Ttykuu

I am having issue making this code more efficient. The problem to be solved is as follows:

By listing the first six prime numbers: 2, 3, 5, 7, 11, and 13, we can
see that the 6th prime is 13.

What is the 10,001st prime number?

I'm looking to complete this in powershell. My code runs well up until about 4.8k primes.

$incNum1 = 1
$incNum2 = 2
$divisNum = 2 * $incNum2 - 1
$highestNum = 0
$k = 1
$nextNum = 2 * $incNum1 + 1

while($k -lt 6000)

 $upTo = [int][Math]::Ceiling(($nextNum / 2))

 $break = $false

 while($divisNum -lt $upTo)
 $modRes = $nextNum % $divisNum


 if($modRes -eq 0)

 $break = $true

 break
 

 $incNum2++
 $divisNum = 2 * $incNum2 - 1
 

 if(!$break)

 $highestNum = $nextNum

 echo $nextNum

 $k++
 

 $incNum2 = 2
 $divisNum = 2 * $incNum2 - 1

 $incNum1++

 $nextNum = 2 * $incNum1 + 1


echo $highestNum

I'd start with

• removing redundancy


• measuring the time automatically


• output to screen slows down, comment it out

depending on the speed of the computer used I get results of ~74..120 seconds.

Compared with 0.450 secs here with matlalb there IS potential to get better ;-)

## Q:Test2018118CR_207250.ps1

$StartTime = get-date
$PrimeNo = 10001

$incNum1 = 0
$highestNum = 0
$k = 1

while($k -lt $PrimeNo)
 $incNum2 = 2
 $divisNum = 2 * $incNum2 - 1
 $incNum1++
 $nextNum = 2 * $incNum1 + 1

 $upTo = [Math]::Ceiling(($nextNum / 2))
 $break = $false
 while($divisNum -lt $upTo)
 $modRes = $nextNum % $divisNum

 if($modRes -eq 0)
 $break = $true
 break
 
 $incNum2++
 $divisNum = 2 * $incNum2 - 1
 
 if(!$break)
 $highestNum = $nextNum
# "0:1" -f $k,$nextNum
 $k++
 


"## PrimeNo: 0 is 1 calculated in 2 seconds" -f $PrimeNo,$highestNum,
 ((Get-Date)-$StartTime).TotalSeconds

## PrimeNo: 10001 is 104743 calculated in 73,6911884 seconds
## PrimeNo: 10001 is 104743 calculated in 118,3481173 seconds

This get down to around 4 seconds on my 2010 pc.

function Get-nthPrime ([int] $nthPrime )
 $approximateMax = $nthPrime * ([math]::Log($nthPrime) + 2) #https://en.wikipedia.org/wiki/Prime_number_theorem
 $isprime = @ #hash to hold values
 $primeCounter = 0 #count primes we've found
 2..$approximateMax 

Usage

PS C:> Get-NthPrime 10001
104743