' Generates Ultra Magic Squares of order 7 for Prime and Natural Numbers
' 16 Magic Sets of 3, Center + Remainder
' Tested with Office 2007 under Windows 7
Sub Priem7d()
Dim a1(1142), a(80), b1(45000), b(45000), c(80)
y = MsgBox("Locked", vbCritical, "Routine Priem7d")
End
n2 = 0: n3 = 0: n9 = 0: k1 = 1: k2 = 1
ShtNm1 = "Lines7": rno11 = 142: rno12 = 156: ShtNm3 = "Klad1": fl10 = 3
' Generate squares
Sheets(ShtNm3).Select
t1 = Timer
If fl10 = 1 Then rno11 = 1: rno12 = 1
For j100 = rno11 To rno12
' Define variables
If fl10 = 1 Then GoSub 2000 ' Read Natural Numbers (j100 = 1 To 1)
If fl10 = 2 Then GoSub 2010 ' Read Prime Numbers From sheet "Pairs7" (j100: As selected)
If fl10 = 3 Then GoSub 2020 ' Read Prime Numbers from sheet "Lines7" (j100: As selected)
a(25) = s2: b(s2) = s2: n20 = 0
For j40 = m1 To (m2 - 1) / 2 'a(40)
If b(a1(j40)) = 0 Then b(a1(j40)) = a1(j40): c(40) = a1(j40) Else GoTo 400
a(40) = a1(j40)
a(10) = 2 * s2 - a(40): If b(a(10)) = 0 Then b(a(10)) = a(10): c(10) = a(10) Else GoTo 100
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)
a(33) = 3 * s2 - a(34) - a(40)
If a(33) < a1(m1) Or a(33) > a1(m2) Then GoTo 330
If b1(a(33)) = 0 Then GoTo 330
If b(a(33)) = 0 Then b(a(33)) = a(33): c(33) = a(33) Else GoTo 330
a(28) = s2 + a(34) - a(40)
If a(28) < a1(m1) Or a(28) > a1(m2) Then GoTo 280
If b1(a(28)) = 0 Then GoTo 280
If b(a(28)) = 0 Then b(a(28)) = a(28): c(28) = a(28) Else GoTo 280
a(22) = 2 * s2 - a(28): If b(a(22)) = 0 Then b(a(22)) = a(22): c(22) = a(22) Else GoTo 220
a(17) = 2 * s2 - a(33): If b(a(17)) = 0 Then b(a(17)) = a(17): c(17) = a(17) Else GoTo 170
a(16) = 2 * s2 - a(34): If b(a(16)) = 0 Then b(a(16)) = a(16): c(16) = a(16) Else GoTo 160
For j38 = m1 To m2 'a(38)
If b(a1(j38)) = 0 Then b(a1(j38)) = a1(j38): c(38) = a1(j38) Else GoTo 380
a(38) = a1(j38)
a(12) = 2 * s2 - a(38): If b(a(12)) = 0 Then b(a(12)) = a(12): c(12) = a(12) Else GoTo 120
For j31 = m1 To m2 'a(31)
If b(a1(j31)) = 0 Then b(a1(j31)) = a1(j31): c(31) = a1(j31) Else GoTo 310
a(31) = a1(j31)
a(46) = -2 * s2 + a(31) + 2 * a(38)
If a(46) < a1(m1) Or a(46) > a1(m2) Then GoTo 460
If b1(a(46)) = 0 Then GoTo 460
If b(a(46)) = 0 Then b(a(46)) = a(46): c(46) = a(46) Else GoTo 460
a(30) = 3 * s2 - a(31) - a(38)
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
a(20) = 2 * s2 - a(30): If b(a(20)) = 0 Then b(a(20)) = a(20): c(20) = a(20) Else GoTo 200
a(19) = 2 * s2 - a(31): If b(a(19)) = 0 Then b(a(19)) = a(19): c(19) = a(19) Else GoTo 190
a(4) = 2 * s2 - a(46): If b(a(4)) = 0 Then b(a(4)) = a(4): c(4) = a(4) Else GoTo 40
For j39 = m1 To m2 'a(39)
If b(a1(j39)) = 0 Then b(a1(j39)) = a1(j39): c(39) = a1(j39) Else GoTo 390
a(39) = a1(j39)
a(32) = 5 * s2 - a(39) - a(31) - 2 * a(38)
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
a(18) = 2 * s2 - a(32): If b(a(18)) = 0 Then b(a(18)) = a(18): c(18) = a(18) Else GoTo 180
a(11) = 2 * s2 - a(39): If b(a(11)) = 0 Then b(a(11)) = a(11): c(11) = a(11) Else GoTo 110
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(26) = 2 * s2 - a(27) - a(34) + a(40)
If a(26) < a1(m1) Or a(26) > a1(m2) Then GoTo 260
If b1(a(26)) = 0 Then GoTo 260
If b(a(26)) = 0 Then b(a(26)) = a(26): c(26) = a(26) Else GoTo 260
a(24) = 2 * s2 - a(26): If b(a(24)) = 0 Then b(a(24)) = a(24): c(24) = a(24) Else GoTo 240
a(23) = 2 * s2 - a(27): If b(a(23)) = 0 Then b(a(23)) = a(23): c(23) = a(23) Else GoTo 230
For j49 = m1 To m2 'a(49): Remainder
If b(a1(j49)) = 0 Then b(a1(j49)) = a1(j49): c(49) = a1(j49) Else GoTo 490
a(49) = a1(j49)
a(41) = a(49) + a(34) - a(40)
If a(41) < a1(m1) Or a(41) > a1(m2) Then GoTo 410
If b1(a(41)) = 0 Then GoTo 410
If b(a(41)) = 0 Then b(a(41)) = a(41): c(41) = a(41) Else GoTo 410
a(9) = 2 * s2 - a(41): If b(a(9)) = 0 Then b(a(9)) = a(9): c(9) = a(9) Else GoTo 90
a(1) = 2 * s2 - a(49): If b(a(1)) = 0 Then b(a(1)) = a(1): c(1) = a(1) Else GoTo 10
For j48 = m1 To m2 'a(48): Remainder
If b(a1(j48)) = 0 Then b(a1(j48)) = a1(j48): c(48) = a1(j48) Else GoTo 480
a(48) = a1(j48)
a(47) = 3 * s2 - a(48) - a(49)
If a(47) < a1(m1) Or a(47) > a1(m2) Then GoTo 470
''If b1(a(47)) = 0 Then GoTo 470
If b(a(47)) = 0 Then b(a(47)) = a(47): c(47) = a(47) Else GoTo 470
a(45) = 7 * s2 - a(48) - a(49) - a(27) - a(31) - a(38) - 2 * a(34) + a(40)
If a(45) < a1(m1) Or a(45) > a1(m2) Then GoTo 450
''If b1(a(45)) = 0 Then GoTo 450
If b(a(45)) = 0 Then b(a(45)) = a(45): c(45) = a(45) Else GoTo 450
a(44) = 3 * s2 - a(48) + a(39) - a(38) - a(40)
If a(44) < a1(m1) Or a(44) > a1(m2) Then GoTo 440
''If b1(a(44)) = 0 Then GoTo 440
If b(a(44)) = 0 Then b(a(44)) = a(44): c(44) = a(44) Else GoTo 440
a(43) = -4 * s2 + 2 * a(48) + a(49) + a(27) - a(39) + 2 * a(34)
If a(43) < a1(m1) Or a(43) > a1(m2) Then GoTo 430
''If b1(a(43)) = 0 Then GoTo 430
If b(a(43)) = 0 Then b(a(43)) = a(43): c(43) = a(43) Else GoTo 430
a(42) = 8 * s2 - a(48) - a(49) - a(31) - 2 * a(38) - 2 * a(34)
If a(42) < a1(m1) Or a(42) > a1(m2) Then GoTo 420
''If b1(a(42)) = 0 Then GoTo 420
If b(a(42)) = 0 Then b(a(42)) = a(42): c(42) = a(42) Else GoTo 420
a(37) = -7 * s2 + 2 * a(48) + a(49) + a(27) - a(39) + a(31) + 2 * a(38) + 2 * a(34)
If a(37) < a1(m1) Or a(37) > a1(m2) Then GoTo 370
''If b1(a(37)) = 0 Then GoTo 370
If b(a(37)) = 0 Then b(a(37)) = a(37): c(37) = a(37) Else GoTo 370
a(36) = 6 * s2 - a(48) - a(49) - a(27) - a(38) - a(34)
If a(36) < a1(m1) Or a(36) > a1(m2) Then GoTo 360
''If b1(a(36)) = 0 Then GoTo 360
If b(a(36)) = 0 Then b(a(36)) = a(36): c(36) = a(36) Else GoTo 360
a(35) = -5 * s2 + a(48) + a(31) + 2 * a(38) + a(34) + a(40)
If a(35) < a1(m1) Or a(35) > a1(m2) Then GoTo 350
''If b1(a(35)) = 0 Then GoTo 350
If b(a(35)) = 0 Then b(a(35)) = a(35): c(35) = a(35) Else GoTo 350
a(29) = s2 - a(48) + a(39) + a(38) - a(34)
If a(29) < a1(m1) Or a(29) > a1(m2) Then GoTo 290
''If b1(a(29)) = 0 Then GoTo 290
If b(a(29)) = 0 Then b(a(29)) = a(29): c(29) = a(29) Else GoTo 290
a(21) = 2 * s2 - a(29): If b(a(21)) = 0 Then b(a(21)) = a(21): c(21) = a(21) Else GoTo 210
a(15) = 2 * s2 - a(35): If b(a(15)) = 0 Then b(a(15)) = a(15): c(15) = a(15) Else GoTo 150
a(14) = 2 * s2 - a(36): If b(a(14)) = 0 Then b(a(14)) = a(14): c(14) = a(14) Else GoTo 140
a(13) = 2 * s2 - a(37): If b(a(13)) = 0 Then b(a(13)) = a(13): c(13) = a(13) Else GoTo 130
a(8) = 2 * s2 - a(42): If b(a(8)) = 0 Then b(a(8)) = a(8): c(8) = a(8) Else GoTo 80
a(7) = 2 * s2 - a(43): If b(a(7)) = 0 Then b(a(7)) = a(7): c(7) = a(7) Else GoTo 70
a(6) = 2 * s2 - a(44): If b(a(6)) = 0 Then b(a(6)) = a(6): c(6) = a(6) Else GoTo 60
a(5) = 2 * s2 - a(45): If b(a(5)) = 0 Then b(a(5)) = a(5): c(5) = a(5) Else GoTo 50
a(3) = 2 * s2 - a(47): If b(a(3)) = 0 Then b(a(3)) = a(3): c(3) = a(3) Else GoTo 30
a(2) = 2 * s2 - a(48): If b(a(2)) = 0 Then b(a(2)) = a(2): c(2) = a(2) Else GoTo 20
GoSub 1850 'Count valid prime numbers
If n10 < n20 Then GoTo 5
n20 = n10 + 1
' n9 = n9 + 1: GoSub 645 'Print results (selected numbers)
n9 = n9 + 1: GoSub 650 'Print results (squares)
' Erase b, c: GoTo 1000 'Print only first square (disable to show intermediate results)
5
b(c(2)) = 0: c(2) = 0
20 b(c(3)) = 0: c(3) = 0
30 b(c(5)) = 0: c(5) = 0
50 b(c(6)) = 0: c(6) = 0
60 b(c(7)) = 0: c(7) = 0
70 b(c(8)) = 0: c(8) = 0
80 b(c(13)) = 0: c(13) = 0
130 b(c(14)) = 0: c(14) = 0
140 b(c(15)) = 0: c(15) = 0
150 b(c(21)) = 0: c(21) = 0
210 b(c(29)) = 0: c(29) = 0
290 b(c(35)) = 0: c(35) = 0
350 b(c(36)) = 0: c(36) = 0
360 b(c(37)) = 0: c(37) = 0
370 b(c(42)) = 0: c(42) = 0
420 b(c(43)) = 0: c(43) = 0
430 b(c(44)) = 0: c(44) = 0
440 b(c(45)) = 0: c(45) = 0
450 b(c(47)) = 0: c(47) = 0
470 b(c(48)) = 0: c(48) = 0
480 Next j48
b(c(1)) = 0: c(1) = 0
10 b(c(9)) = 0: c(9) = 0
90 b(c(41)) = 0: c(41) = 0
410 b(c(49)) = 0: c(49) = 0
490 Next j49
b(c(23)) = 0: c(23) = 0
230 b(c(24)) = 0: c(24) = 0
240 b(c(26)) = 0: c(26) = 0
260 b(c(27)) = 0: c(27) = 0
270 Next j27
b(c(11)) = 0: c(11) = 0
110 b(c(18)) = 0: c(18) = 0
180 b(c(32)) = 0: c(32) = 0
320 b(c(39)) = 0: c(39) = 0
390 Next j39
b(c(4)) = 0: c(4) = 0
40 b(c(19)) = 0: c(19) = 0
190 b(c(20)) = 0: c(20) = 0
200 b(c(30)) = 0: c(30) = 0
300 b(c(46)) = 0: c(46) = 0
460 b(c(31)) = 0: c(31) = 0
310 Next j31
b(c(12)) = 0: c(12) = 0
120 b(c(38)) = 0: c(38) = 0
380 Next j38
b(c(16)) = 0: c(16) = 0
160 b(c(17)) = 0: c(17) = 0
170 b(c(22)) = 0: c(22) = 0
220 b(c(28)) = 0: c(28) = 0
280 b(c(33)) = 0: c(33) = 0
330 b(c(34)) = 0: c(34) = 0
340 Next j34
b(c(10)) = 0: c(10) = 0
100 b(c(40)) = 0: c(40) = 0
400 Next j40
1000 Next j100
t2 = Timer
t10 = Str(t2 - t1) + " sec., " + Str(n9) + " Solutions for sum" + Str(s1)
y = MsgBox(t10, 0, "Routine Priem7d")
End
' Count valid prime numbers
1850 n10 = 0
For i1 = 1 To 49
p1 = a(i1)
''For i2 = 2 To p1 - 1
'' If p1 / i2 = Int(p1 / i2) Then GoTo 1860
''Next i2
''n10 = n10 + 1
If b1(p1) = p1 Then n10 = n10 + 1 'valid primes
1860 Next i1
Return
' Print results (selected numbers)
645 For i1 = 1 To 49
Cells(n9, i1).Value = a(i1)
Next i1
Return
' Print results (squares)
650 n2 = n2 + 1
If n2 = 4 Then
n2 = 1: k1 = k1 + 8: k2 = 1
Else
If n9 > 1 Then k2 = k2 + 8
End If
Cells(k1 + 1, k2 + 1).Select
Cells(k1, k2 + 1).Select
Cells(k1, k2 + 1).Font.Color = -4165632
Cells(k1, k2 + 1).Value = s1 ''n9
Cells(k1, k2 + 2).Value = n10
i3 = 0
For i1 = 1 To 7
For i2 = 1 To 7
i3 = i3 + 1
Cells(k1 + i1, k2 + i2).Value = a(i3)
Next i2
Next i1
Return
' Read Natural Numbers
2000 m1 = 1: m2 = 49: s1 = 175: s2 = 25
For i1 = m1 To m2
a1(i1) = i1
Next i1
Erase b1
For i1 = m1 To m2
b1(a1(i1)) = a1(i1)
Next i1
Return
' Read Prime Numbers From sheet ShtNm1 (e.g. "Pairs7")
2010 s1 = Sheets(ShtNm1).Cells(j100, 3).Value ' MC7
s2 = s1 / 7
nvar1 = Sheets(ShtNm1).Cells(j100, 9).Value
For i1 = 1 To nvar1
a1(i1) = Sheets(ShtNm1).Cells(j100, 9 + i1).Value
Next i1
m1 = 1: m2 = nvar1
If a1(1) = 1 Then m1 = 2: m2 = m2 - 1
Erase b1, b, c
For i1 = m1 To m2
b1(a1(i1)) = a1(i1)
Next i1
Return
' Read Prime Numbers from sheet ShtNm1 (e.g. "Lines7")
2020 m1 = 1: m2 = 49
s1 = Sheets(ShtNm1).Cells(j100, m2 + 1).Value 'ShtNm1 contains likely sequences
s2 = s1 / 7
a2 = 0
For i1 = m1 To m2
a1(i1) = Sheets(ShtNm1).Cells(j100, i1).Value
If a2 < a1(i1) Then a2 = a1(i1) 'Determine Maximum
Next i1
Erase b1, b, c
For i1 = m1 To m2
b1(a1(i1)) = a1(i1)
Next i1
n1 = 0: Erase a1 'Sort a1
For i1 = 1 To a2
If b1(i1) <> 0 Then
n1 = n1 + 1
a1(n1) = b1(i1)
End If
Next i1
' *** Test: Extended Range ***
j101 = Sheets(ShtNm1).Cells(j100, 51).Value 'Record Nr
nvar1 = Sheets("Pairs7").Cells(j101, 9).Value
For i1 = 1 To nvar1
x = Sheets("Pairs7").Cells(j101, 9 + i1).Value
b1(x) = x
Next i1
Return
End Sub
