In this blog, I have written quite a number of articles about prime numbers. In one of my posts, I have emphasized that geometrically, the dots that represent a prime number can only be arranged in a 1 x p rectangular arrangement where p is prime. Composite numbers on the other hand, can be arranged geometrically into more than 1 rectangular arrangements.
Stephen Von Worley has given a more beautiful definition of primes and composites in his Factor Dance Animation . The brilliant animation is a rearrangement of dots (circles) that represent numbers into different groups every second. Its aim is to show the “compositeness” and “primeness” of numbers from 1 up to 10,000. Worley’s program used the algorithm Brent Yorgey, the writer of The Mathematics Less Traveled.
You can read more about the animation at Wolrey’s post titled Dance, Factors, Dance. You may also want to watch the beautiful animation.
The Composite Number Tree by Jeffrey Ventrella is the latest animation I have discovered recently through Colleen Young’s Mathematics, Learning and Web 2.0. The animation consists of numbers “falling from heaven,” each of which attaching itself to its greatest divisor. The prime numbers attached themselves to the main trunk.
The Composite Number Tree can be used as a tool for discussing about prime numbers. It also shows some interesting patterns. Please visit the Composite Number Tree website to read more about it.
A prime number is a integer greater than that is divisible only by 1 and itself. A number that is not prime is composite.
To determine whether a number is prime or not, we have to divide it by all numbers between 1 and itself . For example, to say that 257 is prime, we must be sure that it is not divisible by any number between 1 and 257. In this discussion, the word “numbers” refer to positive integers.
Are you prime or not?
Dividing a number by all numbers between 1 and itself is burdensome especially for large numbers. In this post, we discuss a shorter way of determining if a number is prime and explain why the method works. » Read more