vb.net - Prime Number Visual Basic -

i have assignment , says:

you have been provided working program named prime.
has 1 input single integer.
when “find prime number” button pushed, nth prime number identified.

for example:

if 4 entered , button clicked, response “the 4th prime number 7” displayed. , if 9 entered, response “the 9th prime number 23” displayed.

the program 100% accurate, correct locates nth prime.
problem comes in when try find larger prime number.

for example:

if 10000 entered , button clicked, response “the 10000th prime number 104729” displayed. correct answer; however, took on 48 seconds on i7 computer find solution. imagine how long take find millionth prime number. task analyze problem find more efficient solution make program more useful. first must understand how code provided works. there exercise @ end of document. use run code hand. once understand how works, analyze problem of finding prime number make program operate more efficiently. reason why program slow large numbers because preform lot of unnecessary calculations. not must use own code. cannot use prebuilt prime number routines, functions, or libraries; doing result in 0 assignment. thinking needs done way solve this.

he says best way use arrays, don't know how use arrays solve problem. says keep division (mod) @ minimum if statements.

here code provided us:

option strict on public class form1   private sub positionbox_textchanged(byval sender system.object, byval e system.eventargs) handles positionbox.textchanged     if isnumeric(positionbox.text)         if decimal.parse(positionbox.text) >= 1             findprimebtn.enabled = true         else             findprimebtn.enabled = false         end if     else         findprimebtn.enabled = false     end if end sub  private sub findprimebtn_click(byval sender system.object, byval e system.eventargs) handles findprimebtn.click     dim finalposition long     dim finalprime, long     dim number long = 2     dim currentposition long = 1      dim elapsed system.timespan      dim sw stopwatch = new stopwatch()      sw.start() 'starts clock     dim isprime boolean      finalposition = long.parse(positionbox.text)      = currentposition mod 2     while (currentposition > 2 , <> 0)         isprime = true     end while      while (currentposition <= finalposition)         isprime = true          x = 2 number - 1             if number mod x = 0                 isprime = false             end if         next          if isprime             finalprime = number             currentposition += 1         end if         number += 1     end while      elapsed = sw.elapsed() 'captures elapsed time took compute result      resultlbl.text = "the " + finalposition.tostring() + "th " + finalprime.tostring()     elapsedtimelbl.text = "elapsed time " + elapsed.tostring()  end sub end class 

check out this article , specifically, says: effort can reduced selecting prime numbers candidate factors. furthermore, trial factors need go no further \scriptstyle\sqrt{n} because, if n divisible number p, n = p × q , if q smaller p, n have earlier been detected being divisible q or prime factor of q.

i think wants store primes find in array , iterate through set of primes in array instead of iterating through each or each odd number.

not sure if he'll allow import system.math, square root function is, speeds up. suppose ask...

anyways, i'm not using stored array of found prime numbers, , didn't variable names, if helps, working this:

option strict on imports system.math  public class form1     private sub positionbox_textchanged(byval sender system.object, byval e system.eventargs) handles positionbox.textchanged         if isnumeric(positionbox.text)             if decimal.parse(positionbox.text) >= 1                 findprimebtn.enabled = true             else                 findprimebtn.enabled = false             end if         else             findprimebtn.enabled = false         end if     end sub      private sub findprimebtn_click(byval sender system.object, byval e system.eventargs) handles findprimebtn.click         dim currentprimesequence long = 1         dim finalprimesequence long         dim prime_possible double = 2         dim foundprime double         dim test_div double         'dim long          dim elapsed system.timespan          dim sw stopwatch = new stopwatch()          sw.start() 'starts clock         dim isprime boolean          finalprimesequence = long.parse(positionbox.text)          'even = currentprimesequence mod 2         'while (currentprimesequence > 2 , <> 0)         '   isprime = true         'end while         findprimebtn.enabled = false          while (currentprimesequence <= finalprimesequence)             isprime = true   ' until proven false              test_div = 2             while isprime , (test_div <= sqrt(prime_possible))                 isprime = (prime_possible mod test_div > 0)                 test_div = test_div + 1 - cdbl(test_div > 2)       ' skip odd numbers after 2                 'if test_div = 2                 '   test_div = test_div + 1                 'else                 '   test_div = test_div + 2                 'end if             loop              'for test_div = 2 sqrt(prime_possible)         ' test if divisible number 2 square root of candidate, skip #s             '   if prime_possible mod test_div = 0             '       isprime = false             '       exit       ' or change while isprime , (test_div < prime_possible)             '   end if             'next              if isprime                 foundprime = prime_possible                 if currentprimesequence mod 100000 = 0                     debug.print(cstr(currentprimesequence) + " " + cstr(foundprime) + " " + sw.elapsed().tostring)                 end if                 currentprimesequence += 1             end if             prime_possible += 1         end while          elapsed = sw.elapsed() 'captures elapsed time took compute result          resultlbl.text = "the " + finalprimesequence.tostring() + "th " + foundprime.tostring()         elapsedtimelbl.text = "elapsed time " + elapsed.tostring()         findprimebtn.enabled = true     end sub end class 

on pc, found millionth prime in 28 seconds, can't compare performance across machines.