' Generates Sets of Prime Number Simple Magic Squares of order 4
' Optimized for Sophie Germain Primes
' Tested with Office 2007 under Windows 7
Sub Priem4c2()
Dim a1(400), a(16), b1(200000), b(200000), c(16)
y = MsgBox("Locked", vbCritical, "Routine Priem4c2")
End
n1 = 0: n9 = 0: n10 = 0: k1 = 1: k2 = 1
ShtNm1 = "Pairs1"
' Generate Squares
Sheets("Klad1").Select
t1 = Timer
For j100 = 3106 To 3106
' Refresh Extended Range
Erase b1
For i1 = 1 To 354
x = Sheets("SG1").Cells(i1, 1).Value
b1(x) = x
Next i1
' Read Prime Numbers From sheet ShtNm1
nPrs = Sheets(ShtNm1).Cells(j100, 2).Value
If nPrs < 8 Then GoTo 1000
s1 = 2 * Sheets(ShtNm1).Cells(j100, 1).Value
nVar = Sheets(ShtNm1).Cells(j100, 9).Value
For i1 = 1 To nVar
a1(i1) = Sheets(ShtNm1).Cells(j100, i1 + 9).Value
Next i1
m1 = 1: m2 = nVar
For j16 = m1 To m2 'a(16)
If b1(a1(j16)) = 0 Then GoTo 160
If b(a1(j16)) = 0 Then b(a1(j16)) = a1(j16): c(16) = a1(j16) Else GoTo 160
a(16) = a1(j16)
For j11 = m1 To m2 'a(11)
If b1(a1(j11)) = 0 Then GoTo 110
If b(a1(j11)) = 0 Then b(a1(j11)) = a1(j11): c(11) = a1(j11) Else GoTo 110
a(11) = a1(j11)
For j6 = m1 To m2 'a(6)
If b1(a1(j6)) = 0 Then GoTo 60
If b(a1(j6)) = 0 Then b(a1(j6)) = a1(j6): c(6) = a1(j6) Else GoTo 60
a(6) = a1(j6)
a(1) = s1 - a(6) - a(11) - a(16)
If a(1) < a1(m1) Or a(1) > a1(m2) Then GoTo 10
If b1(a(1)) = 0 Then GoTo 10
If b(a(1)) = 0 Then b(a(1)) = a(1): c(1) = a(1) Else GoTo 10
For j13 = m1 To m2 'a(13)
If b1(a1(j13)) = 0 Then GoTo 130
If b(a1(j13)) = 0 Then b(a1(j13)) = a1(j13): c(13) = a1(j13) Else GoTo 130
a(13) = a1(j13)
For j10 = m1 To m2 'a(10)
If b1(a1(j10)) = 0 Then GoTo 100
If b(a1(j10)) = 0 Then b(a1(j10)) = a1(j10): c(10) = a1(j10) Else GoTo 100
a(10) = a1(j10)
a(7) = s1 - a(6) - a(10) - a(11)
If a(7) < a1(m1) Or a(7) > a1(m2) Then GoTo 70
If b1(a(7)) = 0 Then GoTo 70
If b(a(7)) = 0 Then b(a(7)) = a(7): c(7) = a(7) Else GoTo 70
a(4) = s1 - a(7) - a(10) - a(13)
If a(4) < a1(m1) Or a(4) > a1(m2) Then GoTo 40
If b1(a(4)) = 0 Then GoTo 40
If b(a(4)) = 0 Then b(a(4)) = a(4): c(4) = a(4) Else GoTo 40
For j15 = m1 To m2 'a(15)
If b1(a1(j15)) = 0 Then GoTo 150
If b(a1(j15)) = 0 Then b(a1(j15)) = a1(j15): c(15) = a1(j15) Else GoTo 150
a(15) = a1(j15)
a(14) = s1 - a(13) - a(15) - a(16)
If a(14) < a1(m1) Or a(14) > a1(m2) Then GoTo 140
If b1(a(14)) = 0 Then GoTo 140
If b(a(14)) = 0 Then b(a(14)) = a(14): c(14) = a(14) Else GoTo 140
a(3) = s1 - a(7) - a(11) - a(15)
If a(3) < a1(m1) Or a(3) > a1(m2) Then GoTo 30
If b1(a(3)) = 0 Then GoTo 30
If b(a(3)) = 0 Then b(a(3)) = a(3): c(3) = a(3) Else GoTo 30
a(2) = s1 - a(1) - a(3) - a(4)
If a(2) < a1(m1) Or a(2) > a1(m2) Then GoTo 20
If b1(a(2)) = 0 Then GoTo 20
If b(a(2)) = 0 Then b(a(2)) = a(2): c(2) = a(2) Else GoTo 20
For j12 = m1 To m2 'a(12)
If b1(a1(j12)) = 0 Then GoTo 120
If b(a1(j12)) = 0 Then b(a1(j12)) = a1(j12): c(12) = a1(j12) Else GoTo 120
a(12) = a1(j12)
a(9) = s1 - a(10) - a(11) - a(12)
If a(9) < a1(m1) Or a(9) > a1(m2) Then GoTo 90
If b1(a(9)) = 0 Then GoTo 90
If b(a(9)) = 0 Then b(a(9)) = a(9): c(9) = a(9) Else GoTo 90
a(8) = s1 - a(4) - a(12) - a(16)
If a(8) < a1(m1) Or a(8) > a1(m2) Then GoTo 80
If b1(a(8)) = 0 Then GoTo 80
If b(a(8)) = 0 Then b(a(8)) = a(8): c(8) = a(8) Else GoTo 80
a(5) = s1 - a(1) - a(9) - a(13)
If a(5) < a1(m1) Or a(5) > a1(m2) Then GoTo 50
If b1(a(5)) = 0 Then GoTo 50
If b(a(5)) = 0 Then b(a(5)) = a(5): c(5) = a(5) Else GoTo 50
' Exclude solutions with identical numbers (Back Check)
GoSub 800: If fl1 = 0 Then GoTo 5
n10 = n10 + 1
' n9 = n9 + 1: GoSub 640 'Print results (selected numbers)
n9 = n9 + 1: GoSub 650 'Print results (squares)
' Erase b, c: GoTo 1000 'Print only first square
GoSub 900 'Remove used primes from available primes (option)
Erase b, c: GoTo 160
5
b(c(5)) = 0: c(5) = 0
50 b(c(8)) = 0: c(8) = 0
80 b(c(9)) = 0: c(9) = 0
90 b(c(12)) = 0: c(12) = 0
120 Next j12
b(c(2)) = 0: c(2) = 0
20 b(c(3)) = 0: c(3) = 0
30 b(c(14)) = 0: c(14) = 0
140 b(c(15)) = 0: c(15) = 0
150 Next j15
b(c(4)) = 0: c(4) = 0
40 b(c(7)) = 0: c(7) = 0
70 b(c(10)) = 0: c(10) = 0
100 Next j10
b(c(13)) = 0: c(13) = 0
130 Next j13
b(c(1)) = 0: c(1) = 0
10 b(c(6)) = 0: c(6) = 0
60 Next j6
b(c(11)) = 0: c(11) = 0
110 Next j11
b(c(16)) = 0: c(16) = 0
160 Next j16
n10 = 0
1000 Next j100
t2 = Timer
t10 = Str(t2 - t1) + " sec., " + Str(n9) + " Solutions"
y = MsgBox(t10, 0, "Routine Priem4b")
End
' Print results (selected numbers)
640 Cells(n9, 9).Select
For i1 = 1 To 16
Cells(n9, i1).Value = a(i1)
Next i1
Return
' Print results (squares)
650 n1 = n1 + 1
If n1 = 5 Then
n1 = 1: k1 = k1 + 5: k2 = 1
Else
If n9 > 1 Then k2 = k2 + 5
End If
Cells(k1, k2 + 1).Select
Cells(k1, k2 + 1).Font.Color = -4165632
Cells(k1, k2 + 1).Value = CStr(s1) + ", " + CStr(n10)
i3 = 0
For i1 = 1 To 4
For i2 = 1 To 4
i3 = i3 + 1
Cells(k1 + i1, k2 + i2).Value = a(i3)
Next i2
Next i1
Return
' Exclude solutions with identical numbers
800 fl1 = 1
For j1 = 1 To 16
a2 = a(j1)
For j2 = (1 + j1) To 16
If a2 = a(j2) Then fl1 = 0: Return
Next j2
Next j1
Return
' Remove used primes from available primes
900 For i1 = 1 To 16
b1(a(i1)) = 0
Next i1
Return
End Sub
