Prime and Composite Numbers
“A prime number is a whole number greater than 1 whose only factors are 1 and itself.”
A factor is a whole number that can be divided evenly into another number.
The first few prime numbers are 2, 3, 5, 7, 11, 13, 17, 19, 23, and 29.
“Numbers that have more than two factors are called composite numbers.”
The number 1 is neither prime nor composite.
How To Determine If A Number Is Prime:
Various algorithms have been formulated in an attempt to generate ever-larger prime numbers.
For example, suppose “n” is a whole number, and it is not yet known if n is prime or composite. First, take the square root — or the 1/2 power — of n; then round this number up to the next highest whole number and call the result m. Then find all of the following quotients:
qm = n / m
q(m-1) = n / (m-1)
q(m-2) = n / (m-2)
q(m-3) = n / (m-3)
. . .
q3 = n / 3
q2 = n / 2
The number n is prime if — and only if — none of the q’s, as derived above, are whole numbers.
Examples:
- Is 8 a Prime Number?
No, because it can be made by 2×4=8
- Is 73 a Prime Number?
Yes, as no other whole numbers multiply together to make it.