**Orderliness in Primal Chaos**

Topic

OUR PURPOSE

Carlos Paris' Method

Sack's Spiral

To investigate prime numbers using visual elements

Create our own method of visualizing prime numbers

Jason Davies' Method

How it works...

All positive integers lined up (n = any positive integer)

multiples of positive integers joined together in semi-circles (with diameter of n)

n should be joined with the semi-circles with diameters that are factors of n

Prime number: if there are only two semi-circles (with diameters 1 and n)

Example:

Non Prime Number:

The number 24 will be joined with semi-circles that have a diameter of: 1, 2, 3, 4, 6, 8, 12, and 24 (factors of 24)

Prime Number:

The prime number 19 is only joined with two semi-circles, which will have diameters of 1 and 19 (1 and n)

How it works...

Very similar to Davies' (semi-circle) method

instead of semi-circles, use circles to represent positive integers (n = any positive integer)

multiples of positive integers joined together in circles (with diameter of n)

n should be joined with the circles with diameters that are factors of n

Prime number: if it only two circles (with diameters 1 and n)

Example

Non Prime Number:

The number 18 will be joined with circles that have a diameter of: 1, 2, 3, 6, 9, and 18 (factors of 18)

Prime Number:

The prime number 13 is only joined with two circles, which will have diameters of 1 and 13 (1 and n)

How it works...

positive integers are spiraled in circles

numbers spiraled so that all the square numbers (4, 9, 16...) line up

prime numbers represented by dark dots, on prime numbers represented by light dots

Trend:

prime numbers form parabolas

Usage:

visual representation of prime numbers

used to find factors of composite numbers

Ulam Spiral

How it works...

place positive integers in a grid, spiraling out

dark spots represent prime numbers, light spots/empty space represent non prime numbers

Trend:

prime numbers tend to line up along diagonal lines

prime numbers line up along horizontal and vertical lines (less prominent)

Our Design

How it works...

spiral positive integers around circle into ten "columns"

color in sections containing prime numbers

Trends:

prime numbers are mainly distributed in the rows of odd numbers (except for 5, becuase any number n which is equal to 5mod10 is a multiple of 5)

BIBLIOGRAPHY

" Composite Number." Definition of Composite Number. N.p., 2013. Web. 14 Oct. 2013. <http://www.mathsisfun.com/definitions/composite-number.html>.

Nom, Penny. "Prime Numbers." Prime Numbers. N.p., n.d. Web. 14 Oct. 2013. <http://mathcentral.uregina.ca/qq/database/qq.09.95/hewitt1.html>.

Paris, Carlos. "Primal Chaos (Visualizations)." Primal Chaos. Yola, n.d. Web. 14 Oct. 2013. <http://www.sievesofchaos.com/>.

"Prime Spiral (Ulam Spiral)." Math Images RSS. N.p., n.d. Web. 14 Oct. 2013. <http://mathforum.org/mathimages/index.php/Prime_spiral_%28Ulam_spiral%29>

Sacks, Robert. "Number Spiral." Numberspiral.com. N.p., 2007. Web. 14 Oct. 2013. <http://www.numberspiral.com/index.html>.

Weisstein, Eric W. "Prime Number." Wolfram Mathworld. Mathematica Technology, n.d. Web. 14 Oct. 2013. <http://mathworld.wolfram.com/PrimeNumber.html>.

Wilson, Mark. "Infographic: Visualizing Prime Numbers, For People Who Suck At Math | Co.Design | Business Design." Co.Design. Co.Design, 1 Dec. 2011. Web. 14 Oct. 2013. <http://www.fastcodesign.com/1670397/infographic-visualizing-prime-numbers-for-people-who-suck-at-math>.

**Jung Min & Millie**