The sum of the first N consecutive prime numbers is a zeroless pandigital.
Find N and the corresponding 1-9 pandigital.
The first 8971 primes add up to 394521678.
The first 10474 primes add up to 547128369.
The first 10701 primes add up to 572469138.
N could be 8971, 10474 or 10701.
These are the most satisfying in that no digit is repeated.
If repeated digits are allowed, any of the numbers in the first column below could be N.
The first 25 of all the numbers meeting the criteria follow, regardless of repeated digits:
8971 394521678
10474 547128369
10701 572469138
15474 1245769389
16223 1376249548
16243 1379826584
16285 1387352496
16789 1479315682
17027 1523791648
17676 1648579283
17805 1673998254
18706 1857238649
18781 1872935964
19069 1933827546
20185 2179543686
20673 2291765384
21000 2368647159
21026 2374819465
22880 2836453179
23104 2895147163
24400 3246895173
24417 3251649378
24843 3371952846
25146 3458927361
25814 3654827961
Dim crlf$
Private Sub Form_Load()
Text1.Text = ""
crlf$ = Chr(13) + Chr(10)
Form1.Visible = True
p = 1
Do
p = nxtprm(p): n = n + 1
DoEvents
tot = tot + p
tots$ = LTrim(Str(tot))
good = 0
If InStr(tots, "0") = 0 And Len(tots) > 8 Then
d$ = "123456789"
For i = 1 To Len(tots)
ix = InStr(d, Mid(tots, i, 1))
If ix > 0 Then
d = Left(d, ix - 1) + Mid(d, ix + 1)
If d = "" Then good = 1: Exit For
End If
Next
If good Then
Text1.Text = Text1.Text & n & " " & tot & crlf
ct = ct + 1
End If
End If
Loop Until ct = 25
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
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Posted by Charlie
on 2017-11-21 10:32:45 |
computer solution (spoiler)