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  • 素数的快速列举(二)

           半年前曾在我的BLOG发过一篇文章(http://blog.csdn.net/northwolves/archive/2005/04/18/351998.aspx),对素数的快速列举进行了初步探讨,随后的讨论在http://community.csdn.net/Expert/topic/4395/4395751.xml?temp=.9719355进行, KiteGirl(小仙妹) jiangsheng(蒋晟.MSMVP2004Jan) 给予了很大的启发,特此将改进后的代码与大家共享。

    Sub prime(ByVal n As Long, ByRef prime() As Long)
    ReDim prime(5761495) '10^8以内的素数个数
    Dim a() As Byte, i As Long, temp As Long, half As Long, p As Long, pcount As Long, mytime As Long, k As Integer
    mytime = Timer '计时
    half = n / 2
    ReDim a(1 To half)
    'the first 10 prime
    prime(0) = 2
    prime(1) = 3
    prime(2) = 5
    prime(3) = 7
    prime(4) = 11
    prime(5) = 13
    prime(6) = 17
    prime(7) = 19
    prime(8) = 23
    prime(9) = 29


    pcount = 9

    p = 3

    Do While p * p <= n

    temp = p * p

    For i = temp To n Step 2 * p 'p的倍数
    a(i / 2) = 1 '设为1表示弃去

    Next

    again:
    p = p + 2

    If a(p / 2) = 1 Then GoTo again

    Loop

    '把素数分成8种情况:30n+1,30n+7,30n+11,30n+13,30n+17,30n+19,30n+23,30n+29
    Dim s(7) As Byte
    s(0) = 0
    s(1) = 3
    s(2) = 5
    s(3) = 6
    s(4) = 8
    s(5) = 9
    s(6) = 11
    s(7) = 14

    For i = 15 To half Step 15

    For j = 0 To 7
    temp = i + s(j)
    If temp > half Then Exit For: Exit For
    If a(temp) = 0 Then
    pcount = pcount + 1
    prime(pcount) = 2 * temp + 1 '赋值
    End If
    Next

    Next
    ReDim Preserve prime(pcount) '重设置数组大小节省空间

    Debug.Print "n=" & n & ",prime count=" & pcount & ", The calulating time is " & Timer - mytime & " s"
    End Sub

    Private Sub Command1_Click()
    Dim p() As Long
    Dim i As Long
    For i = 2 To 8
    prime 10 ^ i, p
    Next
    End Sub

    返回:

    n=100,prime count=25, The calulating time is 0.0000 seconds.
    n=1000,prime count=168, The calulating time is 0.0000 seconds.
    n=10000,prime count=1229, The calulating time is 0.0000 seconds.
    n=100000,prime count=9592, The calulating time is 0.0002 seconds.
    n=1000000,prime count=78498, The calulating time is 0.2269 seconds.
    n=10000000,prime count=664579, The calulating time is 2.0719 seconds.
    n=100000000,prime count=5761455, The calulating time is 15.2344 seconds.

    当然,跟C语言的速度还是有一定距离的,但基本上可以满足计算的需要了,编译成EXE文件后还可以更快些。


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  • 原文地址:https://www.cnblogs.com/fengju/p/6336356.html
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