All about flooble | fun stuff | Get a free chatterbox | Free JavaScript | Avatars    
perplexus dot info

Home > Numbers
4 clues (Posted on 2015-01-19) Difficulty: 2 of 5
A palindromic number, below 2000, thrice a square, is the sum of nine consecutive primes.
Enough said.

What number(s) complies(comply)?

No Solution Yet Submitted by Ady TZIDON    
No Rating

Comments: ( Back to comment list | You must be logged in to post comments.)
Solution computer solution Comment 3 of 3 |
This checks all sums of 9 successive primes until the sum exceeds 2000:

DefDbl A-Z
Dim crlf$, pr(9)
Function mform$(x, t$)
  a$ = Format$(x, t$)
  If Len(a$) < Len(t$) Then a$ = Space$(Len(t$) - Len(a$)) & a$
  mform$ = a$
End Function

Private Sub Form_Load()
 Text1.Text = ""
 crlf$ = Chr(13) + Chr(10)
 Form1.Visible = True
 
 pno = 1
 For i = 1 To 9
   pno = nxtprm(pno)
   pr(i) = pno
   Sum = Sum + pno
 Next
 
 Do
   s$ = LTrim(Str(Sum))
   good = 1
   For i = 1 To Len(s$) / 2
     If Mid(s$, i, 1) <> Mid(s$, Len(s$) + 1 - i, 1) Then good = 0: Exit For
   Next
   If good Then
     sq = Sum / 3
     If sq = Int(sq) Then
       sr = Int(Sqr(sq) + 0.5)
       If sr * sr = sq Then
         Text1.Text = Text1.Text & s & " ="
         For i = 1 To 9
           Text1.Text = Text1.Text & " +" & Str(pr(i))
         Next i
         Text1.Text = Text1.Text & crlf
         DoEvents
       End If
     End If
   End If
   Sum = Sum - pr(1)
   For i = 1 To 8
     pr(i) = pr(i + 1)
   Next
   pr(9) = nxtprm(pr(8))
   Sum = Sum + pr(9)
 Loop Until Sum > 2000
 
 
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

Function nxtprm(x)
  Dim n
  n = x + 1
  While prmdiv(n) < n
    n = n + 1
  Wend
  nxtprm = n
End Function

It finds only

363 = + 23 + 29 + 31 + 37 + 41 + 43 + 47 + 53 + 59

It finds no other solutions even when totals through 200,000 are checked (highest prime 22277).

  Posted by Charlie on 2015-01-19 11:47:55
Please log in:
Login:
Password:
Remember me:
Sign up! | Forgot password


Search:
Search body:
Forums (0)
Newest Problems
Random Problem
FAQ | About This Site
Site Statistics
New Comments (7)
Unsolved Problems
Top Rated Problems
This month's top
Most Commented On

Chatterbox:
Copyright © 2002 - 2017 by Animus Pactum Consulting. All rights reserved. Privacy Information