数论问题巅峰对决

ysr

ysr 发表于 2022-5-24 07:39
1000内有3组蔡氏素数:
3, 29,61,2n+1=61
23, 19,41,2n+1=61

1000内有5组蔡氏素数:
5, 29,61,2n+1=63
29, 17,37,2n+1=63
37, 13,29,2n+1=63
53, 5,13,2n+1=63
59, 2,7,2n+1=63
用时9.0000000035495E-03秒

ysr

蔡家雄 发表于 2022-5-24 05:26
三素数猜想

设 2n+1 >=61，且 p1, p2, p3=2*p2+3 都是素数，

1000内有40组蔡氏素数:
3, 29,61,2n+1=61
23, 19,41,2n+1=61
47, 7,17,2n+1=61
5, 29,61,2n+1=63
29, 17,37,2n+1=63
37, 13,29,2n+1=63
53, 5,13,2n+1=63
59, 2,7,2n+1=63
7, 29,61,2n+1=65
31, 17,37,2n+1=65
61, 2,7,2n+1=65
29, 19,41,2n+1=67
41, 13,29,2n+1=67
53, 7,17,2n+1=67
11, 29,61,2n+1=69
31, 19,41,2n+1=69
43, 13,29,2n+1=69
59, 5,13,2n+1=69
13, 29,61,2n+1=71
37, 17,37,2n+1=71
61, 5,13,2n+1=71
67, 2,7,2n+1=71
47, 13,29,2n+1=73
59, 7,17,2n+1=73
17, 29,61,2n+1=75
37, 19,41,2n+1=75
41, 17,37,2n+1=75
61, 7,17,2n+1=75
71, 2,7,2n+1=75
19, 29,61,2n+1=77
43, 17,37,2n+1=77
67, 5,13,2n+1=77
73, 2,7,2n+1=77
41, 19,41,2n+1=79
53, 13,29,2n+1=79
23, 29,61,2n+1=81
43, 19,41,2n+1=81
47, 17,37,2n+1=81
67, 7,17,2n+1=81
71, 5,13,2n+1=81
用时1.79999999977909E-02秒

ysr

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

q = Val(Text1)
m = 61
Do While m <= 81

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


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


If InStr(a, "*") = 0 And InStr(B, "*") = 0 And InStr(c, "*") = 0 Then
s = s + 1
Print p1, p2, p3, p4
Text2 = Text2 & CStr(p1) & ", " & CStr(p2) & "," & p3 & ",2n+1=" & m & vbCrLf

Else
s = s
End If
p1 = Val(p1 + 2)
Loop
m = Val(m + 2)
Loop
Combo1 = q & "内有" & s & "组蔡氏素数:" & vbCrLf & Text2 & "用时" & Timer - t & "秒"

End Sub

蔡家雄

三素数猜想

设 2n+1 >=61，且 p1, p2, p3=2*p2+3 都是素数，

则 2n+1=p1+2*p2 与 2n+4=p1+p3 至少有一对素数解。

蔡氏三素数猜想是偶数哥猜与奇数哥猜合二为一的素数解。

ysr

蔡家雄 发表于 2022-5-24 11:28
三素数猜想

设 2n+1 >=61，且 p1, p2, p3=2*p2+3 都是素数，

1000内有3543组蔡氏素数:
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/
603/605/607/609/611/613/615/617/619/621/623/625/627/629/631/633/635/637/639/641/
643/645/647/649/651/653/655/657/659/661/663/665/667/669/671/673/675/677/679/681/
683/685/687/689/691/693/695/697/699/701/703/705/707/709/711/713/715/717/719/721/
723/725/727/729/731/733/735/737/739/741/743/745/747/749/751/753/755/757/759/761/
763/765/767/769/771/773/775/777/779/781/783/785/787/789/791/793/795/797/799/801/
803/805/807/809/811/813/815/817/819/821/823/825/827/829/831/833/835/837/839/841/
843/845/847/849/851/853/855/857/859/861/863/865/867/869/871/873/875/877/879/881/
883/885/887/889/891/893/895/897/899/901/903/905/907/909/911/913/915/917/919/921/
923/925/927/929/931/933/935/937/939/941/943/945/947/949/951/953/955/957/959/961/
963/965/967/969/971/973/975/977/979/981/983/985/987/989/991/993/995/997/999/1001/
用时5991.044秒

ysr

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

q = Val(Text1)
m = 363
Do While m <= 1001

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


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


If InStr(a, "*") = 0 And InStr(B, "*") = 0 And InStr(c, "*") = 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

三素数猜想（加3型）

设 2n+1 >=61，且 p1, p2, p3=2*p2+3 都是素数，

则 2n+1=p1+2*p2 与 2n+4=p1+p3 至少有一对素数解。

蔡氏三素数猜想是偶数哥猜与奇数哥猜合二为一的素数解。

三素数猜想（减3型）

设 2n+3 >=9，且 p1, p2, p3=2*p2 -3 都是素数，

则 2n+3=p1+2*p2 与 2n=p1+p3 至少有一对素数解。

ysr

蔡家雄 发表于 2022-5-24 22:01
三素数猜想（加3型）

设 2n+1 >=61，且 p1, p2, p3=2*p2+3 都是素数，

1000内有858组蔡氏素数:
9/11/13/15/17/19/21/23/25/27/29/31/33/35/37/39/41/43/45/47/
49/51/53/55/57/59/61/63/65/67/69/71/73/75/77/79/81/83/85/87/
89/91/93/95/97/99/101/103/105/107/109/111/113/115/117/119/121/123/125/127/
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/用时34.4420000000011秒

蔡家雄

蔡氏四素数猜想

设 2n+15 >=49，且 p1, p2, p3=2*p2 -15, p4=2*p2+15 都是素数，

则 2n=p1+p3 与 2n+15=p1+2*p2 及 2n+30=p1+p4 至少有一对素数解。

蔡氏四素数猜想是偶数哥猜与奇数哥猜合二为一的素数解。

ysr

蔡家雄 发表于 2022-5-25 15:08
蔡氏四素数猜想

设 2n+15 >=49，且 p1, p2, p3=2*p2 -15, p4=2*p2+15 都是素数，

2n+5=49~63的解：
1000内有24组蔡氏素数:
3, 23,31,61,2n+1=49
11, 19,23,53,2n+1=49
23, 13,11,41,2n+1=49
5, 23,31,61,2n+1=51
13, 19,23,53,2n+1=51
29, 11,7,37,2n+1=51
47, 2,11,19,2n+1=51
7, 23,31,61,2n+1=53
31, 11,7,37,2n+1=53
17, 19,23,53,2n+1=55
29, 13,11,41,2n+1=55
11, 23,31,61,2n+1=57
19, 19,23,53,2n+1=57
31, 13,11,41,2n+1=57
53, 2,11,19,2n+1=57
13, 23,31,61,2n+1=59
37, 11,7,37,2n+1=59
3, 29,43,73,2n+1=61
23, 19,23,53,2n+1=61
5, 29,43,73,2n+1=63
17, 23,31,61,2n+1=63
37, 13,11,41,2n+1=63
41, 11,7,37,2n+1=63
59, 2,11,19,2n+1=63
用时0.016000000001398秒