Determining Prime Numbers
Positive whole numbers, otherwise known as integers, can be classified into two types: prime or composite. A number is said to be prime if it has no other divisor except 1 and itself. For example, 17 is a prime number since there is no whole number that can divide it and produce an integer quotient other than 1 and 17.
Otherwise, the number is composite, pertaining to the fact that it is divisible by positive numbers that are not equal to one or itself. An instance is the number 24, which is divisible by 2, 3, 4, 6, 8 and 12 aside from 1 and 24.
Note that zero and one are neither prime nor composite, thus they are known to be special numbers.
Here are some examples:
Example 1: 27
27 is equal to 9 x 3 and 1 x 27. Having four divisors, it is classified as a composite number.
Example 2: 36
36 is equivalent to 6 x 6, 9 x 4, 18 x 2, 12 x 3 and 36 x 1. Thus it is a composite number.
A good rule to remember is that all even numbers or multiples of 5 (those digits ending with 5 or 0) are composite, since they are divisible by 2 and 5 respectively.
Example 3: 23
The number only has two divisors: 23 and 1. Aside from those, none can be found (unless you consider decimals, but prime and composite numbers only apple to positive whole numbers). Hence it is a prime number.
But what if you are given a number so large you cannot decipher whether it is prime or composite...and you only have two minutes to answer? This is when the following methods of testing a prime number comes into the frame.
The Divisibility Test
This test can be done if you are well and truly acquainted with all the divisibility rules as listed below (but there are more aside from that!):
This test involves only one single step: test whether all numbers below the given number divides the latter. For example, 13 cannot be divided by any number lower that itself except 1. Thus it is prime.
Here is another example:
The above pattern of non-divisibility goes on until you reach the number 37, thus it is prime.
However, if you are given a number like 367, this method becomes impractical, hasty and downright time-wasting. This is when you use the second method.
The Prime Number Test
This test is relatively more practical since you only have to get the square root of the number (rounded off) and test all prime numbers below it for divisibility. If none divides the given number, it is prime.
Let us work on the example given earlier:
The square root of 367 is 19.15724, which can be rounded off as 19.
This goes on until you reach the lowest prime number - 2. Hence the given number is prime.
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