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 A prime nonuplet (Posted on 2017-12-27)
p is a 4-digit prime number. p+30 is also prime. There are 9 primes from p to p+30 inclusive. What is p? What are the 9 primes in the nonuplet?

 No Solution Yet Submitted by Math Man Rating: 5.0000 (1 votes)

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 computer solution (spoiler) | Comment 1 of 4
The 9 primes are:

1277 1279 1283 1289 1291 1297 1301 1303 1307

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

Text1.Text = ""
crlf\$ = Chr(13) + Chr(10)
Form1.Visible = True

p = 1000
Do
p = nxtprm(p)
pr(0) = p
For i = 9 To 1 Step -1
pr(i) = pr(i - 1)
Next
If pr(9) > 0 Then
If pr(1) - pr(9) <= 30 Then
For i = 9 To 1 Step -1
Text1.Text = Text1.Text & pr(i) & " "
Next
Text1.Text = Text1.Text & crlf
End If
End If
DoEvents
Loop Until p > 10030

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

 Posted by Charlie on 2017-12-27 12:47:03

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