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Prime divisors (Posted on 2005-01-04) Difficulty: 3 of 5
6300846559 is such that 6 is divisible by 2; 63, by 3; 630, by 5; 6300, by 7; and, in general, if you take its first N digits, it will be divisible by the N-th prime.

There is only one other such 10 digit number: can you find it?

See The Solution Submitted by e.g.    
Rating: 3.7500 (4 votes)

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Solution Solution (VB program) | Comment 1 of 11

The only two 10 digit numbers like this are 8757193191 and 6300846559.

Not meaning to provoke any more chatterbox jokes, but the following Visual Basic program found both numbers in ZERO elapsed time:

Imports System
Imports System.IO
Imports System.Text
Imports System.Runtime.InteropServices
Imports System.Math
Module Module1
    Sub Main()
        Randomize()
        Dim strstarttime As String
        Dim strendtime As String
        Dim strend As String
        Dim intdigits(10) As Double
        Dim dblwork As Double
        strstarttime = TimeOfDay
        Console.WriteLine("Start of execution: " & strstarttime)
        For index1 As Integer = 2 To 9
            intdigits(0) = index1
            dblwork = ( _
            ((10 ^ 0) * intdigits(0)) _
            )
            If (dblwork / 2) = Fix(dblwork / 2) Then
                digit_1(intdigits, dblwork)
            End If
        Next
        strendtime = TimeOfDay
        Console.WriteLine(" ")
        Console.WriteLine("Start of execution: " & strstarttime)
        strendtime = TimeOfDay
        Console.WriteLine("End of execution: " & strendtime)
        strend = "?"
        Console.WriteLine(" ")
        While strend <> "X"
            Console.WriteLine("Please enter X to exit program...")
            strend = UCase(Console.ReadLine())
        End While
    End Sub

    Sub digit_1(ByRef intdigits, ByRef dblwork)
        For index1 As Integer = 0 To 9
            intdigits(1) = index1
            dblwork = ( _
            ((10 ^ 1) * intdigits(0)) _
            + ((10 ^ 0) * intdigits(1)) _
            )
            If (dblwork / 3) = Fix(dblwork / 3) Then
                digit_2(intdigits, dblwork)
            End If
        Next
    End Sub

    Sub digit_2(ByRef intdigits, ByRef dblwork)
        For index1 As Integer = 0 To 9
            intdigits(2) = index1
            dblwork = ( _
            ((10 ^ 2) * intdigits(0)) _
            + ((10 ^ 1) * intdigits(1)) _
            + ((10 ^ 0) * intdigits(2)) _
            )
            If (dblwork / 5) = Fix(dblwork / 5) Then
                digit_3(intdigits, dblwork)
            End If
        Next
    End Sub

    Sub digit_3(ByRef intdigits, ByRef dblwork)
        For index1 As Integer = 0 To 9
            intdigits(3) = index1
            dblwork = ( _
            ((10 ^ 3) * intdigits(0)) _
            + ((10 ^ 2) * intdigits(1)) _
            + ((10 ^ 1) * intdigits(2)) _
            + ((10 ^ 0) * intdigits(3)) _
            )
            If (dblwork / 7) = Fix(dblwork / 7) Then
                digit_4(intdigits, dblwork)
            End If
        Next
    End Sub

    Sub digit_4(ByRef intdigits, ByRef dblwork)
        For index1 As Integer = 0 To 9
            intdigits(4) = index1
            dblwork = ( _
            ((10 ^ 4) * intdigits(0)) _
            + ((10 ^ 3) * intdigits(1)) _
            + ((10 ^ 2) * intdigits(2)) _
            + ((10 ^ 1) * intdigits(3)) _
            + ((10 ^ 0) * intdigits(4)) _
            )
            If (dblwork / 11) = Fix(dblwork / 11) Then
                digit_5(intdigits, dblwork)
            End If
        Next
    End Sub

    Sub digit_5(ByRef intdigits, ByRef dblwork)
        For index1 As Integer = 0 To 9
            intdigits(5) = index1
            dblwork = ( _
            ((10 ^ 5) * intdigits(0)) _
            + ((10 ^ 4) * intdigits(1)) _
            + ((10 ^ 3) * intdigits(2)) _
            + ((10 ^ 2) * intdigits(3)) _
            + ((10 ^ 1) * intdigits(4)) _
            + ((10 ^ 0) * intdigits(5)) _
            )
            If (dblwork / 13) = Fix(dblwork / 13) Then
                digit_6(intdigits, dblwork)
            End If
        Next
    End Sub

    Sub digit_6(ByRef intdigits, ByRef dblwork)
        For index1 As Integer = 0 To 9
            intdigits(6) = index1
            dblwork = ( _
            ((10 ^ 6) * intdigits(0)) _
            + ((10 ^ 5) * intdigits(1)) _
            + ((10 ^ 4) * intdigits(2)) _
            + ((10 ^ 3) * intdigits(3)) _
            + ((10 ^ 2) * intdigits(4)) _
            + ((10 ^ 1) * intdigits(5)) _
            + ((10 ^ 0) * intdigits(6)) _
            )
            If (dblwork / 17) = Fix(dblwork / 17) Then
                digit_7(intdigits, dblwork)
            End If
        Next
    End Sub

    Sub digit_7(ByRef intdigits, ByRef dblwork)
        For index1 As Integer = 0 To 9
            intdigits(7) = index1
            dblwork = ( _
            ((10 ^ 7) * intdigits(0)) _
            + ((10 ^ 6) * intdigits(1)) _
            + ((10 ^ 5) * intdigits(2)) _
            + ((10 ^ 4) * intdigits(3)) _
            + ((10 ^ 3) * intdigits(4)) _
            + ((10 ^ 2) * intdigits(5)) _
            + ((10 ^ 1) * intdigits(6)) _
            + ((10 ^ 0) * intdigits(7)) _
            )
            If (dblwork / 19) = Fix(dblwork / 19) Then
                digit_8(intdigits, dblwork)
            End If
        Next
    End Sub

    Sub digit_8(ByRef intdigits, ByRef dblwork)
        For index1 As Integer = 0 To 9
            intdigits(8) = index1
            dblwork = ( _
            ((10 ^ 8) * intdigits(0)) _
            + ((10 ^ 7) * intdigits(1)) _
            + ((10 ^ 6) * intdigits(2)) _
            + ((10 ^ 5) * intdigits(3)) _
            + ((10 ^ 4) * intdigits(4)) _
            + ((10 ^ 3) * intdigits(5)) _
            + ((10 ^ 2) * intdigits(6)) _
            + ((10 ^ 1) * intdigits(7)) _
            + ((10 ^ 0) * intdigits(8)) _
            )
            If (dblwork / 23) = Fix(dblwork / 23) Then
                digit_9(intdigits, dblwork)
            End If
        Next
    End Sub

    Sub digit_9(ByRef intdigits, ByRef dblwork)
        For index1 As Integer = 0 To 9
            intdigits(9) = index1
            dblwork = ( _
            ((10 ^ 9) * intdigits(0)) _
            + ((10 ^ 8) * intdigits(1)) _
            + ((10 ^ 7) * intdigits(2)) _
            + ((10 ^ 6) * intdigits(3)) _
            + ((10 ^ 5) * intdigits(4)) _
            + ((10 ^ 4) * intdigits(5)) _
            + ((10 ^ 3) * intdigits(6)) _
            + ((10 ^ 2) * intdigits(7)) _
            + ((10 ^ 1) * intdigits(8)) _
             + ((10 ^ 0) * intdigits(9)) _
            )
            If (dblwork / 29) = Fix(dblwork / 29) Then
                digit_10(intdigits, dblwork)
            End If
        Next
    End Sub

    Sub digit_10(ByRef intdigits, ByRef dblwork)
        Console.WriteLine(dblwork)
    End Sub
End Module

 

 


  Posted by Penny on 2005-01-04 15:44:05
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