数论问题巅峰对决

ysr · 发表于 2022-5-26 23:33

ysr 发表于 2022-5-26 11:44
2n+5=49~63的解：
1000内有24组蔡氏素数:
3, 23,31,61,2n+1=49

1000内有24组蔡氏素数:
49/51/53/55/57/59/61/63/用时5.31599999999371秒

ysr · 发表于 2022-5-26 23:39

ysr 发表于 2022-5-26 15:33
1000内有24组蔡氏素数:
49/51/53/55/57/59/61/63/用时5.31599999999371秒

1000内有1789组蔡氏素数:
63/65/67/69/71/73/75/77/79/81/83/85/87/89/91/93/95/97/99/101/
103/105/107/109/111/113/115/117/119/121/123/125/127/129/131/133/135/137/139/141/
143/145/147/149/151/153/155/157/159/161/163/165/167/169/171/173/175/177/179/181/
183/185/187/189/191/193/195/197/199/201/203/205/207/209/211/213/215/217/219/221/
223/225/227/229/231/233/235/237/239/241/243/245/247/249/251/253/255/257/259/261/
263/265/267/269/271/273/275/277/279/281/283/285/287/289/291/293/295/297/299/301/
303/305/307/309/311/313/315/317/319/321/323/325/327/329/331/333/335/337/339/341/
343/345/347/349/351/353/355/357/359/361/363/365/367/369/371/373/375/377/379/381/
383/385/387/389/391/393/395/397/399/401/403/405/407/409/411/413/415/417/419/421/
423/425/427/429/431/433/435/437/439/441/443/445/447/449/451/453/455/457/459/461/
463/465/467/469/471/473/475/477/479/481/483/485/487/489/491/493/495/497/499/501/
503/505/507/509/511/513/515/517/519/521/523/525/527/529/531/533/535/537/539/541/
543/545/547/549/551/553/555/557/559/561/563/565/567/569/571/573/575/577/579/581/
583/585/587/589/591/593/595/597/599/601/603/用时270.613999999997秒

ysr · 发表于 2022-5-26 23:42

Private Sub Command1_Click()
Dim a, B, q
Dim t As Double
t = Timer

q = Val(Text1)
m = 63
Do While m <= 603

p1 = 3
Do While p1 <= q And p1 <= m
p2 = Abs(Val((p1 - m) / 2))
p3 = Abs(Val(2 * p2 - 15))
p4 = Val(2 * p2 + 15)

a = fenjieyinzi(Val(p1))
B = fenjieyinzi(Val(p2))
c = fenjieyinzi(Val(p3))
d = fenjieyinzi(Val(p4))

If InStr(a, "*") = 0 And InStr(B, "*") = 0 And InStr(c, "*") = 0 And InStr(d, "*") = 0 Then
s = s + 1
Print p1, p2, p3, p4
s101 = s101 & "/" & m

Else
s = s
End If
p1 = Val(p1 + 2)
Loop
m = Val(m + 2)
Loop
s103 = Mid(s101, 1)
Dim i As Integer
Dim ak(), s105, cr(), f
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)
Next
Print ak(1)
   n = 0
      For k = 1 To j1
         For i = 1 To j1

n = n + 1
         ReDim Preserve cr(1 To n)
         m = Val(ak(k))
         f(m) = ""
   Next
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
      MsgBox "ok"
   MsgBox s104  '显示数组

Text2 = s104

Combo1 = q & "内有" & s & "组蔡氏素数:" & vbCrLf & Text2 & "用时" & Timer - t & "秒"

End Sub

蔡家雄 · 发表于 2022-5-27 17:47

六素数猜想

设 2n+105 > 10^4，且 p1, p2, p3=2*p2 -105, p4=2*p2 -15, p5=2*p2+15, p6=2*p2+105 都是素数，

则 2n=p1+p3 , 2n+90=p1+p4 , 2n+105=p1+2*p2 , 2n+120=p1+p5 , 2n+210=p1+p6 至少有一对素数解。

ysr · 发表于 2022-5-27 21:31

蔡家雄发表于 2022-5-27 09:47
六素数猜想

设 2n+105 > 10^4，且 p1, p2, p3=2*p2 -105, p4=2*p2 -15, p5=2*p2+15, p6=2*p2+105 都是素 ...

10003~10101的解：
1000内有49组蔡氏素数:
10003/10005/10009/10011/10015/10017/10023/10025/10027/10031/10033/10035/10037/10039/10045/10047/10053/10059/10061/10063/
10065/10067/10069/10071/10077/10083/10085/10087/10089/10091/10093/10095/10099/10101/用时16.8550000000071秒

ysr · 发表于 2022-5-27 21:32

Private Sub Command1_Click()
Dim a, B, q
Dim t As Double
t = Timer

q = Val(Text1)
m = 10001
Do While m <= 10101

p1 = 3
Do While p1 <= q And p1 <= m
p2 = Abs(Val((p1 - m) / 2))
p3 = Abs(Val(2 * p2 - 105))
p4 = Abs(Val(2 * p2 - 15))
p5 = Val(2 * p2 + 15)
p6 = Val(2 * p2 + 105)

a = fenjieyinzi(Val(p1))
B = fenjieyinzi(Val(p2))
c = fenjieyinzi(Val(p3))
d = fenjieyinzi(Val(p4))
f1 = fenjieyinzi(Val(p5))
g = fenjieyinzi(Val(p6))
If InStr(a, "*") = 0 And InStr(B, "*") = 0 And InStr(c, "*") = 0 And InStr(d, "*") = 0 And InStr(f1, "*") = 0 And InStr(g, "*") = 0 Then
s = s + 1
Print p1, p2, p3, p4
s101 = s101 & "/" & m

Else
s = s
End If
p1 = Val(p1 + 2)
Loop
m = Val(m + 2)
Loop
s103 = Mid(s101, 1)
Dim i As Integer
Dim ak(), s105, cr(), f
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)
Next
Print ak(1)
   n = 0
      For k = 1 To j1
         For i = 1 To j1

n = n + 1
         ReDim Preserve cr(1 To n)
         m = Val(ak(k))
         f(m) = ""
   Next
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
      MsgBox "ok"
   MsgBox s104  '显示数组

Text2 = s104

Combo1 = q & "内有" & s & "组蔡氏素数:" & vbCrLf & Text2 & "用时" & Timer - t & "秒"

End Sub

ysr · 发表于 2022-5-27 21:33

10103~10301的解：
1000内有105组蔡氏素数:
10101/10103/10105/10107/10113/10119/10121/10123/10127/10129/10133/10135/10137/10143/10147/10149/10151/10153/10155/10163/
10165/10173/10175/10179/10183/10185/10187/10189/10193/10197/10203/10207/10209/10211/10213/10215/10217/10219/10221/10233/
10237/10241/10243/10245/10249/10251/10253/10255/10257/10261/10263/10267/10269/10273/10275/10277/10279/10281/10285/10291/
10293/10295/10297/10299/10301/用时12.0689999999936秒

ysr · 发表于 2022-5-28 10:22

10000内有430组蔡氏素数:
10001/10003/10005/10007/10009/10011/10013/10015/10017/10019/10021/10023/10025/10027/10029/10031/10033/10035/10037/10039/
10041/10043/10045/10047/10049/10051/10053/10055/10057/10059/10061/10063/10065/10067/10069/10071/10073/10075/10077/10079/
10081/10083/10085/10087/10089/10091/10093/10095/10097/10099/10101/用时23.8539999999994秒

蔡家雄 · 发表于 2022-5-28 21:13

蔡氏奇数分拆

设 2n+15 >=33,

则 2n+15=p1+2*p2 , 2n+45=p3+2*p2 , 2n+75=p4+2*p2 均有素数解。

注：p2 可以等于2，2也是素数。

ysr · 发表于 2022-5-28 21:44

蔡家雄发表于 2022-5-28 13:13
蔡氏奇数分拆

设 2n+15 >=33,

10000内有110组蔡氏素数:
33/35/37/39/41/43/45/47/49/51/53/55/57/59/61/63/65/67/69/71/
73/75/77/79/81/83/85/87/89/91/93/95/97/99/101/用时5.24600000000524秒

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