_11 (Lattice Max known)

6/(5+1) = 1
42/(6+1) = 6
143100/(224+1) = 636
775304/(486+1) = 1592

Like I said, especially given that these two progressions are ones I came across in the process of writing that last post to you, "hmmmm..."

RELATED PROGRESSIONS
Integer averages of first n noncomposites for some n.
http://oeis.org/A179860
1, 2, 6, 636, 1592, 2574, 292656, 917042, 1108972, 1678508, 3334890730, 3981285760, 28567166356, 32739591796, 83332116034

a(n) is the sum of the first A179859(n) noncomposites.
http://oeis.org/A179861
1, 6, 42, 143100, 775304, 1891890, 14646554832, 130985694070, 188757015148, 419047914740, 1055777525624570390, 1492138298614167680, 70288308055831268412, 91779857115464381780, 571686203669195590338

Numbers n that divide the sum of the first n noncomposites.
http://oeis.org/A179859
1, 3, 7, 225, 487, 735, 50047, 142835, 170209, 249655, 316585343, 374788043, 2460457827, 2803329305, 6860334657

This number, in particular, I find interesting...
142835 = 5*7^2*11*53 = (142857 - par_8) = (142857 - 22)
vs. 1/7 = .142857 (repeating)
Indexing from 0, 142857 is the 24th Kaprekar Number

1, 3, 7 and 225, the 1st 4 terms in that last sequence above == (2^1 - 1)^1, (2^2 - 1)^1, (2^3 - 1)^1, (2^4 - 1)^2.

- RF
 
  • #113
update:
http://dl.dropbox.com/u/13155084/prime.png [Broken]
 
Last edited by a moderator:
<h2>1. What is a Visual Prime Pattern?</h2><p>A Visual Prime Pattern is a recurring and identifiable visual element or design that is present in a variety of different images or visual media. It can be a shape, color, texture, or any other visual characteristic that is consistently found in a group of images.</p><h2>2. How is a Visual Prime Pattern identified?</h2><p>A Visual Prime Pattern is identified through a process of visual analysis and comparison. Scientists use software and algorithms to analyze large sets of images and identify common visual elements that occur across multiple images.</p><h2>3. What is the purpose of identifying Visual Prime Patterns?</h2><p>The purpose of identifying Visual Prime Patterns is to gain a better understanding of visual information and how it is perceived and processed by the human brain. It can also help in the development of new technologies for image recognition and organization.</p><h2>4. Can Visual Prime Patterns be found in non-visual media?</h2><p>Yes, Visual Prime Patterns can also be found in non-visual media such as audio and text. In these cases, they may refer to recurring patterns in sound or language that can be identified through similar analysis techniques.</p><h2>5. How can Visual Prime Patterns be used in practical applications?</h2><p>Visual Prime Patterns can be used in a variety of practical applications, such as in image and video editing, advertising and marketing, and even in the development of artificial intelligence. By understanding how visual elements are perceived and processed, we can create more effective and visually appealing designs and technologies.</p>

1. What is a Visual Prime Pattern?

A Visual Prime Pattern is a recurring and identifiable visual element or design that is present in a variety of different images or visual media. It can be a shape, color, texture, or any other visual characteristic that is consistently found in a group of images.

2. How is a Visual Prime Pattern identified?

A Visual Prime Pattern is identified through a process of visual analysis and comparison. Scientists use software and algorithms to analyze large sets of images and identify common visual elements that occur across multiple images.

3. What is the purpose of identifying Visual Prime Patterns?

The purpose of identifying Visual Prime Patterns is to gain a better understanding of visual information and how it is perceived and processed by the human brain. It can also help in the development of new technologies for image recognition and organization.

4. Can Visual Prime Patterns be found in non-visual media?

Yes, Visual Prime Patterns can also be found in non-visual media such as audio and text. In these cases, they may refer to recurring patterns in sound or language that can be identified through similar analysis techniques.

5. How can Visual Prime Patterns be used in practical applications?

Visual Prime Patterns can be used in a variety of practical applications, such as in image and video editing, advertising and marketing, and even in the development of artificial intelligence. By understanding how visual elements are perceived and processed, we can create more effective and visually appealing designs and technologies.

Similar threads

  • Linear and Abstract Algebra
Replies
1
Views
4K
  • Linear and Abstract Algebra
Replies
15
Views
7K
Replies
9
Views
6K
Replies
2
Views
794
  • Special and General Relativity
Replies
9
Views
3K
  • Linear and Abstract Algebra
Replies
13
Views
3K
  • Special and General Relativity
Replies
5
Views
1K
Replies
1
Views
2K
  • Special and General Relativity
2
Replies
40
Views
2K
  • General Discussion
Replies
33
Views
4K
Back
Top