基础理论中的两个重要定理的证明

ysr · 发表于 2026-4-2 01:17

本帖最后由 ysr 于 2026-4-1 17:19 编辑

在10000内的这样的素数组有1 组：
(199 409 619 829 1039 1249 1459 1669 1879 2089 )
命题：公差为210的10生素数组有且只有1组，其中有的组中间可能还有其他素数。

ysr · 发表于 2026-4-2 01:20

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 Sub Command1_Click()
Dim a, b
a = Val(Text1)
p1 = 3
Do While p1 <= a
p1 = p1: p2 = p1 + 210: p3 = p2 + 210
p4 = p3 + 210: p5 = p4 + 210: p6 = p5 + 210: p7 = p6 + 210
p8 = p7 + 210: p9 = p8 + 210: p10 = p9 + 210
p11 = fenjieyinzi(Val(p1)): p12 = fenjieyinzi(Val(p2)): p13 = fenjieyinzi(Val(p3))
p14 = fenjieyinzi(Val(p4)): p15 = fenjieyinzi(Val(p5)): p16 = fenjieyinzi(Val(p6)): p17 = fenjieyinzi(Val(p7))
p18 = fenjieyinzi(Val(p8)): p19 = fenjieyinzi(Val(p9)): p20 = fenjieyinzi(Val(p10))
If InStr(p11, "*") = 0 And InStr(p12, "*") = 0 And InStr(p13, "*") = 0 And InStr(p14, "*") = 0 And InStr(p15, "*") = 0 And InStr(p16, "*") = 0 And InStr(p17, "*") = 0 And InStr(p18, "*") = 0 And InStr(p19, "*") = 0 And InStr(p20, "*") = 0 Then
s11 = s11 & "(" & p1 & " " & p2 & " " & p3 & " " & p4 & " " & p5 & " " & p6 & " " & p7 & " " & p8 & " " & p9 & " " & p10 & " )  " & vbCrLf

s12 = s12 + 1
End If

p1 = p1 + 2
Loop
If s12 >= 1 Then
Text2 = "在" & Text1 & "内的这样的素数组有" & s12 & " 组： " & vbCrLf & s11
Else
Text2 = "wu  jie"
End If

Combo1 = Text2

End Sub

Private Sub Command2_Click()
Text1 = ""
Text2 = ""
Text3 = ""
Combo1 = ""
Form21.Cls
End Sub

ysr · 发表于 2026-4-2 07:14

本帖最后由 ysr 于 2026-4-2 23:51 编辑

在10000内的这样的素数组有3 组：
(13 223 433 643 853 1063 3373 3583 3793 4003 )
(1453 1663 1873 2083 2293 2503 4813 5023 5233 5443 )
(1663 1873 2083 2293 2503 2713 5023 5233 5443 5653 )
命题：前6项公差为210第七项差2310后3项公差210的10生素数组可能仅仅3组，其中有的组中间可能还有其他素数。

ysr · 发表于 2026-4-2 08:13

本帖最后由 ysr 于 2026-4-2 23:52 编辑

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 Sub Command1_Click()
Dim a, b
a = Val(Text1)
p1 = 3
Do While p1 <= a
p1 = p1: p2 = p1 + 210: p3 = p2 + 210
p4 = p3 + 210: p5 = p4 + 210: p6 = p5 + 210: p7 = p6 + 2310
p8 = p7 + 210: p9 = p8 + 210: p10 = p9 + 210
p11 = fenjieyinzi(Val(p1)): p12 = fenjieyinzi(Val(p2)): p13 = fenjieyinzi(Val(p3))
p14 = fenjieyinzi(Val(p4)): p15 = fenjieyinzi(Val(p5)): p16 = fenjieyinzi(Val(p6)): p17 = fenjieyinzi(Val(p7))
p18 = fenjieyinzi(Val(p8)): p19 = fenjieyinzi(Val(p9)): p20 = fenjieyinzi(Val(p10))
If InStr(p11, "*") = 0 And InStr(p12, "*") = 0 And InStr(p13, "*") = 0 And InStr(p14, "*") = 0 And InStr(p15, "*") = 0 And InStr(p16, "*") = 0 And InStr(p17, "*") = 0 And InStr(p18, "*") = 0 And InStr(p19, "*") = 0 And InStr(p20, "*") = 0 Then
s11 = s11 & "(" & p1 & " " & p2 & " " & p3 & " " & p4 & " " & p5 & " " & p6 & " " & p7 & " " & p8 & " " & p9 & " " & p10 & " )  " & vbCrLf

s12 = s12 + 1
End If

p1 = p1 + 2
Loop
If s12 >= 1 Then
Text2 = "在" & Text1 & "内的这样的素数组有" & s12 & " 组： " & vbCrLf & s11
Else
Text2 = "wu  jie"
End If

Combo1 = Text2

End Sub

Private Sub Command2_Click()
Text1 = ""
Text2 = ""
Text3 = ""
Combo1 = ""
Form21.Cls
End Sub

ysr · 发表于 2026-4-3 08:01

在10000内的这样的素数组有1 组：
(3499 3709 3919 4129 4339 4549 4759 4969 5179 7489 )
命题：前9项公差为210后一项差2310的10生素数组有且只有1组，其中有的组中间可能还有其他素数。

ysr · 发表于 2026-4-3 08:10

在10000内的这样的素数组有2 组：
(1873 2083 2293 4603 4813 5023 5233 5443 5653 7963 )
(8317 8527 8737 11047 11257 11467 11677 11887 12097 14407 )
命题：前3项公差为210第4项差2310后5项公差210第十项差2310的10生素数组有且只有2组，其中有的组中间可能还有其他素数。

ysr · 发表于 2026-4-3 08:11

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 Sub Command1_Click()
Dim a, b
a = Val(Text1)
p1 = 3
Do While p1 <= a
p1 = p1: p2 = p1 + 210: p3 = p2 + 210
p4 = p3 + 2310: p5 = p4 + 210: p6 = p5 + 210: p7 = p6 + 210
p8 = p7 + 210: p9 = p8 + 210: p10 = p9 + 2310
p11 = fenjieyinzi(Val(p1)): p12 = fenjieyinzi(Val(p2)): p13 = fenjieyinzi(Val(p3))
p14 = fenjieyinzi(Val(p4)): p15 = fenjieyinzi(Val(p5)): p16 = fenjieyinzi(Val(p6)): p17 = fenjieyinzi(Val(p7))
p18 = fenjieyinzi(Val(p8)): p19 = fenjieyinzi(Val(p9)): p20 = fenjieyinzi(Val(p10))
If InStr(p11, "*") = 0 And InStr(p12, "*") = 0 And InStr(p13, "*") = 0 And InStr(p14, "*") = 0 And InStr(p15, "*") = 0 And InStr(p16, "*") = 0 And InStr(p17, "*") = 0 And InStr(p18, "*") = 0 And InStr(p19, "*") = 0 And InStr(p20, "*") = 0 Then
s11 = s11 & "(" & p1 & " " & p2 & " " & p3 & " " & p4 & " " & p5 & " " & p6 & " " & p7 & " " & p8 & " " & p9 & " " & p10 & " )  " & vbCrLf

s12 = s12 + 1
End If

p1 = p1 + 2
Loop
If s12 >= 1 Then
Text2 = "在" & Text1 & "内的这样的素数组有" & s12 & " 组： " & vbCrLf & s11
Else
Text2 = "wu  jie"
End If

Combo1 = Text2

End Sub

Private Sub Command2_Click()
Text1 = ""
Text2 = ""
Text3 = ""
Combo1 = ""
Form21.Cls
End Sub

ysr · 发表于 2026-4-3 08:19

在10000内的这样的素数组有1 组：
(3823 6133 8443 10753 13063 15373 17683 19993 22303 )
命题：公差为2310的9生素数组有且只有1组，其中有的组中间可能还有其他素数。

ysr · 发表于 2026-4-3 08:23

本帖最后由 ysr 于 2026-4-3 02:30 编辑

在500000内的这样的素数组有3 组：
(122069 124799 127529 130259 132989 135719 138449 141179 143909 146639 )
(123059 125789 128519 131249 133979 136709 139439 142169 144899 147629 )
(158633 161363 164093 166823 169553 172283 175013 177743 180473 183203 )

命题：公差为2730的10生素数组有且只有3组，其中有的组中间可能还有其他素数。

ysr · 发表于 2026-4-3 08:35

本帖最后由 ysr 于 2026-4-3 02:38 编辑

在500000内的这样的素数组有1 组：
(150343 153913 157483 161053 164623 168193 171763 175333 178903 182473 )

命题：公差为3570的10生素数组有且只有1组，中间可能还有其他素数。

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