《数论探秘》电子版

ysr

146376311461999846452517590847与146376311461999846452517640847之间有28对差大于200的素数对:
146376311461999846452517594943/210
146376311461999846452517596383/330
146376311461999846452517600501/308
146376311461999846452517603093/254
146376311461999846452517604359/272
146376311461999846452517605073/506
146376311461999846452517606987/210
146376311461999846452517608361/270
146376311461999846452517608773/256
146376311461999846452517611211/378
146376311461999846452517612231/260
146376311461999846452517614353/316
146376311461999846452517617137/286
146376311461999846452517621247/228
146376311461999846452517624987/264
146376311461999846452517625731/392
146376311461999846452517626673/312
146376311461999846452517630901/208
146376311461999846452517631459/292
146376311461999846452517632199/248
146376311461999846452517632853/246
146376311461999846452517634143/222
146376311461999846452517636007/214
146376311461999846452517636717/216
146376311461999846452517637603/250
146376311461999846452517638589/260
146376311461999846452517639517/216
146376311461999846452517640209/240
用时11282.845秒

ysr

146,376,311,462,000,611,635,662,592,031

ysr

146376311462000611635662592031~146376311462000611635662595031之间的素数有46个：（用时389.875秒）
146376311462000611635662592257  146376311462000611635662592317  146376311462000611635662592383  146376311462000611635662592397  146376311462000611635662592419  146376311462000611635662592473  146376311462000611635662592523  146376311462000611635662592557  146376311462000611635662592857  146376311462000611635662592979
146376311462000611635662593051  146376311462000611635662593061  146376311462000611635662593063  146376311462000611635662593153  146376311462000611635662593217  146376311462000611635662593219  146376311462000611635662593229  146376311462000611635662593241  146376311462000611635662593277  146376311462000611635662593331
146376311462000611635662593343  146376311462000611635662593349  146376311462000611635662593439  146376311462000611635662593453  146376311462000611635662593457  146376311462000611635662593469  146376311462000611635662593691  146376311462000611635662593753  146376311462000611635662593777  146376311462000611635662593819
146376311462000611635662593907  146376311462000611635662594099  146376311462000611635662594143  146376311462000611635662594167  146376311462000611635662594221  146376311462000611635662594249  146376311462000611635662594377  146376311462000611635662594453  146376311462000611635662594539  146376311462000611635662594567
146376311462000611635662594621  146376311462000611635662594749  146376311462000611635662594869  146376311462000611635662594941  146376311462000611635662594969  146376311462000611635662594993  

ysr

146376311461999846452517640209与146376311461999846452517690209之间有41对差大于200的素数对:
146376311461999846452517643017/336
146376311461999846452517643269/252
146376311461999846452517645459/212
146376311461999846452517646243/270
146376311461999846452517646689/222
146376311461999846452517651031/258
146376311461999846452517652029/272
146376311461999846452517652819/202
146376311461999846452517653301/288
146376311461999846452517653643/234
146376311461999846452517655711/298
146376311461999846452517656523/374
146376311461999846452517656899/228
146376311461999846452517657873/240
146376311461999846452517658651/388
146376311461999846452517659127/240
146376311461999846452517661653/210
146376311461999846452517662119/216
146376311461999846452517662961/258
146376311461999846452517664611/222
146376311461999846452517665103/210
146376311461999846452517665487/284
146376311461999846452517665929/216
146376311461999846452517667003/372
146376311461999846452517667591/208
146376311461999846452517669913/202
146376311461999846452517670449/212
146376311461999846452517670891/228
146376311461999846452517671439/276
146376311461999846452517672397/240
146376311461999846452517672927/240
146376311461999846452517674427/338
146376311461999846452517675457/528
146376311461999846452517676743/222
146376311461999846452517679599/210
146376311461999846452517681453/216
146376311461999846452517684187/288
146376311461999846452517685207/384
146376311461999846452517687289/288
146376311461999846452517688603/210
146376311461999846452517690529/322
用时-53163.923秒

ysr

146376311462000611635662593061  146376311462000611635662593063是一对孪生素数
146376311462000611635662593217  146376311462000611635662593219 是一对孪生素数

ysr

146376311462000611635662592031与146376311462000611635662595031之间有3对差大于200的素数对:
146376311462000611635662592257/228
146376311462000611635662592857/300
146376311462000611635662593691/222
用时687.966999999999秒

ysr

146376311462000611635662592029~146376311462000611635662592257之间的素数有1个：（用时31.08398秒）
146376311462000611635662592257  

ysr

146376311462000611635662592029=*这是合数，有30位，用时1.089844秒

146376311462000611635662592029=71277497*2478937589*828424178513.

ysr

判断素数的程序代码：

Private Function zhengchuqyushu(sa As String) As String
If InStr(sa, "/") = 0 Then
zhengchuqyushu = 0
Else
zhengchuqyushu = Mid(sa, InStr(sa, "/") + 1)
End If


End Function


Private Function zhengchuqy(sa As String) As String
If InStr(sa, "/") = 0 Then
zhengchuqy = sa
Else
zhengchuqy = Left(sa, InStr(sa, "/") - 1)
End If


End Function


Public Function MBBC(D1 As String) As String 'kai pingfang
If Len(D1) < 10 Then
jss = Int(Sqr(D1))
JW = Val(D1) - (jss) ^ 2
  If JW = 0 Then
  MBBC = jss
  Else
  MBBC = jss & "/" & JW
    End If
Else
Dim x 'shuju changdu
x = Len(D1) \ 4
D2 = String(4 - Len(D1) + 4 * x, "0") & D1
Dim a() As String
ReDim a(4 To 4 * x + 4)
Dim b() As String
ReDim b(2 To 2 * x)
Dim I, J, js
  For I = 4 To 4 * x + 4 Step 4
  
a(I) = Mid(D2, I - 3, 4)
js = Int(Sqr(Val(a(4) & a(8))))
JW = Val(a(4) & a(8)) - (js) ^ 2
Next
   J = 4
   Do While J <= 2 * x
   
   jws = MPC1(JW & "0000", a(2 * J + 4))
   If MBJC(Trim(jws), MbC(Trim(js), 200)) <= 0 Then
    b(J) = "00"
    Else
    jwc = Left(jws, Len(jws) - Len(MbC(Trim(js), 200)) + 2) \ Left(MbC(Trim(js), 200), 2)
    If Len(jwc) > 2 Then
     b(J) = 99
     Else
     b(J) = jwc
     End If
   
     
     Do While MBJC(Trim(jws), MbC(MPC1(b(J), MbC(Trim(js), 200)), b(J))) = -1
     
     b(J) = b(J) - 1
     
               Loop
          End If
          JW = MPC(Trim(jws), MbC(MPC1(MbC(200, Trim(js)), b(J)), b(J)))
      
     js = MPC1(MbC(Trim(js), 100), Trim(b(J)))
     
      
   J = J + 2
   If JW = 0 Then
      
   MBBC = js
   Else
   MBBC = js & "/" & JW
   End If
   Loop
   
End If
End Function

Public Function MBJC(D1 As String, D2 As String) As String ';bijiao
If Len(D1) <= 10 And Len(D2) <= 10 Then
If Val(D1) > Val(D2) Then
MBJC = 1
Else
If Val(D1) = Val(D2) Then
MBJC = 0
Else
MBJC = -1
End If
End If
Else

If Len(D1) > Len(D2) Then
MBJC = 1
Else
If Len(D1) < Len(D2) Then
MBJC = -1
Else
If Len(D1) = Len(D2) Then
Dim x, Y
x = Len(D1) \ 4: Y = Len(D2) \ 4
Dim a() As String, b() As String
ReDim a(4 To 4 * x + 4)
ReDim b(4 To 4 * Y + 4)
If Val(Left(D1, Len(D1) - 4 * x)) > Val(Left(D2, Len(D2) - 4 * Y)) Then
  MBJC = 1
  Else
  If Val(Left(D1, Len(D1) - 4 * x)) < Val(Left(D2, Len(D2) - 4 * Y)) Then
  MBJC = -1
  Else
  For I = 4 To 4 * x Step 4
  a(I) = Mid(D1, Len(D1) - I + 1, 4)
  b(I) = Mid(D2, Len(D2) - I + 1, 4)
  Next
  J = 4 * x
  Do While a(J) = b(J) And J >= 8
  
  J = J - 4
     Loop
     
     
   If Val(a(J)) - Val(b(J)) > 0 Then
   MBJC = 1
   Else
   If Val(a(J)) - Val(b(J)) < 0 Then
   MBJC = -1
   Else
   MBJC = 0
   End If
   
  End If
  
  
  
End If
End If
End If
End If
End If
End If
End Function

Public Function MCC(D1 As String, D2 As String) As String ';除数少于8位的除法
If Len(D1) < Len(D2) Then
   MCC = "0" & "/" & D1
   Else
   If Len(D1) < 9 Then
    MCC = Val(D1) \ Val(D2) & "/" & Val(D1) - (Val(D1) \ Val(D2)) * Val(D2)
     If Mid(MCC, InStr(MCC, "/") + 1) = 0 Then
  MCC = Left(MCC, InStr(MCC, "/") - 1)
Else
MCC = MCC
End If
   
    Else
   
   Dim x ';fen duan changdu
   x = Len(D1)
   
     
   
     Dim a() As String
      ReDim a(1 To x)  ';定义数组的储存空间
      For I = 1 To x Step 1  ';把被除数各位放在a()中
       a(I) = Mid(D1, I, 1)
        
      
       Next I
      Dim b() As String
      JW = 0
     ReDim b(1 To x)
     For J = 1 To x Step 1
    b(J) = Val(JW & a(J)) \ Val(D2)
      JW = Val(JW & a(J)) - Val(b(J)) * Val(D2)
       Next J
       For r = 1 To x
       If JW = 0 Then
          MCC = MCC & b(r)
          Else
          CJ = CJ & b(r)
          MCC = CJ & "/" & JW
      
    End If
   
    For I = 1 To Len(MCC)
   If Not Mid(MCC, I, 1) = "0" Then
       Exit For
   End If
Next
strtmp = Mid(MCC, I)
If Len(strtmp) = 0 Then
MCC = "0"
Else
MCC = strtmp
End If
   
   Next
   
   End If
     
     End If
   
End Function

Public Function MCC1(D1 As String, D2 As String) As String ';大整数的除法
Dim ss
ss = MBJC(D1, D2)
If ss = -1 Then
MCC1 = "0" & "/" & D1
  Else
  If ss = 0 Then
   MCC1 = 1
   Else
   If Len(D1) = Len(D2) Then
     s = Val(Left(D1, 1)) \ Val(Left(D2, 1))

Do While MBJC(MbC(Trim(s), Trim(D2)), D1) = 1
  s = s - 1
  Loop
  If MBJC(MbC(Trim(s), Trim(D2)), D1) = 0 Then
   MCC1 = s
   Else
   MCC1 = s & "/" & MPC(Trim(D1), MbC(Trim(s), Trim(D2)))

End If
    Else
    If Len(D2) < 9 Then
     MCC1 = MCC(D1, D2)
     Else
    Dim x, Y ';定义分段长度
    x = Len(D1): Y = Len(D2)
   
Dim JW, jcc, jss, jcs

  Dim a() As String, b() As String
  
  ReDim a(1 To x)
  ReDim b(1 To Y)
  For I = 1 To x
  a(I) = Mid(D1, I, 1)
  Next
  For J = 1 To Y
  b(J) = Mid(D2, J, 1)
  Next
  jcc = Val(a(1) & a(2)) \ Val(b(1) & b(2))
   
      
        
  jss = MbC(Trim(jcc), D2)
   For i1 = 1 To Y
    jws = jws & a(i1)
      Next
      
      Do While MBJC(Trim(jws), Trim(jss)) = -1
      jcc = jcc - 1
      jss = MbC(Trim(jcc), D2)
      Loop
  JW = MPC(Trim(jws), Trim(jss))
  
    z = x - Y
   
    Dim c() As String
    ReDim c(1 To z)
    For s = 1 To z
     If MBJC(JW & a(s + Y), D2) = -1 Then
       c(s) = "0"
       Else
     jwc = Val(Left(JW & a(s + Y), 3)) \ Val(Left(D2, 2))
      If Len(jwc) > 1 Then
      c(s) = "9"
       Else
        c(s) = jwc
         End If
      
     Do While MBJC(JW & a(s + Y), MbC(Val(c(s)), D2)) = -1
    c(s) = Right(10000 + Val(c(s) - 1), 1)
     Loop
     End If
   
     JW = MPC(JW & a(s + Y), MbC(Val(c(s)), D2))
     
    jcc = jcc & c(s)
    Next s
    If JW = 0 Then
    MCC1 = jcc
    Else
    MCC1 = jcc & "/" & JW
    End If
   
  For I = 1 To Len(MCC1)
    If Not Mid(MCC1, I, 1) = "0" Then
        Exit For
    End If
Next
strtmp = Mid(MCC1, I)
  If Len(strtmp) = 0 Then
  MCC1 = "0"
  Else
MCC1 = strtmp
End If
   
   
   
    End If
   
   
   
   
   
  
  End If
End If
End If
End Function
Public Function MbC(D1 As String, D2 As String) As String '乘法
Dim x, Y '两数长度
x = Len(D1): Y = Len(D2)
Dim a() As Integer
ReDim a(1 To x + Y, 1 To Y)
Dim I, J, C1, C2, CJ, JW
For J = Y To 1 Step -1 'D2
JW = 0 '进位清0
C2 = Mid$(D2, J, 1) '每位数
For I = x To 1 Step -1 'D1
  C1 = Mid$(D1, I, 1) '每位数
  CJ = C1 * C2 + JW '计算乘积
  c = I + J: r = Y + 1 - J
  a(c, r) = CJ Mod 10 '本位
  JW = CJ \ 10 '进位
Next
a(c - 1, r) = JW
Next
Dim b() As Integer
ReDim b(1 To x + Y)
JW = 0
For I = x + Y To 1 Step -1
Bit = JW
For J = 1 To Y
  Bit = Bit + a(I, J)
Next
b(I) = Bit Mod 10
JW = Bit \ 10
Next
If b(1) > 0 Then
MbC = MbC & b(1)
Else
MbC = MbC
End If
For I = 2 To x + Y
MbC = MbC & b(I)
Next
End Function

Public Function MPC(D1 As String, D2 As String) As String ';jianfaqi
Dim x, Y ';两数长度
If Len(D1) >= Len(D2) Then
D4 = String(Len(D1) - Len(D2), "0") & D2
d3 = D1
Else
D4 = D2
d3 = String(Len(D2) - Len(D1), "0") & D1
End If
x = Len(d3): Y = Len(D4)
Dim a() As Integer, B1() As Integer, C1() As Integer, E1() As Integer
ReDim a(1 To x)
ReDim B1(1 To Y)
ReDim C1(1 To x)
ReDim E1(1 To x)
Dim I, J, C2, CJ, JW
For J = Y To 1 Step -1 ';D2
JW = 1 ';yu jie weichuzhi
B1(J) = Mid(D4, J, 1) ';每位数
For I = x To 1 Step -1  ';D1
   a(I) = Mid(d3, I, 1) ';每位数
   C1(I) = 10 + a(I) - B1(I) - 1 + JW ';计算jia
   JW = C1(I) \ 10
   E1(I) = C1(I) Mod 10
  Next
  Next
  For r = 1 To x
  MPC = MPC & E1(r)
  For I = 1 To Len(MPC)
    If Not Mid(MPC, I, 1) = "0" Then
        Exit For
    End If
Next
strtmp = Mid(MPC, I)
  If Len(strtmp) = 0 Then
  MPC = "0"
  Else
MPC = strtmp
End If
  Next
  
  
End Function
  Public Function MPC1(D1 As String, D2 As String) As String 'jiafa
Dim x, Y '两数长度

If Len(D1) >= Len(D2) Then
D4 = String(Len(D1) - Len(D2), "0") & D2
d3 = D1
Else
D4 = D2
d3 = String(Len(D2) - Len(D1), "0") & D1
End If
x = Len(d3): Y = Len(D4)
Dim a() As Integer, B1() As Integer, C1() As Integer, E1() As Integer
ReDim a(1 To x)
ReDim B1(1 To Y)
ReDim C1(1 To x)
ReDim E1(1 To x)
Dim I, J, C2, CJ, JW
For J = Y To 1 Step -1 'D2
JW = 0 '进位清0
B1(J) = Mid$(D4, J, 1) '每位数
For I = x To 1 Step -1  'D1
   a(I) = Mid$(d3, I, 1) '每位数
   C1(I) = a(I) + B1(I) + JW '计算jia
   JW = C1(I) \ 10
   E1(I) = C1(I) Mod 10
  Next
  Next
  For r = 1 To x
  If JW = 0 Then
  MPC1 = MPC1 & E1(r)
  Else
  jc = jc & E1(r)
  MPC1 = JW & jc
  End If
  Next
  
End Function


Private Function zzxc(sa As String, sb As String) As String
Dim a, b, c, d, r
  a = Trim(sa)
  b = Trim(sb)
  If Len(a) < 10 And Len(b) < 10 Then
  
  If Val(a) > Val(b) Then
     c = a
     d = b
  Else
     c = b
     d = a
  End If
Do Until Val(c) Mod Val(d) = 0
     r = c Mod d
     c = d
     d = r
  Loop
  
  Else
  
  If MBJC(Trim(a), Trim(b)) >= 1 Then
  c = a
  d = b
  Else
  c = b
  d = a
  End If
  Do Until zhengchuqyushu(MCC1(Trim(c), Trim(d))) = 0
  r = zhengchuqyushu(MCC1(Trim(c), Trim(d)))
  c = d
  d = r
  Loop
  End If

  
  zzxc = d
  
End Function

Private Function qniyuan(sa As String, sb As String) As String
Dim n, p, a, b, c, d, r
  n = Trim(sa)
  p = Trim(sb)
  a = 1
  b = 0
  c = 0
  d = 1
  If Len(n) < 10 And Len(p) < 10 Then
  
  If Val(n) > Val(p) Then
     m = n
     q = p
     s1 = 1
  Else
     m = p
     q = n
     s1 = 0
  End If
Do Until Val(m) Mod Val(q) = 0
    s = m \ q
     r = m Mod q
     s1 = s1 + 1
     If s1 Mod 2 = 1 Then
     a = a
     b = a * s + b
     c = c
     d = c * s + d
     Else
     b = b
     a = a + b * s
     d = d
     c = c + d * s
     End If
     m = q
     q = r
  Loop
  If Val(a + b * m) = p Then
  b = b
  a = a + b * (m - 1)
  d = d
  c = c + d * (m - 1)
  Else
  If Val(b + a * m) = p Then
  a = a
  b = b + a * m
  c = c
  d = d + c * m
  Else
  b = b
  a = a + b * (m - 1)
  d = d
  c = c + d * (m - 1)
  End If
  End If
x = (a + b) Mod p
  Y = (c + d) Mod n
  
  
  Else
  
  If MBJC(Trim(n), Trim(p)) >= 1 Then
  m = n
  q = p
  s1 = 1
  Else
  m = p
  q = n
  s1 = 0
  End If
  Do Until zhengchuqyushu(MCC1(Trim(m), Trim(q))) = 0
  s = zhengchuqy(MCC1(Trim(m), Trim(q)))
  r = zhengchuqyushu(MCC1(Trim(m), Trim(q)))
  s1 = s1 + 1
  If s1 Mod 2 = 1 Then
  a = a
  b = MPC1(MbC(Trim(a), Trim(s)), Trim(b))
  c = c
  d = MPC1(MbC(Trim(c), Trim(s)), Trim(d))
  Else
  b = b
  a = MPC1(Trim(a), MbC(Trim(b), Trim(s)))
  d = d
  c = MPC1(Trim(c), MbC(Trim(d), Trim(s)))
  End If
  
  m = q
  q = r
  Loop
  
  If MPC1(Trim(a), MbC(Trim(b), Trim(m))) = p Then
  b = b
  a = MPC1(Trim(a), MbC(Trim(b), MPC(Trim(m), 1)))
  d = d
  c = MPC1(Trim(c), MbC(Trim(d), MPC(Trim(m), 1)))
  Else
  If MPC1(Trim(b), MbC(Trim(a), Trim(m))) = p Then
  a = a
  b = MPC1(Trim(b), MbC(Trim(a), Trim(m)))
  c = c
  d = MPC1(Trim(d), MbC(Trim(c), Trim(m)))
  Else
  b = b
  a = MPC1(Trim(a), MbC(Trim(b), MPC(Trim(m), 1)))
  d = d
  c = MPC1(Trim(c), MbC(Trim(d), MPC(Trim(m), 1)))
  End If
  End If
Do While Left(a, 1) = "0"
    a = Mid(a, 2)
Loop
  
  End If
  
  qniyuan = a
End Function

Private Function qksmimo(sa As String, sb As String, sc As String) As String
Dim c, e, n, d
c = Trim(sa)
e = Trim(sb)
n = Trim(sc)
d = 1
If Len(c) < 5 And Len(e) < 5 And Len(n) < 5 Then
c = Val(c): n = Val(n)
Do While e > 0
If Right(e, 1) Mod 2 = 0 Then
c = c * c Mod n
e = e / 2

Else
d = d * c Mod n
e = e - 1
End If
Loop
Else
c = c
Do While MBJC(Trim(e), 1) >= 0
If Right(e, 1) Mod 2 = 0 Then
c = zhengchuqyushu(MCC1(MbC(Trim(c), Trim(c)), Trim(n)))
e = zhengchuqy(MCC1(Trim(e), 2))
Else
d = zhengchuqyushu(MCC1(MbC(Trim(c), Trim(d)), Trim(n)))
e = MPC(Trim(e), 1)
End If
Loop
End If

qksmimo = d
End Function

Private Function fenjieyinzi(sa As String) As String
Dim x, a, b
x = sa
b = Int(Sqr(Val(x)) / 2)
If x = 3 Or x = 2 Then
a = True
Else
If x Mod 2 = 0 Then
a = False
Else

For I = 3 To 2 * b + 1 Step 2
If x Mod I = 0 Then
a = False
Exit For

Else: a = True

End If
Next
End If
End If
If a = True Then
fenjieyinzi = "这是个素数"
Else
fenjieyinzi = "2*2"
End If

End Function


Private Sub Command1_Click()
Dim a, n
n = Trim(Text1)
If Len(n) < 6 Then
Text2 = fenjieyinzi(Trim(n))
Else
n1 = MPC(Trim(n), 1)
a = 123
'a为明文
a1 = zzxc(Trim(n), Trim(a))
If Val(a1) > 1 Then
Text2 = a1 & "*"
Else
c = 999
'c为公约
Do While zzxc(Trim(n1), Trim(c)) > 1
c = Val(c - 1)
Loop
d = qniyuan(Trim(c), Trim(n1))
'd为逆元为私钥
a2 = qksmimo(Trim(a), Trim(c), Trim(n))
'a2为密文
a3 = qksmimo(Trim(a2), Trim(d), Trim(n))
If MBJC(Trim(a3), Trim(a)) = 0 Then
Text2 = "这是素数有" & Len(n) & "位"
Else
Text2 = "2*2"
End If
End If
End If
End Sub

Private Sub Command2_Click()
Text1 = ""
Text2 = ""

End Sub

ysr

146376311462000611635662590257与146376311462000611635662592257之间有2对差大于200的素数对:
146376311462000611635662592001/222
146376311462000611635662592257/256
用时4136.149秒