高手编的快速计算16（1.6×10^9)亿内孪生素数的程序

ysr · 发表于 2026-9-23 14:24

虽然波动性跟踪的很好，但是增加了许多解的个数大于实际的偶数，不过差值变小了而已。所以，该值只能是对波动性研究的参考，不能用于证明。
能用于证明的是绝对下限值，这是理论上的下限，是定理，大于等于4的偶数都成立的，是铁的事实。所以，哥德巴赫猜想远远成立。

ysr · 发表于 2026-9-23 14:30

重新发一下这个程序，稍改动，去掉了过程中间弹出来的需要手动点击的窗口程序，代码如下：

Private Sub Command1_Click()
Dim a, b, c
a = Val(Text1)
b = Val(Text2)
If Right(a, 1) Mod 2 = 0 Then
a = a
Else
a = Val(a + 1)
End If

a1 = a
Do While a1 <= b
c = fenjieyinzi1(Val(a1))
c2 = fenjieyinzi2(Val(a1))
gl1 = (Val(a1)) ^ 0.5
g = Mid(c, InStr(c, "=") + 1)
sa = fenjieyinzi(Val(a1))
sa = "*" & Trim(sa)
sa = paixu1(Trim(sa))
k = paixu12(Trim(sa), Val(gl1))
lg = Mid(c2, InStr(c2, "=") + 1)
lg = Mid(lg, 1, InStr(lg, "而") - 1)
klg = Val(k) * Val(lg)
lg = Int(Val(lg))
c3 = Mid(c2, InStr(c2, "为") + 1, InStr(c2, ">") - 1)
m = Val(c3)
ls = fenjieyinzi3(Val(a1))
c1 = c1 & c & " /差为" & Val(g - lg) & "/" & c2 & vbCrLf & "实际区间平均值G/(m-1)为" & Val(g) / (Val(m) - 1) & "  KLG=" & klg & vbCrLf & "小根拆：" & vbCrLf & ls

a1 = a1 + 2
Loop
Text3 = c1
jc = "（如下文字和数据中的小于＜和大于＞是代表尖括号，其中的斜杠/只有在“LG/(m-1)”中间的斜杠/是除号，其他都是间隔号）" & vbCrLf
Combo1 = jc & "偶数/ 方根/  GM/  G/差 G-LG/ 偶数/  P/ m/ <LG/(m-1)区间理论平均值>/ LG" & vbCrLf & c1
End Sub

Private Sub Command2_Click()
Text1 = ""
Text2 = ""
Text3 = ""
Combo1 = ""
Form1.Cls
End Sub
Private Function fenjieyinzi(sa As String) As String
Dim x, a, b, k As String
a = Val(sa)

x = 3
If a <= 1 Or a > Int(a) Then
If a = 1 Then
fenjieyinzi = "它既不是质数，也不是合数"

Else
MsgBox "error"
End If

Else

Do While a / 2 = Int(a / 2) And a >= 4

If b = 0 Then
fenjieyinzi = fenjieyinzi & "2"
b = 1
Else
fenjieyinzi = fenjieyinzi & "*2"
End If
a = a / 2
k = a

Loop

Do While a > 1
Do While x <= Sqr(a)
Do While a / x = Int(a / x) And a >= x * x

If b = 0 Then
fenjieyinzi = fenjieyinzi & x
b = 1
Else
fenjieyinzi = fenjieyinzi & "*" & x
End If
a = a / x
Loop

x = x + 2
Loop

k = a
a = 1
Loop

If b = 1 Then
fenjieyinzi = fenjieyinzi & "*" & k
Else
fenjieyinzi = "这是一个质数"
End If

End If

End Function
Private Function fenjieyinzi1(sa As String) As String
Dim a, b
a = Val(sa)
m = Sqr(a)
a1 = 3
s = 0
Do While a1 <= m
b = a - a1
c = fenjieyinzi(Val(a1))
d = fenjieyinzi(Val(b))
If InStr(c, "*") = 0 And InStr(d, "*") = 0 Then
s = s + 1
Print a1, "+", b
'ls2 = ls2 & CStr(a1) & "+ " & CStr(b) & vbCrLf
Else
s = s
End If
a1 = a1 + 2
Loop
a2 = a1
s1 = s
Do While a2 <= a / 2
b1 = a - a2
c1 = fenjieyinzi(Val(a2))
d1 = fenjieyinzi(Val(b1))

If InStr(c1, "*") = 0 And InStr(d1, "*") = 0 Then
s1 = s1 + 1
Print a2, "+", b1
'ls2 = ls2 & CStr(a2) & "+ " & CStr(b1) & vbCrLf
Else
s1 = s1
End If
a2 = a2 + 2

Loop
fenjieyinzi1 = a & "/方根" & m & "/GM是" & s & " / G=" & s1
End Function
Private Function fenjieyinzi2(sa As String) As String
Dim a, b
a = Val(sa)
m = Sqr(a)
m1 = Int(m)
a2 = m1
a1 = 3
s = 1
b = 1
Do While a2 <= m And InStr(fenjieyinzi(Val(a2)), "*") <> 0
a2 = a2 - 1
Loop
Do While a1 <= a2
c = fenjieyinzi(Val(a1))
If InStr(Trim(c), "*") = 0 Then
s = s + 1
b = b * Val(1 - 2 / a1)
Else
s = s
End If
a1 = a1 + 2
Loop
b2 = (a2 ^ 2 / 4) * b
b1 = (a / 4) * b
s1 = s
Do While a1 <= 4 * a2
c = fenjieyinzi(Val(a1))
If InStr(Trim(c), "*") = 0 Then
s1 = s1 + 1
b = b * Val(1 - 2 / a1)
Else
s1 = s1
End If

a1 = a1 + 2
Loop
b3 = (a / 4) * b
If s = 1 Then

fenjieyinzi2 = "  /" & a & " /" & a2 & " /m为" & s & ">  区间的理论平均值LG/(m-1)为" & b2 / s - 1 & "  LG=" & b1 & "而CLG是" & b3
Else
fenjieyinzi2 = " /" & a & " /" & a2 & " /<m为" & s & ">  区间的理论平均值LG/(m-1)为" & b2 / (s - 1) & "  LG=" & b1 & "而CLG是" & b3
End If

End Function

Private Function fenjieyinzi3(sa As String) As String
Dim a, b
a = Val(sa)
m = Sqr(a)
a1 = 3
s = 0
Do While a1 <= m
b = a - a1
c = fenjieyinzi(Val(a1))
d = fenjieyinzi(Val(b))
If InStr(c, "*") = 0 And InStr(d, "*") = 0 Then
s = s + 1
Print a1, "+", b
ls2 = ls2 & CStr(a1) & "+ " & CStr(b) & vbCrLf
Else
s = s
End If
a1 = a1 + 2
Loop
a2 = a1
s1 = s
Do While a2 <= a / 2
b1 = a - a2
c1 = fenjieyinzi(Val(a2))
d1 = fenjieyinzi(Val(b1))

If InStr(c1, "*") = 0 And InStr(d1, "*") = 0 Then
s1 = s1 + 1
Print a2, "+", b1
'ls2 = ls2 & CStr(a2) & "+ " & CStr(b1) & vbCrLf
Else
s1 = s1
End If
a2 = a2 + 2

Loop
fenjieyinzi3 = ls2
End Function

Private Function paixu12(a As String, sb As String) As String
Dim i As Integer
Dim ak(), s105, cr(), k
s103 = a
Set f = CreateObject("Scripting.Dictionary")
s105 = Split(s103, "/")
j1 = UBound(s105)
Print j1
k = 1
For k1 = 1 To j1
   n1 = n1 + 1
   ReDim Preserve ak(1 To n1)
   ak(n1) = s105(n1)
   k2 = ak(n1)
   Print ak(n1)
   If k2 <> 2 And k2 < Val(sb) Then
   k = k * (k2 - 1) / (k2 - 2)
   Else
   k = k
   End If
Next
paixu12 = k
End Function
Private Function paixu1(a As String) As String
Dim i As Integer
Dim ak(), s105, cr(), f
s103 = a
Set f = CreateObject("Scripting.Dictionary")
s105 = Split(s103, "*")
j1 = UBound(s105)
Print j1
For k = 1 To j1
   n1 = n1 + 1
   ReDim Preserve ak(1 To n1)
   ak(n1) = s105(n1)
   Print ak(n1)
Next


      For k = 1 To j1

         ReDim Preserve cr(1 To k)
         m = Val(ak(k))
         f(m) = ""
   Next

   n = 0
   m = f.Keys
   For i = 0 To f.Count - 1
      ReDim Preserve cr(1 To i + 1)
      cr(i + 1) = m(i)
   Next
   For i = 1 To UBound(cr) - 1
      For j = i + 1 To UBound(cr)
         If cr(i) > cr(j) Then
            temp = cr(j)
            cr(j) = cr(i)
            cr(i) = temp  'c数组是排序好的
         End If
      Next j

   ' If i Mod 20 = 0 Then
   ' s104 = s104 & temp & "/" & vbCrLf
   ' Else
   ' s104 = s104 & temp & "/"
   ' End If
Next i

   For i = 1 To UBound(cr)
      If i Mod 20 = 0 Then
      s104 = s104 & "/" & cr(i) & vbCrLf
      Else
      s104 = s104 & "/" & cr(i)
      End If
   Next
      Print temp

   paixu1 = s104
End Function

ysr · 发表于 2026-9-23 14:45

其中的KLG是乘以波动因子K的连乘积结果，能够跟踪实际值，接近或稍大于实际，差值不大而已。仅仅用于参考而不能用于证明。
说明影响解的个数的因素：除了不同的奇素因子的个数多少，主要的就是奇素因子的大小，越小的影响越大，其他因素就是素因子疏密不均匀分布也有影响，只是影响较小而已。

ysr · 发表于 2026-9-24 12:47

用波动因子乘以过度筛选的连乘积CLG会怎么样呢？可能会接近实际而不会大于实际，下面试试吧！

ysr · 发表于 2026-9-24 12:59

（如下文字和数据中的小于＜和大于＞是代表尖括号，其中的斜杠/只有在“LG/(m-1)”中间的斜杠/是除号，其他都是间隔号）
偶数/ 方根/  GM/  G/差 G-LG/ 偶数/  P/ m/ <LG/(m-1)区间理论平均值>/ LG
218090/方根467.001070662584/GM是10 / G=1539 /差为364/ /218090 /467 /<m为91>  区间的理论平均值LG/(m-1)为13.0614716990477  LG=1175.53784306443而CLG是796.171830275771
实际区间平均值G/(m-1)为17.1  KCLG=1076.73405583071
小根拆：
3+ 218087
7+ 218083
13+ 218077
43+ 218047
109+ 217981
157+ 217933
181+ 217909
241+ 217849
373+ 217717
409+ 217681
218092/方根467.003211980389/GM是16 / G=1351 /差为176/ /218092 /467 /<m为91>  区间的理论平均值LG/(m-1)为13.0614716990477  LG=1175.5486233647而CLG是796.179131590185
实际区间平均值G/(m-1)为15.0111111111111  KCLG=955.414957908222
小根拆：
5+ 218087
11+ 218081
23+ 218069
71+ 218021
89+ 218003
113+ 217979
191+ 217901
233+ 217859
263+ 217829
269+ 217823
311+ 217781
353+ 217739
359+ 217733
401+ 217691
431+ 217661
449+ 217643
218094/方根467.005353288375/GM是15 / G=2293 /差为1118/ /218094 /467 /<m为91>  区间的理论平均值LG/(m-1)为13.0614716990477  LG=1175.55940366497而CLG是796.186432904599
实际区间平均值G/(m-1)为25.4777777777778  KCLG=1609.51344104893
小根拆：
7+ 218087
11+ 218083
13+ 218081
17+ 218077
47+ 218047
73+ 218021
113+ 217981
157+ 217937
193+ 217901
271+ 217823
313+ 217781
347+ 217747
367+ 217727
397+ 217697
433+ 217661
218096/方根467.007494586543/GM是7 / G=1152 /差为-23/ /218096 /467 /<m为91>  区间的理论平均值LG/(m-1)为13.0614716990477  LG=1175.57018396524而CLG是796.193734219013
实际区间平均值G/(m-1)为12.8  KCLG=818.202341506364
小根拆：
13+ 218083
19+ 218077
127+ 217969
163+ 217933
349+ 217747
379+ 217717
409+ 217687
218098/方根467.009635874893/GM是11 / G=1125 /差为-50/ /218098 /467 /<m为91>  区间的理论平均值LG/(m-1)为13.0614716990477  LG=1175.58096426551而CLG是796.201035533427
实际区间平均值G/(m-1)为12.5  KCLG=796.201035533427
小根拆：
11+ 218087
17+ 218081
29+ 218069
191+ 217907
197+ 217901
239+ 217859
269+ 217829
317+ 217781
359+ 217739
401+ 217697
431+ 217667

ysr · 发表于 2026-9-24 13:06

通过上面的数据可以看到，虽然波动因子乘以过度筛选的连乘积CLG得到的KCLG也是波动的，但是远没有超过实际值G，虽然接近但仍然有差距，不过差距变小一点而已。
但不能用于证明，做证据需要证明到无穷仍然是小于实际的。可用于证明的是绝对下限公式，我的书中早有了。

ysr · 发表于 2026-9-24 13:17

代码如下：

Private Sub Command1_Click()
Dim a, b, c
a = Val(Text1)
b = Val(Text2)
If Right(a, 1) Mod 2 = 0 Then
a = a
Else
a = Val(a + 1)
End If

a1 = a
Do While a1 <= b
c = fenjieyinzi1(Val(a1))
c2 = fenjieyinzi2(Val(a1))
gl1 = (Val(a1)) ^ 0.5
g = Mid(c, InStr(c, "=") + 1)
sa = fenjieyinzi(Val(a1))
sa = "*" & Trim(sa)
sa = paixu1(Trim(sa))
k = paixu12(Trim(sa), Val(gl1))
lg = Mid(c2, InStr(c2, "=") + 1)
lg = Mid(lg, 1, InStr(lg, "而") - 1)
klg = Val(k) * Val(lg)
lg = Int(Val(lg))
c3 = Mid(c2, InStr(c2, "为") + 1, InStr(c2, ">") - 1)
m = Val(c3)
clg = Mid(c2, InStr(c2, "是") + 1)
kclg = Val(k) * Val(clg)
ls = fenjieyinzi3(Val(a1))
c1 = c1 & c & " /差为" & Val(g - lg) & "/" & c2 & vbCrLf & "实际区间平均值G/(m-1)为" & Val(g) / (Val(m) - 1) & "  KCLG=" & kclg & vbCrLf & "小根拆：" & vbCrLf & ls

a1 = a1 + 2
Loop
Text3 = c1
jc = "（如下文字和数据中的小于＜和大于＞是代表尖括号，其中的斜杠/只有在“LG/(m-1)”中间的斜杠/是除号，其他都是间隔号）" & vbCrLf
Combo1 = jc & "偶数/ 方根/  GM/  G/差 G-LG/ 偶数/  P/ m/ <LG/(m-1)区间理论平均值>/ LG" & vbCrLf & c1
End Sub

Private Sub Command2_Click()
Text1 = ""
Text2 = ""
Text3 = ""
Combo1 = ""
Form1.Cls
End Sub
Private Function fenjieyinzi(sa As String) As String
Dim x, a, b, k As String
a = Val(sa)

x = 3
If a <= 1 Or a > Int(a) Then
If a = 1 Then
fenjieyinzi = "它既不是质数，也不是合数"

Else
MsgBox "error"
End If

Else

Do While a / 2 = Int(a / 2) And a >= 4

If b = 0 Then
fenjieyinzi = fenjieyinzi & "2"
b = 1
Else
fenjieyinzi = fenjieyinzi & "*2"
End If
a = a / 2
k = a

Loop

Do While a > 1
Do While x <= Sqr(a)
Do While a / x = Int(a / x) And a >= x * x

If b = 0 Then
fenjieyinzi = fenjieyinzi & x
b = 1
Else
fenjieyinzi = fenjieyinzi & "*" & x
End If
a = a / x
Loop

x = x + 2
Loop

k = a
a = 1
Loop

If b = 1 Then
fenjieyinzi = fenjieyinzi & "*" & k
Else
fenjieyinzi = "这是一个质数"
End If

End If

End Function
Private Function fenjieyinzi1(sa As String) As String
Dim a, b
a = Val(sa)
m = Sqr(a)
a1 = 3
s = 0
Do While a1 <= m
b = a - a1
c = fenjieyinzi(Val(a1))
d = fenjieyinzi(Val(b))
If InStr(c, "*") = 0 And InStr(d, "*") = 0 Then
s = s + 1
Print a1, "+", b
'ls2 = ls2 & CStr(a1) & "+ " & CStr(b) & vbCrLf
Else
s = s
End If
a1 = a1 + 2
Loop
a2 = a1
s1 = s
Do While a2 <= a / 2
b1 = a - a2
c1 = fenjieyinzi(Val(a2))
d1 = fenjieyinzi(Val(b1))

If InStr(c1, "*") = 0 And InStr(d1, "*") = 0 Then
s1 = s1 + 1
Print a2, "+", b1
'ls2 = ls2 & CStr(a2) & "+ " & CStr(b1) & vbCrLf
Else
s1 = s1
End If
a2 = a2 + 2

Loop
fenjieyinzi1 = a & "/方根" & m & "/GM是" & s & " / G=" & s1
End Function
Private Function fenjieyinzi2(sa As String) As String
Dim a, b
a = Val(sa)
m = Sqr(a)
m1 = Int(m)
a2 = m1
a1 = 3
s = 1
b = 1
Do While a2 <= m And InStr(fenjieyinzi(Val(a2)), "*") <> 0
a2 = a2 - 1
Loop
Do While a1 <= a2
c = fenjieyinzi(Val(a1))
If InStr(Trim(c), "*") = 0 Then
s = s + 1
b = b * Val(1 - 2 / a1)
Else
s = s
End If
a1 = a1 + 2
Loop
b2 = (a2 ^ 2 / 4) * b
b1 = (a / 4) * b
s1 = s
Do While a1 <= 4 * a2
c = fenjieyinzi(Val(a1))
If InStr(Trim(c), "*") = 0 Then
s1 = s1 + 1
b = b * Val(1 - 2 / a1)
Else
s1 = s1
End If

a1 = a1 + 2
Loop
b3 = (a / 4) * b
If s = 1 Then

fenjieyinzi2 = "  /" & a & " /" & a2 & " /m为" & s & ">  区间的理论平均值LG/(m-1)为" & b2 / s - 1 & "  LG=" & b1 & "而CLG是" & b3
Else
fenjieyinzi2 = " /" & a & " /" & a2 & " /<m为" & s & ">  区间的理论平均值LG/(m-1)为" & b2 / (s - 1) & "  LG=" & b1 & "而CLG是" & b3
End If

End Function

Private Function fenjieyinzi3(sa As String) As String
Dim a, b
a = Val(sa)
m = Sqr(a)
a1 = 3
s = 0
Do While a1 <= m
b = a - a1
c = fenjieyinzi(Val(a1))
d = fenjieyinzi(Val(b))
If InStr(c, "*") = 0 And InStr(d, "*") = 0 Then
s = s + 1
Print a1, "+", b
ls2 = ls2 & CStr(a1) & "+ " & CStr(b) & vbCrLf
Else
s = s
End If
a1 = a1 + 2
Loop
a2 = a1
s1 = s
Do While a2 <= a / 2
b1 = a - a2
c1 = fenjieyinzi(Val(a2))
d1 = fenjieyinzi(Val(b1))

If InStr(c1, "*") = 0 And InStr(d1, "*") = 0 Then
s1 = s1 + 1
Print a2, "+", b1
'ls2 = ls2 & CStr(a2) & "+ " & CStr(b1) & vbCrLf
Else
s1 = s1
End If
a2 = a2 + 2

Loop
fenjieyinzi3 = ls2
End Function

Private Function paixu12(a As String, sb As String) As String
Dim i As Integer
Dim ak(), s105, cr(), k
s103 = a
Set f = CreateObject("Scripting.Dictionary")
s105 = Split(s103, "/")
j1 = UBound(s105)
Print j1
k = 1
For k1 = 1 To j1
   n1 = n1 + 1
   ReDim Preserve ak(1 To n1)
   ak(n1) = s105(n1)
   k2 = ak(n1)
   Print ak(n1)
   If k2 <> 2 And k2 < Val(sb) Then
   k = k * (k2 - 1) / (k2 - 2)
   Else
   k = k
   End If
Next
paixu12 = k
End Function
Private Function paixu1(a As String) As String
Dim i As Integer
Dim ak(), s105, cr(), f
s103 = a
Set f = CreateObject("Scripting.Dictionary")
s105 = Split(s103, "*")
j1 = UBound(s105)
Print j1
For k = 1 To j1
   n1 = n1 + 1
   ReDim Preserve ak(1 To n1)
   ak(n1) = s105(n1)
   Print ak(n1)
Next


      For k = 1 To j1

         ReDim Preserve cr(1 To k)
         m = Val(ak(k))
         f(m) = ""
   Next

   n = 0
   m = f.Keys
   For i = 0 To f.Count - 1
      ReDim Preserve cr(1 To i + 1)
      cr(i + 1) = m(i)
   Next
   For i = 1 To UBound(cr) - 1
      For j = i + 1 To UBound(cr)
         If cr(i) > cr(j) Then
            temp = cr(j)
            cr(j) = cr(i)
            cr(i) = temp  'c数组是排序好的
         End If
      Next j

   ' If i Mod 20 = 0 Then
   ' s104 = s104 & temp & "/" & vbCrLf
   ' Else
   ' s104 = s104 & temp & "/"
   ' End If
Next i

   For i = 1 To UBound(cr)
      If i Mod 20 = 0 Then
      s104 = s104 & "/" & cr(i) & vbCrLf
      Else
      s104 = s104 & "/" & cr(i)
      End If
   Next
      Print temp

   paixu1 = s104
End Function

ysr · 发表于 2026-9-25 14:48

1000000000其1/2内的总素数：26355867,1000000000/2内的最大素数：499999993，拆分素数对：2274205,用时：31343.559秒

71  + 999999929
107  + 999999893
239  + 999999761
401  + 999999599
509  + 999999491
647  + 999999353
677  + 999999323
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887  + 999999113
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11987  + 999988013
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15767  + 999984233
15923  + 999984077
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16889  + 999983111
16937  + 999983063
17333  + 999982667
17417  + 999982583
17609  + 999982391
……………………………………………………………………后面还有不发了

ysr · 发表于 2026-10-3 07:46

（如下文字和数据中的小于＜和大于＞是代表尖括号，其中的斜杠/只有在“LG/(m-1)”中间的斜杠/是除号，其他都是间隔号）
偶数/ 方根/  GM/  G/差 G-LG/ 偶数/  P/ m/ <LG/(m-1)区间理论平均值>/ LG
464904586/方根21561.6461801969/GM是163 / G=857562 /差为-113028/ /464904586 /21559 /<m为2419>  区间的理论平均值LG/(m-1)为401.303524219694  LG=970590.14074054而CLG是748732.654982194
实际区间平均值G/(m-1)为354.657568238213  KLG=970590.14074054
小根拆：
233+ 464904353
269+ 464904317
317+ 464904269
347+ 464904239
353+ 464904233
449+ 464904137
647+ 464903939
719+ 464903867
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464904588/方根21561.6462265756/GM是325 / G=1738947 /差为768357/ /464904588 /21559 /<m为2419>  区间的理论平均值LG/(m-1)为401.303524219694  LG=970590.144915978而CLG是748732.658203211
实际区间平均值G/(m-1)为719.167493796526  KLG=1968520.85729438
小根拆：
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