数论问题巅峰对决

ysr

1000内有122组蔡氏素数:
7, 37,67,5,5,2n=32
11, 41,71,3,7,2n=32
23, 53,83,3,3,2n=32
13, 43,73,3,7,2n=34
11, 41,71,5,5,2n=36
13, 43,73,5,5,2n=38
23, 53,83,3,5,2n=38
29, 59,89,3,3,2n=38
7, 37,67,3,11,2n=40
7, 37,67,5,7,2n=42
11, 41,71,3,11,2n=44
23, 53,83,3,7,2n=44
29, 59,89,3,5,2n=44
7, 37,67,3,13,2n=46
11, 41,71,5,7,2n=46
13, 43,73,3,11,2n=46
37, 67,97,3,3,2n=46
13, 43,73,5,7,2n=48
23, 53,83,5,5,2n=48
11, 41,71,3,13,2n=50
29, 59,89,3,7,2n=50
41, 71,101,3,3,2n=50
13, 43,73,3,13,2n=52
37, 67,97,3,5,2n=52
43, 73,103,3,3,2n=52
29, 59,89,5,5,2n=54
7, 37,67,7,7,2n=56
23, 53,83,3,11,2n=56
41, 71,101,3,5,2n=56
7, 37,67,3,17,2n=58
23, 53,83,5,7,2n=58
37, 67,97,3,7,2n=58
43, 73,103,3,5,2n=58
11, 41,71,7,7,2n=60
7, 37,67,5,11,2n=62
11, 41,71,3,17,2n=62
13, 43,73,7,7,2n=62
23, 53,83,3,13,2n=62
29, 59,89,3,11,2n=62
37, 67,97,5,5,2n=62
41, 71,101,3,7,2n=62
53, 83,113,3,3,2n=62
7, 37,67,3,19,2n=64
13, 43,73,3,17,2n=64
29, 59,89,5,7,2n=64
43, 73,103,3,7,2n=64
11, 41,71,5,11,2n=66
41, 71,101,5,5,2n=66
11, 41,71,3,19,2n=68
13, 43,73,5,11,2n=68
29, 59,89,3,13,2n=68
43, 73,103,5,5,2n=68
53, 83,113,3,5,2n=68
13, 43,73,3,19,2n=70
37, 67,97,3,11,2n=70
7, 37,67,5,13,2n=72
23, 53,83,7,7,2n=72
37, 67,97,5,7,2n=72
23, 53,83,3,17,2n=74
41, 71,101,3,11,2n=74
53, 83,113,3,7,2n=74
7, 37,67,3,23,2n=76
11, 41,71,5,13,2n=76
37, 67,97,3,13,2n=76
41, 71,101,5,7,2n=76
43, 73,103,3,11,2n=76
67, 97,127,3,3,2n=76
13, 43,73,5,13,2n=78
23, 53,83,5,11,2n=78
29, 59,89,7,7,2n=78
43, 73,103,5,7,2n=78
53, 83,113,5,5,2n=78
11, 41,71,3,23,2n=80
23, 53,83,3,19,2n=80
29, 59,89,3,17,2n=80
41, 71,101,3,13,2n=80
71, 101,131,3,3,2n=80
13, 43,73,3,23,2n=82
43, 73,103,3,13,2n=82
67, 97,127,3,5,2n=82
7, 37,67,7,11,2n=84
29, 59,89,5,11,2n=84
29, 59,89,3,19,2n=86
37, 67,97,7,7,2n=86
53, 83,113,3,11,2n=86
71, 101,131,3,5,2n=86
11, 41,71,7,11,2n=88
23, 53,83,5,13,2n=88
37, 67,97,3,17,2n=88
53, 83,113,5,7,2n=88
67, 97,127,3,7,2n=88
79, 109,139,3,3,2n=88
13, 43,73,7,11,2n=90
41, 71,101,7,7,2n=90
7, 37,67,5,17,2n=92
23, 53,83,3,23,2n=92
37, 67,97,5,11,2n=92
41, 71,101,3,17,2n=92
43, 73,103,7,7,2n=92
53, 83,113,3,13,2n=92
67, 97,127,5,5,2n=92
71, 101,131,3,7,2n=92
7, 37,67,3,29,2n=94
29, 59,89,5,13,2n=94
37, 67,97,3,19,2n=94
43, 73,103,3,17,2n=94
79, 109,139,3,5,2n=94
11, 41,71,5,17,2n=96
41, 71,101,5,11,2n=96
71, 101,131,5,5,2n=96
7, 37,67,7,13,2n=98
11, 41,71,3,29,2n=98
13, 43,73,5,17,2n=98
29, 59,89,3,23,2n=98
41, 71,101,3,19,2n=98
43, 73,103,5,11,2n=98
7, 37,67,3,31,2n=100
13, 43,73,3,29,2n=100
23, 53,83,7,11,2n=100
43, 73,103,3,19,2n=100
67, 97,127,3,11,2n=100
79, 109,139,3,7,2n=100
用时1.40099999999802秒

ysr

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

q = Val(Text1)
m = 32
Do While m <= 100

p1 = 3
Do While p1 <= q And p1 <= m
p2 = Val(p1 + 30)
p3 = Val(p1 + 60)
p4 = fenjieyinzi1(Val(m - p1))
p5 = Val(m - p1) / Val(p4)
Print p1, p2, p3, p4
a = fenjieyinzi(Val(p1))
b = fenjieyinzi(Val(p2))
c = fenjieyinzi(Val(p3))
d = fenjieyinzi(Val(p4))
f = fenjieyinzi(Val(p5))

If InStr(a, "*") = 0 And InStr(b, "*") = 0 And InStr(c, "*") = 0 And InStr(d, "*") = 0 And InStr(f, "*") = 0 Then
s = s + 1

Text2 = Text2 & CStr(p1) & ", " & CStr(p2) & "," & p3 & "," & p4 & "," & p5 & ",2n=" & 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

ysr

1000内有111组蔡氏素数:
29, 59,89,11,181,2n=2020
37, 67,97,3,661,2n=2020
43, 73,103,3,659,2n=2020
53, 83,113,7,281,2n=2020
79, 109,139,3,647,2n=2020
97, 127,157,3,641,2n=2020
137, 167,197,7,269,2n=2020
163, 193,223,3,619,2n=2020
167, 197,227,17,109,2n=2020
181, 211,241,3,613,2n=2020
251, 281,311,29,61,2n=2020
307, 337,367,3,571,2n=2020
349, 379,409,3,557,2n=2020
359, 389,419,11,151,2n=2020
379, 409,439,3,547,2n=2020
389, 419,449,7,233,2n=2020
431, 461,491,7,227,2n=2020
547, 577,607,3,491,2n=2020
617, 647,677,23,61,2n=2020
631, 661,691,3,463,2n=2020
727, 757,787,3,431,2n=2020
881, 911,941,17,67,2n=2020
953, 983,1013,11,97,2n=2020
37, 67,97,5,397,2n=2022
41, 71,101,7,283,2n=2022
53, 83,113,11,179,2n=2022
79, 109,139,29,67,2n=2022
107, 137,167,5,383,2n=2022
181, 211,241,7,263,2n=2022
277, 307,337,5,349,2n=2022
337, 367,397,5,337,2n=2022
349, 379,409,7,239,2n=2022
379, 409,439,31,53,2n=2022
389, 419,449,23,71,2n=2022
419, 449,479,7,229,2n=2022
431, 461,491,37,43,2n=2022
461, 491,521,7,223,2n=2022
557, 587,617,5,293,2n=2022
617, 647,677,5,281,2n=2022
631, 661,691,13,107,2n=2022
709, 739,769,13,101,2n=2022
823, 853,883,11,109,2n=2022
827, 857,887,5,239,2n=2022
877, 907,937,5,229,2n=2022
881, 911,941,7,163,2n=2022
907, 937,967,5,223,2n=2022
911, 941,971,11,101,2n=2022
41, 71,101,3,661,2n=2024
43, 73,103,7,283,2n=2024
67, 97,127,19,103,2n=2024
79, 109,139,5,389,2n=2024
97, 127,157,41,47,2n=2024
167, 197,227,3,619,2n=2024
181, 211,241,19,97,2n=2024
307, 337,367,17,101,2n=2024
337, 367,397,7,241,2n=2024
401, 431,461,3,541,2n=2024
461, 491,521,3,521,2n=2024
547, 577,607,7,211,2n=2024
587, 617,647,3,479,2n=2024
613, 643,673,17,83,2n=2024
631, 661,691,7,199,2n=2024
709, 739,769,5,263,2n=2024
797, 827,857,3,409,2n=2024
877, 907,937,31,37,2n=2024
7, 37,67,3,673,2n=2026
41, 71,101,5,397,2n=2026
43, 73,103,3,661,2n=2026
67, 97,127,3,653,2n=2026
97, 127,157,3,643,2n=2026
107, 137,167,19,101,2n=2026
197, 227,257,31,59,2n=2026
233, 263,293,11,163,2n=2026
337, 367,397,3,563,2n=2026
449, 479,509,19,83,2n=2026
461, 491,521,5,313,2n=2026
557, 587,617,13,113,2n=2026
709, 739,769,3,439,2n=2026
727, 757,787,3,433,2n=2026
823, 853,883,3,401,2n=2026
827, 857,887,11,109,2n=2026
877, 907,937,3,383,2n=2026
881, 911,941,5,229,2n=2026
907, 937,967,3,373,2n=2026
911, 941,971,5,223,2n=2026
953, 983,1013,29,37,2n=2026
7, 37,67,43,47,2n=2028
23, 53,83,5,401,2n=2028
37, 67,97,11,181,2n=2028
43, 73,103,5,397,2n=2028
67, 97,127,37,53,2n=2028
71, 101,131,19,103,2n=2028
107, 137,167,17,113,2n=2028
137, 167,197,31,61,2n=2028
163, 193,223,5,373,2n=2028
211, 241,271,23,79,2n=2028
233, 263,293,5,359,2n=2028
277, 307,337,17,103,2n=2028
337, 367,397,19,89,2n=2028
349, 379,409,23,73,2n=2028
379, 409,439,17,97,2n=2028
389, 419,449,11,149,2n=2028
571, 601,631,31,47,2n=2028
587, 617,647,11,131,2n=2028
613, 643,673,5,283,2n=2028
617, 647,677,17,83,2n=2028
631, 661,691,11,127,2n=2028
823, 853,883,5,241,2n=2028
881, 911,941,31,37,2n=2028
907, 937,967,19,59,2n=2028
991, 1021,1051,17,61,2n=2028
用时3.06999999999243秒

ysr

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

q = Val(Text1)
m = 402
Do While m <= 500

p1 = 3
Do While p1 <= q And p1 <= m
p2 = Val(p1 + 30)
p3 = Val(p1 + 60)
p4 = fenjieyinzi1(Val(m - p1))
p5 = Val(m - p1) / Val(p4)
Print p1, p2, p3, p4
a = fenjieyinzi(Val(p1))
b = fenjieyinzi(Val(p2))
c = fenjieyinzi(Val(p3))
d = fenjieyinzi(Val(p4))
f1 = fenjieyinzi(Val(p5))

If InStr(a, "*") = 0 And InStr(b, "*") = 0 And InStr(c, "*") = 0 And InStr(d, "*") = 0 And InStr(f1, "*") = 0 Then
s = s + 1

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

Private Function fenjieyinzi1(sa As String) As String
Dim a, b
Dim x As String
x = sa

y = fenjieyinzi3(Val(x))

If InStr(y, "*") = 0 Then
fenjieyinzi1 = y
Else
fenjieyinzi1 = Left(y, InStr(y, "*") - 1)
End If



End Function

Private Function fenjieyinzi3(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
fenjieyinzi3 = 1

Else
MsgBox "error"
End If
  
Else

Do While a / 2 = Int(a / 2) And a >= 4
  
If b = 0 Then
fenjieyinzi3 = fenjieyinzi3 & "2"
b = 1
Else
fenjieyinzi3 = fenjieyinzi3 & "*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
fenjieyinzi3 = fenjieyinzi3 & x
b = 1
Else
fenjieyinzi3 = fenjieyinzi3 & "*" & x
End If
a = a / x
Loop
  
x = x + 2
Loop
  
k = a
a = 1
Loop
  
If b = 1 Then
fenjieyinzi3 = fenjieyinzi3 & "*" & k
Else
fenjieyinzi3 = sa
End If
  
  
  
  

End If

End Function

蔡家雄

陈氏-蔡氏偶数分拆

设 2n >=32，且 p1, p2=p1+30, p3=p1+60, p4, p5 都是素数，

则 2n=p1+p4*p5 , 2n+30=p2+p4*p5 , 2n+60=p3+p4*p5 至少有一组素数(p1, p2, p3, p4, p5)解。

陈氏-蔡氏偶数分拆

设 2n >=62，且 p1, p2=p1+210, p3=p1+420, p4, p5 都是素数，

则 2n=p1+p4*p5 , 2n+210=p2+p4*p5 , 2n+420=p3+p4*p5 至少有一组素数(p1, p2, p3, p4, p5)解。


陈氏-蔡氏偶数分拆

设 2n >=10^3，设 30C =300，600，2700，3600，3900，6000，7200，9000，

且 p1, p2=p1+30, p3=p1+30C, p4, p5 都是素数，

则 2n=p1+p4*p5 , 2n+30=p2+p4*p5 , 2n+30C=p3+p4*p5 至少有一组素数(p1, p2, p3, p4, p5)解。

ysr

蔡家雄 发表于 2022-6-2 22:52
陈氏-蔡氏偶数分拆

设 2n >=32，且 p1, p2=p1+30, p3=p1+60, p4, p5 都是素数，

30c=300，2n=32~100时：
500内有108组蔡氏素数:
7, 37,307,5,5,2n=32
11, 41,311,3,7,2n=32
17, 47,317,3,5,2n=32
13, 43,313,3,7,2n=34
11, 41,311,5,5,2n=36
13, 43,313,5,5,2n=38
17, 47,317,3,7,2n=38
7, 37,307,3,11,2n=40
31, 61,331,3,3,2n=40
7, 37,307,5,7,2n=42
17, 47,317,5,5,2n=42
11, 41,311,3,11,2n=44
7, 37,307,3,13,2n=46
11, 41,311,5,7,2n=46
13, 43,313,3,11,2n=46
31, 61,331,3,5,2n=46
37, 67,337,3,3,2n=46
13, 43,313,5,7,2n=48
11, 41,311,3,13,2n=50
17, 47,317,3,11,2n=50
13, 43,313,3,13,2n=52
17, 47,317,5,7,2n=52
31, 61,331,3,7,2n=52
37, 67,337,3,5,2n=52
7, 37,307,7,7,2n=56
17, 47,317,3,13,2n=56
31, 61,331,5,5,2n=56
7, 37,307,3,17,2n=58
37, 67,337,3,7,2n=58
11, 41,311,7,7,2n=60
7, 37,307,5,11,2n=62
11, 41,311,3,17,2n=62
13, 43,313,7,7,2n=62
37, 67,337,5,5,2n=62
53, 83,353,3,3,2n=62
7, 37,307,3,19,2n=64
13, 43,313,3,17,2n=64
31, 61,331,3,11,2n=64
11, 41,311,5,11,2n=66
17, 47,317,7,7,2n=66
31, 61,331,5,7,2n=66
11, 41,311,3,19,2n=68
13, 43,313,5,11,2n=68
17, 47,317,3,17,2n=68
53, 83,353,3,5,2n=68
59, 89,359,3,3,2n=68
13, 43,313,3,19,2n=70
31, 61,331,3,13,2n=70
37, 67,337,3,11,2n=70
7, 37,307,5,13,2n=72
17, 47,317,5,11,2n=72
37, 67,337,5,7,2n=72
17, 47,317,3,19,2n=74
53, 83,353,3,7,2n=74
59, 89,359,3,5,2n=74
7, 37,307,3,23,2n=76
11, 41,311,5,13,2n=76
37, 67,337,3,13,2n=76
67, 97,367,3,3,2n=76
13, 43,313,5,13,2n=78
53, 83,353,5,5,2n=78
11, 41,311,3,23,2n=80
31, 61,331,7,7,2n=80
59, 89,359,3,7,2n=80
13, 43,313,3,23,2n=82
17, 47,317,5,13,2n=82
31, 61,331,3,17,2n=82
67, 97,367,3,5,2n=82
73, 103,373,3,3,2n=82
7, 37,307,7,11,2n=84
59, 89,359,5,5,2n=84
17, 47,317,3,23,2n=86
31, 61,331,5,11,2n=86
37, 67,337,7,7,2n=86
53, 83,353,3,11,2n=86
11, 41,311,7,11,2n=88
31, 61,331,3,19,2n=88
37, 67,337,3,17,2n=88
53, 83,353,5,7,2n=88
67, 97,367,3,7,2n=88
73, 103,373,3,5,2n=88
79, 109,379,3,3,2n=88
13, 43,313,7,11,2n=90
7, 37,307,5,17,2n=92
37, 67,337,5,11,2n=92
53, 83,353,3,13,2n=92
59, 89,359,3,11,2n=92
67, 97,367,5,5,2n=92
83, 113,383,3,3,2n=92
7, 37,307,3,29,2n=94
17, 47,317,7,11,2n=94
37, 67,337,3,19,2n=94
59, 89,359,5,7,2n=94
73, 103,373,3,7,2n=94
79, 109,379,3,5,2n=94
11, 41,311,5,17,2n=96
31, 61,331,5,13,2n=96
7, 37,307,7,13,2n=98
11, 41,311,3,29,2n=98
13, 43,313,5,17,2n=98
59, 89,359,3,13,2n=98
73, 103,373,5,5,2n=98
83, 113,383,3,5,2n=98
7, 37,307,3,31,2n=100
13, 43,313,3,29,2n=100
31, 61,331,3,23,2n=100
67, 97,367,3,11,2n=100
79, 109,379,3,7,2n=100
用时0.341999999996915秒

ysr

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

q = Val(Text1)
m = 32
Do While m <= 100

p1 = 3
Do While p1 <= q And p1 <= m
p2 = Val(p1 + 30)

p4 = fenjieyinzi1(Val(m - p1))
p5 = Val(m - p1) / Val(p4)
Print p1, p2, p3, p4
a = fenjieyinzi(Val(p1))
b = fenjieyinzi(Val(p2))

d = fenjieyinzi(Val(p4))
f = fenjieyinzi(Val(p5))
p7 = 3
Do While zzxc(Val(m), Val(p7)) > 1
p7 = p7 + 2
Loop


If InStr(a, "*") = 0 And InStr(b, "*") = 0 And InStr(d, "*") = 0 And InStr(f, "*") = 0 And p4 = Val(p7) Then
s = s + 1

Text2 = Text2 & CStr(p1) & ", " & CStr(p2) & "," & p3 & "," & p4 & "," & p5 & ",2n=" & 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

陈氏-蔡氏偶数分拆（全部解）

设 2n >=32，且 p1, p2=p1+30, p3=p1+60, p4, p5 都是素数，

则 2n=p1+p4*p5 , 2n+30=p2+p4*p5 , 2n+60=p3+p4*p5 至少有一组素数(p1, p2, p3, p4, p5)解。


陈氏-蔡氏偶数分拆（全部解）

设 2n >=62，且 p1, p2=p1+210, p3=p1+420, p4, p5 都是素数，

则 2n=p1+p4*p5 , 2n+210=p2+p4*p5 , 2n+420=p3+p4*p5 至少有一组素数(p1, p2, p3, p4, p5)解。

陈氏-蔡氏偶数分拆（最小解）

设 2n >=96，且 p1, p2=p1+210, p3=p1+420, p4, p5 都是素数，

且 p4 <=p5,  且 p4 是与2n, 2n+210, 2n+420 都互素的最小素数，

则 2n=p1+p4*p5 , 2n+210=p2+p4*p5 , 2n+420=p3+p4*p5 至少有一组素数(p1, p2, p3, p4, p5)解。


陈氏-蔡氏偶数分拆（全部解）

设 2n >=62，且 p1, p2=p1+30, p3=p1+600, p4, p5 都是素数，

则 2n=p1+p4*p5 , 2n+30=p2+p4*p5 , 2n+600=p3+p4*p5 至少有一组素数(p1, p2, p3, p4, p5)解。