' Generates Simple Magic Squares of order 6 for Prime Numbers
' Symmetrical Main Diagonals, Optimized for Twin Primes
' Tested with Office 2007 under Windows 7
Sub Priem6a2()
Dim a1(400), a(36), b1(50000), b(50000), c(36)
y = MsgBox("Locked", vbCritical, "Routine Priem6a")
End
n1 = 0: n9 = 0: n10 = 0: k1 = 1: k2 = 1
ShtNm1 = "Pairs1"
Sheets("Klad1").Select
t1 = Timer
' Extended Range
Erase b1
For i1 = 1 To 175
x = Sheets("Primes2").Cells(i1, 1).Value
b1(x) = x
Next i1
For j100 = 2 To 149
' Read Prime Numbers From sheet ShtNm1
nPrs = Sheets(ShtNm1).Cells(j100, 2).Value
If nPrs < 12 Then GoTo 1000
Pr6 = Sheets(ShtNm1).Cells(j100, 1).Value
s1 = 3 * Pr6
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
' Diagonal Rbtm/Ltop
For j36 = m1 + 3 To m2 / 2 'a(36)
If b(a1(j36)) = 0 Then b(a1(j36)) = a1(j36): c(36) = a1(j36) Else GoTo 315
a(36) = a1(j36)
a(1) = Pr6 - a(36): If b(a(1)) = 0 Then b(a(1)) = a(1): c(1) = a(1) Else GoTo 10
For j29 = j36 To m2 'a(29)
If b(a1(j29)) = 0 Then b(a1(j29)) = a1(j29): c(29) = a1(j29) Else GoTo 290
a(29) = a1(j29)
a(8) = Pr6 - a(29): If b(a(8)) = 0 Then b(a(8)) = a(8): c(8) = a(8) Else GoTo 80
For j22 = j29 To m2 'a(22)
If b(a1(j22)) = 0 Then b(a1(j22)) = a1(j22): c(22) = a1(j22) Else GoTo 220
a(22) = a1(j22)
a(15) = Pr6 - a(22): If b(a(15)) = 0 Then b(a(15)) = a(15): c(15) = a(15) Else GoTo 150
' Diagonal Lbtm/Rtop
For j31 = m1 To m2 'a(31)
If b(a1(j31)) = 0 Then b(a1(j31)) = a1(j31): c(31) = a1(j31) Else GoTo 316
a(31) = a1(j31)
a(6) = Pr6 - a(31): If b(a(6)) = 0 Then b(a(6)) = a(6): c(6) = a(6) Else GoTo 60
For j26 = j31 To m2 'a(26)
If b(a1(j26)) = 0 Then b(a1(j26)) = a1(j26): c(26) = a1(j26) Else GoTo 260
a(26) = a1(j26)
a(11) = Pr6 - a(26): If b(a(11)) = 0 Then b(a(11)) = a(11): c(11) = a(11) Else GoTo 110
For j21 = j26 To m2 'a(21)
If b(a1(j21)) = 0 Then b(a1(j21)) = a1(j21): c(21) = a1(j21) Else GoTo 210
a(21) = a1(j21)
a(16) = Pr6 - a(21): If b(a(16)) = 0 Then b(a(16)) = a(16): c(16) = a(16) Else GoTo 160
'Row 1
For j35 = m1 To m2 'a(35)
If b(a1(j35)) = 0 Then b(a1(j35)) = a1(j35): c(35) = a1(j35) Else GoTo 350
a(35) = a1(j35)
For j34 = m1 To m2 'a(34)
If b(a1(j34)) = 0 Then b(a1(j34)) = a1(j34): c(34) = a1(j34) Else GoTo 340
a(34) = a1(j34)
For j33 = m1 To m2 'a(33)
If b(a1(j33)) = 0 Then b(a1(j33)) = a1(j33): c(33) = a1(j33) Else GoTo 330
a(33) = a1(j33)
a(32) = s1 - a(31) - a(33) - a(34) - a(35) - a(36)
If a(32) < a1(m1) Or a(32) > a1(m2) Then GoTo 320
If b1(a(32)) = 0 Then GoTo 320
If b(a(32)) = 0 Then b(a(32)) = a(32): c(32) = a(32) Else GoTo 320
'Column 2
For j23 = m1 To m2 'a(23)
If b(a1(j23)) = 0 Then b(a1(j23)) = a1(j23): c(23) = a1(j23) Else GoTo 230
a(23) = a1(j23)
For j17 = m1 To m2 'a(17)
If b(a1(j17)) = 0 Then b(a1(j17)) = a1(j17): c(17) = a1(j17) Else GoTo 170
a(17) = a1(j17)
a(5) = s1 - a(11) - a(17) - a(23) - a(29) - a(35)
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
'Column 5
For j20 = m1 To m2 'a(20)
If b(a1(j20)) = 0 Then b(a1(j20)) = a1(j20): c(20) = a1(j20) Else GoTo 200
a(20) = a1(j20)
For j14 = m1 To m2 'a(14)
If b(a1(j14)) = 0 Then b(a1(j14)) = a1(j14): c(14) = a1(j14) Else GoTo 140
a(14) = a1(j14)
a(2) = s1 - a(8) - a(14) - a(20) - a(26) - a(32)
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
'Row 6
For j3 = m1 To m2 'a(3)
If b(a1(j3)) = 0 Then b(a1(j3)) = a1(j3): c(3) = a1(j3) Else GoTo 30
a(3) = a1(j3)
a(4) = s1 - a(1) - a(2) - a(3) - a(5) - a(6)
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
'Column 3
For j28 = m1 To m2 'a(28)
If b(a1(j28)) = 0 Then b(a1(j28)) = a1(j28): c(28) = a1(j28) Else GoTo 280
a(28) = a1(j28)
a(10) = s1 - a(4) - a(16) - a(22) - a(28) - a(34)
If a(10) < a1(m1) Or a(10) > a1(m2) Then GoTo 100
If b1(a(10)) = 0 Then GoTo 100
If b(a(10)) = 0 Then b(a(10)) = a(10): c(10) = a(10) Else GoTo 100
'Column 4
For j27 = m1 To m2 'a(27)
If b(a1(j27)) = 0 Then b(a1(j27)) = a1(j27): c(27) = a1(j27) Else GoTo 270
a(27) = a1(j27)
a(9) = s1 - a(3) - a(15) - a(21) - a(27) - a(33)
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
'Row 3
For j24 = m1 To m2 'a(24)
If b(a1(j24)) = 0 Then b(a1(j24)) = a1(j24): c(24) = a1(j24) Else GoTo 240
a(24) = a1(j24)
a(19) = s1 - a(20) - a(21) - a(22) - a(23) - a(24)
If a(19) < a1(m1) Or a(19) > a1(m2) Then GoTo 190
If b1(a(19)) = 0 Then GoTo 190
If b(a(19)) = 0 Then b(a(19)) = a(19): c(19) = a(19) Else GoTo 190
'Row 4
For j18 = m1 To m2 'a(18)
If b(a1(j18)) = 0 Then b(a1(j18)) = a1(j18): c(18) = a1(j18) Else GoTo 180
a(18) = a1(j18)
a(13) = s1 - a(14) - a(15) - a(16) - a(17) - a(18)
If a(13) < a1(m1) Or a(13) > a1(m2) Then GoTo 130
If b1(a(13)) = 0 Then GoTo 130
If b(a(13)) = 0 Then b(a(13)) = a(13): c(13) = a(13) Else GoTo 130
'Remainder
For j12 = m1 To m2 'a(12)
If b(a1(j12)) = 0 Then b(a1(j12)) = a1(j12): c(12) = a1(j12) Else GoTo 120
a(12) = a1(j12)
a(7) = s1 - a(8) - a(9) - a(10) - a(11) - a(12)
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(25) = s1 - a(1) - a(7) - a(13) - a(19) - a(31)
If a(25) < a1(m1) Or a(25) > a1(m2) Then GoTo 250
If b1(a(25)) = 0 Then GoTo 250
If b(a(25)) = 0 Then b(a(25)) = a(25): c(25) = a(25) Else GoTo 250
a(30) = s1 - a(12) - a(18) - a(24) - a(6) - a(36)
If a(30) < a1(m1) Or a(30) > a1(m2) Then GoTo 300
If b1(a(30)) = 0 Then GoTo 300
If b(a(30)) = 0 Then b(a(30)) = a(30): c(30) = a(30) Else GoTo 300
' Exclude solutions with identical numbers (Back Check)
GoSub 800: If fl1 = 0 Then GoTo 5
' 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
5
b(c(30)) = 0: c(30) = 0
300 b(c(25)) = 0: c(25) = 0
250 b(c(7)) = 0: c(7) = 0
70 b(c(12)) = 0: c(12) = 0
120 Next j12
b(c(13)) = 0: c(13) = 0
130 b(c(18)) = 0: c(18) = 0
180 Next j18
b(c(19)) = 0: c(19) = 0
190 b(c(24)) = 0: c(24) = 0
240 Next j24
b(c(9)) = 0: c(9) = 0
90 b(c(27)) = 0: c(27) = 0
270 Next j27
b(c(10)) = 0: c(10) = 0
100 b(c(28)) = 0: c(28) = 0
280 Next j28
b(c(4)) = 0: c(4) = 0
40 b(c(3)) = 0: c(3) = 0
30 Next j3
b(c(2)) = 0: c(2) = 0
20 b(c(14)) = 0: c(14) = 0
140 Next j14
b(c(20)) = 0: c(20) = 0
200 Next j20
b(c(5)) = 0: c(5) = 0
50 b(c(17)) = 0: c(17) = 0
170 Next j17
b(c(23)) = 0: c(23) = 0
230 Next j23
b(c(32)) = 0: c(32) = 0
320 b(c(33)) = 0: c(33) = 0
330 Next j33
b(c(34)) = 0: c(34) = 0
340 Next j34
b(c(35)) = 0: c(35) = 0
350 Next j35
b(c(16)) = 0: c(16) = 0
160 b(c(21)) = 0: c(21) = 0
210 Next j21
b(c(11)) = 0: c(11) = 0
110 b(c(26)) = 0: c(26) = 0
260 Next j26
b(c(6)) = 0: c(6) = 0
60 b(c(31)) = 0: c(31) = 0
316 Next j31
b(c(15)) = 0: c(15) = 0
150 b(c(22)) = 0: c(22) = 0
220 Next j22
b(c(8)) = 0: c(8) = 0
80 b(c(29)) = 0: c(29) = 0
290 Next j29
b(c(1)) = 0: c(1) = 0
10 b(c(36)) = 0: c(36) = 0
315 Next j36
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, 37).Select
For i1 = 1 To 36
Cells(n9, i1).Value = a(i1)
Next i1
Return
' Print results (squares)
650 n1 = n1 + 1
If n1 = 5 Then
n1 = 1: k1 = k1 + 7: k2 = 1
Else
If n9 > 1 Then k2 = k2 + 7
End If
Cells(k1, k2 + 1).Select
Cells(k1, k2 + 1).Font.Color = -4165632
Cells(k1, k2 + 1).Value = s1
i3 = 0
For i1 = 1 To 6
For i2 = 1 To 6
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 36
a2 = a(j1): If a2 = 0 Then GoTo 810
For j2 = (1 + j1) To 36
If a2 = a(j2) Then fl1 = 0: Return
Next j2
810 Next j1
Return
End Sub
