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Largest pandigital prime. (Posted on 2015-08-07) Difficulty: 2 of 5
A number is n-digit pandigital if it makes use of all the digits
1 to n exactly once.
For example, 2143 is a 4-digit pandigital and is also prime.

What is the largest n-digit pandigital prime that exists?

No Solution Yet Submitted by Ady TZIDON    
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Solution computer solution Comment 1 of 1
The sum of the digits 1 through 9 is divisible by 3, so n can't be 9; eliminating the 9 doesn't solve this problem, so n can't be 8. There's no reason n can't be 7, so the program permutes the digits 1 through 7:

DefDbl A-Z
Dim wd(10) As String, w As String, sz, crlf$

Private Sub Form_Load()
 Text1.Text = ""
 crlf$ = Chr(13) + Chr(10)
 Form1.Visible = True
  mx = 0
  s$ = "1234567": h$ = s$
  Do
    n = Val(s)
    If prmdiv(n) = n Then
      If n > mx Then
        mx = n
        sv = n
        DoEvents
      End If
    End If
    permute s
  Loop Until h = s
Text1.Text = Text1.Text & sv & " done" & crlf

End Sub
Function prmdiv(num)
 Dim n, dv, q
 If num = 1 Then prmdiv = 1: Exit Function
 n = Abs(num): If n > 0 Then limit = Sqr(n) Else limit = 0
 If limit <> Int(limit) Then limit = Int(limit + 1)
 dv = 2: GoSub DivideIt
 dv = 3: GoSub DivideIt
 dv = 5: GoSub DivideIt
 dv = 7
 Do Until dv > limit
   GoSub DivideIt: dv = dv + 4 '11
   GoSub DivideIt: dv = dv + 2 '13
   GoSub DivideIt: dv = dv + 4 '17
   GoSub DivideIt: dv = dv + 2 '19
   GoSub DivideIt: dv = dv + 4 '23
   GoSub DivideIt: dv = dv + 6 '29
   GoSub DivideIt: dv = dv + 2 '31
   GoSub DivideIt: dv = dv + 6 '37
 Loop
 If n > 1 Then prmdiv = n
 Exit Function

DivideIt:
 Do
  q = Int(n / dv)
  If q * dv = n And n > 0 Then
    prmdiv = dv: Exit Function
   Else
    Exit Do
  End If
 Loop

 Return
End Function

The answer is:

7652413 

  Posted by Charlie on 2015-08-07 12:21:30
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