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Calling spade a spade (Posted on 2018-10-07) Difficulty: 2 of 5
S is the smallest sum of the squares of the first prime numbers that is a palindrome.
What else can be said about S?

No Solution Yet Submitted by Ady TZIDON    
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Solution computer solution Comment 1 of 1
There's a trivial case, where the "sum" is only of the first prime itself: 2^2 = 4, which is technically palindromic.

However the sum of the squares of the first seven primes is also palindromic:

pr squ

 2   4
 3   9
 5  25
 7  49
11 121
13 169
17 289
   ---
   666 sum of squares
The sum has also come to be called the Number of the Beast from the New Testament book Revelation, or Apocalypse, with various interpretations of what that means. Most commonly it's taken as the Hebrew-alphabet numbering equivalent to the name Nero.     


DefDbl A-Z
Dim crlf$
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
  
  p = 1
  Do
    p = nxtprm(p)
    p2 = p * p
    tot = tot + p2
    If isPalin(tot) Then
      Text1.Text = Text1.Text & p & Str(tot) & crlf
      p1 = 1
      Do
        p1 = nxtprm(p1)
        Text1.Text = Text1.Text & p1 & Str(p1 * p1) & crlf
      Loop Until p1 = p
    End If
    
    DoEvents
  Loop
  
  
  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 Or n < 2
    n = n + 1
  Wend
  nxtprm = n
End Function

Function isPalin(n)
 s$ = LTrim(Str(n))
 
 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
 
 isPalin = good
End Function


  Posted by Charlie on 2018-10-07 11:11:39
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