See Hahn Chapter "Loops"

Problem $1$: The Prime Directive $[$MG Also$]$

Filename:

Function Declaration:

function $[$isItPrime$]=$ primeDirective$($numberToTest$)$ A number is prime if it is not an exact multiple of any other number except itself

and $1,$ i$.$e$.$ if it has no factors except itself and $1.$ The easiest plan of attack then is

as follows. Suppose P is the number to be tested. See if any numbers N can be

found that divide into $P$ without remainder. If there are none, $P$ is prime. Which

numbers $N$ should we try? Well, we can speed things up by restricting $P$ to odd

numbers, so we only have to try odd divisors N $.$ When do we stop testing? When

$N=P?$ No$,$ we can stop a lot sooner. In fact, we can stop once $N$ reaches $\sqrt[\phantom{2}]{?}P,$ since if

there is a factor greater than $\sqrt[\phantom{2}]{?}P$ there must be a corresponding one less than $\sqrt[\phantom{2}]{?}P,$

which we would have found. And where do we start? Well, since $N=1$ will be a

factor of any P $,$ we should start at $N=3.$ The structure plan is as follows

Input $P$ from the input parameter of the function

Initialize $N$ to $3$

Find remainder $R$ when $P$ is divided by $N$

While $R0$ and repeat:

Increase $N$ by $2$

Find $R$ when $P$ is divided by $N$

If $R0$ then

$P$ is prime

Else

$P$ is not prime

Stop

Return the correct value

Note that there may be no repeats

$R$ might be zero the first time.

Note also that there are two conditions under which the loop may stop.

Consequently, an if is required after completion of the loop to determine which

condition stopped it$.$

Write the function. Then try it out on the following numbers: $4058879($not prime$),$

$193707721($prime$)$ and $2147483647($prime$).$ Code to call your function

isNumberPrime $=$ round$($rand$*100000)$;

primResult $=$ primeDirective$($isNumberPrime$)$;

$[$By using Matlab$]$