Prime Factors

[PhilOfPerth]

Code: (Select All)

ReDim PF(0) As Long

ReDim Shared As Long Prime_Factors(1 To 168)

Screen _NewImage(1280, 900, 32)

_Delay .5

_ScreenMove _Middle



Init



Do

    Input "Give me a number from 1 to 1016064 (0 quits) =>"; num

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

    GetPF num, PF()

    For i = 0 To UBound(PF)

        Print PF(i);

    Next

    Print

Loop





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

Building upon the IsPrime function, we now have a means to break a number down into its prime factors.

For example:

12 = 2 * 2 * 3
124 = 2 * 2 * 31

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Next step for what I'm working on and playing around with will be fraction simplification.

Take a value like 12 / 16...  that can simplify down to 3 / 4.  This should now have me on the route to do that easily. 

(Break the nominator (top number) down to its prime factors.  Check those values against the denominator (bottom number).  If they divide evenly (mod = 0) then reduce both numbers by that factor.)

Nice! Wish I could do that!