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Adding consecutive primes (Posted on 2016-10-11) Difficulty: 3 of 5
The longest sum of consecutive primes below 1000 that adds to a prime, contains n terms, and is equal to S.

Find n and S.

Inspired by Project Euler.

No Solution Yet Submitted by Ady TZIDON    
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Solution computer solution Comment 1 of 1
DefDbl A-Z
Dim pr(200), crlf$, maxlen, maxval

Private Sub Form_Load()
 Text1.Text = ""
 crlf$ = Chr(13) + Chr(10)
 Form1.Visible = True
 
 Do
   p = nxtprm(p): ct = ct + 1
   pr(ct) = p
 Loop Until p > 1000
 ct = ct - 1
 
 For a = 1 To ct - 1
   tot = pr(a)
   For b = a + 1 To ct
     tot = tot + pr(b)
     If prmdiv(tot) = tot Then
       If b - a + 1 > maxlen Then
         maxlen = b - a + 1: maxlena = a: maxlenb = b
         maxlentot = tot
       End If
       If tot > maxval Then
         maxval = tot: maxvala = a: maxvalb = b
       End If
     End If
     DoEvents
   Next
 Next
 
 Text1.Text = Text1.Text & ct & crlf
 
 Text1.Text = Text1.Text & maxlen & Str(pr(maxlena)) & Str(pr(maxlenb))
 Text1.Text = Text1.Text & "          " & maxlentot & crlf
 Text1.Text = Text1.Text & maxval & Str(pr(maxvala)) & Str(pr(maxvalb)) & 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
Function nxtprm(x)
  Dim n
  If x = 0 Then nxtprm = 2: Exit Function
  n = x + 1
  While prmdiv(n) < n
    n = n + 1
  Wend
  nxtprm = n
End Function

reports

168
163 13 997          76099
76099 13 997

indicating that there are 168 primes under 1000. The longest range that adds up to a prime is 163 primes long, from 13 to 997, adding up to 76099.  This is also the largest such total.

So n is 163 and S is 76099.

  Posted by Charlie on 2016-10-11 13:45:47
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