数论问题巅峰对决

ysr

代码（主程序）如下：

Private Sub Command1_Click() '求由2个孪生素数对组成的4生素数组的程序
Dim A, B
A = Val(Text1)
a1 = A
q = Val(Text2)
ts = Timer
m = Sqr(q)
t = Val(Text4)

s = 0
k = q

k1 = k
a2 = A
Do While a2 <= m
k2 = Val(k * 105)
B1 = a2 * k2 - 2
b2 = a2 * k2 + 2
B3 = MPC(Trim(B1), Trim(2))
b4 = MPC1(Trim(b2), 2)

C1 = fenjieyinzi0(Val(B1))
C2 = fenjieyinzi0(Val(b2))
c3 = fenjieyinzi0(Trim(B3))
D1 = fenjieyinzi0(Trim(b4))
B5 = a2 * k - 2
b6 = a2 * k + 2
B7 = MPC(Trim(B5), Trim(2))
b8 = MPC1(Trim(b6), 2)

C5 = fenjieyinzi0(Val(B5))
C6 = fenjieyinzi0(Val(b6))
c7 = fenjieyinzi0(Trim(B7))
D8 = fenjieyinzi0(Trim(b8))

If InStr(C1, "*") = 0 And InStr(D1, "*") = 0 And InStr(C2, "*") = 0 And InStr(c3, "*") = 0 And InStr(C5, "*") = 0 And InStr(D8, "*") = 0 And InStr(C6, "*") = 0 And InStr(c7, "*") = 0 Then
s = s + 1
Print B1, b2, B3, b4
Text3 = Text3 & "/" & B3 & "/" & B1 & "/" & b2 & "/" & b4 & "m=" & a2 & "k=" & k & vbCrLf
Else
s = s
End If
a2 = a2 + 1

Loop
a2 = a2
s1 = s
Do While a2 <= t
k2 = Val(k * 105)
  B1 = a2 * k2 - 2
b2 = a2 * k2 + 2
B3 = MPC(Trim(B1), Trim(2))
b4 = MPC1(Trim(b2), 2)

C1 = fenjieyinzi0(Val(B1))
C2 = fenjieyinzi0(Val(b2))
c3 = fenjieyinzi0(Trim(B3))
D1 = fenjieyinzi0(Trim(b4))
B5 = a2 * k - 2
b6 = a2 * k + 2
B7 = MPC(Trim(B5), Trim(2))
b8 = MPC1(Trim(b6), 2)

C5 = fenjieyinzi0(Val(B5))
C6 = fenjieyinzi0(Val(b6))
c7 = fenjieyinzi0(Trim(B7))
D8 = fenjieyinzi0(Trim(b8))
If InStr(C1, "*") = 0 And InStr(D1, "*") = 0 And InStr(C2, "*") = 0 And InStr(c3, "*") = 0 And InStr(C5, "*") = 0 And InStr(D8, "*") = 0 And InStr(C6, "*") = 0 And InStr(c7, "*") = 0 Then
s1 = s1 + 1
Print B1, b2, B3, b4
Text3 = Text3 & "/" & B3 & "/" & B1 & "/" & b2 & "/" & b4 & "m=" & a2 & "k=" & k & vbCrLf
Else
s1 = s1
End If
a2 = a2 + 1

Loop
Combo1 = k1 & "与" & t & "之间的k*105有" & s1 & "组8生素数对: (用时" & Timer - ts & "秒）" & vbCrLf & Text3

End Sub

ysr

109841~109849之间的素数有4个：
109841  109843  109847  109849  
109845*105=11533725
11533721~11533729之间的素数有4个：
11533721  11533723  11533727  11533729

这就是一组8生素数，而且11533725/109845=105.

ysr

1与10000之间的k*21有1组8生素数对: (用时3.271484秒）
/43781/43783/43787/43789m=2085k=1
43785/2085=21.

ysr

蔡家雄 发表于 2021-7-25 09:04
素数阶乘的8生素数，可以有吗 ?

（ p , p+3! , p+5! , p+7! , p+11! , p+13! , p+17! , p+19! ）

因为19！=121,645,100,408,832,000，数据大，所以程序运行时间长，有空的时候可以试试。

ysr

蔡家雄 发表于 2021-7-25 02:35
定义：若 m±2 和 m±4 是 四生素数，则称 m 为 双中数。

奇数双中比猜想：一奇数均可表为两个双中数之 ...

1与100000之间的k*23有1组8生素数对: (用时20.45313秒）
/79691/79693/79697/79699m=3465k=1

ysr

蔡家雄 发表于 2021-7-26 05:30
蔡氏8生素数猜想：设 (2n+1) 为任一奇数，

8生素数 p, p+2, p+6, p+8, (2n+1)p+8n, (2n+1)p+8n+2, (2n+1 ...

上班呢，下班再说，数据多，时间长，晚上试试吧。

ysr

ysr 发表于 2021-7-25 12:35
因为19！=121,645,100,408,832,000，数据大，所以程序运行时间长，有空的时候可以试试。

10000与100000之间的素数打头有0组8生素数对: (用时17481.67秒）时间长没有到100万呢。
代码如下：

Private Sub Command1_Click() '求由2个孪生素数对组成的4生素数组的程序
Dim A, B
A = Val(Text1)
a1 = A
q = Val(Text2)
ts = Timer
m = Sqr(q)
t = Val(Text4)

s = 0
k = q

k1 = k
a2 = A
Do While a2 <= m
k2 = Val(k * 105)
B1 = a2
B2 = MPC1(Trim(a2), jcjs(3))
b3 = MPC1(Trim(B1), jcjs(5))
b4 = MPC1(Trim(B1), jcjs(7))

C1 = fenjieyinzi0(Val(B1))
C2 = fenjieyinzi0(Val(B2))
c3 = fenjieyinzi0(Trim(b3))
D1 = fenjieyinzi0(Trim(b4))
b5 = MPC1(Trim(a2), jcjs(11))
b6 = MPC1(Trim(a2), jcjs(13))
b7 = MPC1(Trim(B1), jcjs(17))
b8 = MPC1(Trim(B1), jcjs(19))

C5 = fenjieyinzi0(Val(b5))
C6 = fenjieyinzi0(Val(b6))
c7 = fenjieyinzi0(Trim(b7))
D8 = fenjieyinzi0(Trim(b8))

If InStr(C1, "*") = 0 And InStr(D1, "*") = 0 And InStr(C2, "*") = 0 And InStr(c3, "*") = 0 And InStr(C5, "*") = 0 And InStr(D8, "*") = 0 And InStr(C6, "*") = 0 And InStr(c7, "*") = 0 Then
s = s + 1
Print B1, B2, b3, b4
Text3 = Text3 & "/" & B1 & "/" & B2 & "/" & b3 & "/" & b4 & "/" & b5 & "/" & b6 & "/" & b7 & "/" & b8 & "m=" & a2 & "k=" & k & vbCrLf
Else
s = s
End If
a2 = a2 + 2

Loop
a2 = a2
s1 = s
Do While a2 <= t
k2 = Val(k * 105)
B1 = a2
B2 = MPC1(Trim(a2), jcjs(3))
b3 = MPC1(Trim(B1), jcjs(5))
b4 = MPC1(Trim(B1), jcjs(7))

C1 = fenjieyinzi0(Val(B1))
C2 = fenjieyinzi0(Val(B2))
c3 = fenjieyinzi0(Trim(b3))
D1 = fenjieyinzi0(Trim(b4))
b5 = MPC1(Trim(a2), jcjs(11))
b6 = MPC1(Trim(a2), jcjs(13))
b7 = MPC1(Trim(B1), jcjs(17))
b8 = MPC1(Trim(B1), jcjs(19))

C5 = fenjieyinzi0(Val(b5))
C6 = fenjieyinzi0(Val(b6))
c7 = fenjieyinzi0(Trim(b7))
D8 = fenjieyinzi0(Trim(b8))
If InStr(C1, "*") = 0 And InStr(D1, "*") = 0 And InStr(C2, "*") = 0 And InStr(c3, "*") = 0 And InStr(C5, "*") = 0 And InStr(D8, "*") = 0 And InStr(C6, "*") = 0 And InStr(c7, "*") = 0 Then
s1 = s1 + 1
Print B1, B2, b3, b4
Text3 = Text3 & "/" & B1 & "/" & B2 & "/" & b3 & "/" & b4 & "/" & b5 & "/" & b6 & "/" & b7 & "/" & b8 & "m=" & a2 & "k=" & k & vbCrLf
Else
s1 = s1
End If
a2 = a2 + 2

Loop
Combo1 = k1 & "与" & t & "之间的素数打头有" & s1 & "组8生素数对: (用时" & Timer - ts & "秒）" & vbCrLf & Text3

End Sub

ysr

ysr 发表于 2021-7-26 06:57
10000与100000之间的素数打头有0组8生素数对: (用时17481.67秒）时间长没有到100万呢。
代码如下：

这个确实有解找到一个：
1030000与1040000之间的素数打头有1组8生素数对: (用时959.1289秒）
/1034003/1034009/1034123/1039043/40950803/6228054803/355687429130003/121645100409866003p=1034003.

ysr

《数论探秘》电子版：欢迎朋友审阅并探讨沟通！

ysr

蔡家雄 发表于 2021-7-27 11:37
定义：若 m±2 和 m±4 是 四生素数，则称 m 为 双中数。

奇数双中比猜想：一奇数均可表为两个双中数之 ...

1与3000000之间的m*k*25有1组8生素数对: (用时399.061秒）
/67423121/67423123/67423127/67423129m=2696925k=1