ReDim PF(0) As Long

ReDim Shared As Long Prime_Factors(1 To 168)

Dim As Long num1, num2

Screen _NewImage(1280, 900, 32)

_Delay .5

_ScreenMove _Middle



Init



Do

    Input "Give me the top number of your fraction (from 1 to 1016064.  0 quits) =>"; num1

    If num1 <= 0 Or num1 >= 1016064 Then System

    Input "Give me the bottom number of your fraction (from 1 to 1016064.  0 quits) =>"; num2

    If num2 <= 0 Or num2 >= 1016064 Then System

    Simplify num1, num2

    Print "Simplied those two values become: "; num1; "/"; num2

Loop







Sub Simplify (num1 As Long, num2 As Long)

    ReDim PF(0) As Long

    GetPF num1, PF()

    For i = 1 To UBound(PF)

        If num2 Mod PF(i) = 0 Then

            num1 = num1 \ PF(i)

            num2 = num2 \ PF(i)

        End If

    Next

End Sub







Sub GetPF (num, PF() As Long)

    ReDim PF(1000) As Long

    If num < 1 _Orelse num > 1016064 Then Exit Sub

    limit = Int(Sqr(num))

    PF(0) = 1

    If num > 1 Then

        count = 1

        Do

            factor_on = 0

            Do

                factor_on = factor_on + 1

                temp = Prime_Factors(factor_on)

                If IsPrime(num) Then

                    PF(count) = num

                    finished = -1

                    Exit Do

                ElseIf num Mod temp = 0 Then

                    PF(count) = temp

                    count = count + 1

                    num = num \ temp

                    Exit Do

                End If

            Loop

        Loop Until finished

    End If

    ReDim _Preserve PF(count) As Long

End Sub













Function IsPrime (num)

    'to check for any given number less than 1,016,064, we only have to do a maximum of 170 comparisons

    'as the max value we ever have to check against is the SQR of our number.

    'for example, no value higher than 10 could ever be a factor in 100 and be prime!

    'so for numbers less than 1,000,000, all we need do is compare them against factors less than 1,000.

    'and there's not that many of them, as you can see below!

    If num < 2 _Orelse num > 1016064 Then Exit Function

    Static As Long Prime_Array_Init, Factor_Count(1 To 10)

    Dim As Long factor_on, i, j, factor

    If Prime_Array_Init = 0 Then

        Prime_Array_Init = -1

        Restore Prime_Factor_Count

        For i = 1 To 10: Read Factor_Count(i): Next



    End If



    IsPrime = -1

    For j = 1 To 10 'broken down to give 10 quick exit points so we don't check every value for an answer.

        For i = 1 To Factor_Count(j)

            factor_on = factor_on + 1

            factor = Prime_Factors(factor_on)

            If num <= factor Then

                Exit Function

            Else

                If num Mod factor = 0 Then IsPrime = 0: Exit Function

            End If

        Next

        If num < factor * factor Then Exit Function

    Next



    Exit Function

    Prime_Factor_Count: 'each value here represents the number of prime factors in number increments of 100

    'for example, there are 25 prime numbers between 1 and 100, 21 primes between 101 and 200, ect...

    Data 25,21,16,16,17,14,16,14,15,14

End Function



Sub Init

    Restore prime_data:

    For i = 1 To 168: Read Prime_Factors(i): Next

    Exit Sub

    prime_data:

    Data 2,3,5,7,11,13,17,19,23,29,31,37,41,43,47,53,59,61,67,71,73,79,83,89,97: 'factors up to 10,000 (100 ^ 2)

    Data 101,103,107,109,113,127,131,137,139,149,151,157,163,167,173,179,181,191,193,197,199: 'up to 44,100 (210 ^ 2)

    Data 211,223,227,229,233,239,241,251,257,263,269,271,277,281,283,293: 'up to 93,636 (306 ^ 2)

    Data 307,311,313,317,331,337,347,349,353,359,367,373,379,383,389,397: 'up to 160,000 (400 ^ 2)

    Data 401,409,419,421,431,433,439,443,449,457,461,463,467,479,487,491,499: 'up to 252,004 (502 ^ 2)

    Data 503,509,521,523,541,547,557,563,569,571,577,587,593,599: 'up to 360,000 (600 ^ 2)

    Data 601,607,613,617,619,631,641,643,647,653,659,661,673,677,683,691: 'up to 490,000 (700 ^ 2)

    Data 701,709,719,727,733,739,743,751,757,761,769,773,787,797: 'up to 652,864 (808 ^ 2)

    Data 809,811,821,823,827,829,839,853,857,859,863,877,881,883,887: 'up to 820,836 (906 ^ 2)

    Data 907,911,919,929,937,941,947,953,967,971,977,983,991,997: 'up to 1,01,064 (1008 ^ 2)





End Sub