朋友，请看一下重要启示！

ysr

可能是循环的，循环节有6 个,可能的循环节是518134715025906735751295336787564766839378238341968911917098445595854922279792746113989637305699481865284974093264248704663212435233160621761658031088082901554404145077720207253886010362694300

ysr

Private Sub Command1_Click()
'判断小数是否循环的简单程序并输出可能的循环节
Dim a, b, ak()
a = Trim(Text1)
b = InStr(Trim(a), ".")
c = Mid(a, Val(b + 1))
c = qqdl(Trim(c))
'去前导0的程序
d = Len(a)
h = Left(c, 5)
f = Split(a, h)
J = UBound(f)
For k = 1 To J
      
       ReDim Preserve ak(1 To k)
      ak(k) = f(k)
    Next
If J > 1 Then
Text2 = "可能是循环的，循环节有" & J & " 个,可能的循环节是" & h & ak(1)
Else
Text2 = "不循环"
End If
End Sub

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

End Sub

Private Function qqdl(sa As String) As String

  
  For I = 1 To Len(sa)
    If Not Mid(sa, I, 1) = "0" Then
        Exit For
    End If
Next
strTmp = Mid(sa, I)
  If Len(strTmp) = 0 Then
  qqdl = "0"
  Else
qqdl = strTmp
End If
End Function

ysr

Private Sub Command1_Click()
'验证素数的原根的程序
Dim A, B
A = Trim(Text1)
jB = Trim(Text2)
g = 10
c = MCC1(MPC(Trim(A), 1), Trim(jB))
J = qksmimo(Trim(g), Trim(jB), Trim(A))
j1 = qksmimo(Trim(g), Trim(c), Trim(A))
If J > 1 And j1 > 1 Then
Text3 = g & "是该素数的原根"
Else
Text3 = g & "不是原根"
End If

End Sub



Private Sub Command2_Click()
Text1 = ""
Text2 = ""
Text3 = ""
Combo1 = ""

End Sub

ysr

程序用法举例如下：

框1：输入：29484081443918291801600463101876546530549424781270631658342853728313216934769556000297342398244699141404947881779779424408806582548005915062131296706953121226446340097

框2： 输入：2305843009213693951

框3：输出：10是该素数的原根

ysr

Private Sub Command1_Click()
'验证素数的原根的程序
Dim a, b
a = Trim(Text1)
jB = Trim(Text2)
jB1 = qxdcm(2, 4)
g = 10
c = MCC1(MPC(Trim(a), 1), Trim(jB))
C1 = MCC1(MPC(Trim(a), 1), Trim(jB1))
j = qksmimo(Trim(g), Trim(jB), Trim(a))
j1 = qksmimo(Trim(g), Trim(c), Trim(a))
j2 = qksmimo(Trim(g), Trim(C1), Trim(a))
If j <> 1 And j1 <> 1 And j2 <> 1 Then
Text3 = g & "是该素数的原根,素数是  " & a
Else
Text3 = g & "不是原根"
End If

End Sub



Private Sub Command2_Click()
Text1 = ""
Text2 = ""
Text3 = ""
Combo1 = ""

End Sub

Private Function qxdcm(sa As String, sb As String) As String

Dim a, b
a = sa: b = sb
If b = 1 Then
qxdcm = a
ElseIf b = 0 Then
qxdcm = 1
Else
a1 = a
Do While b > 1
s = Int(Log(b) / Log(2))
s1 = 0
Do While s1 < s
a = MbC(Trim(a), Trim(a))
s1 = s1 + 1
Loop
a2 = a
b = b - 2 ^ s
a = a1
If s2 > 0 Then
a3 = MbC(Trim(a3), Trim(a2))
Else
a3 = a2
End If
s2 = s2 + 1
Loop
If b = 1 Then
qxdcm = MbC(Trim(a3), Trim(a1))
Else
qxdcm = a3
End If

End If

End Function

ysr

/1550/1552/1554/1556/1558/1560/1562/1564/1566/1568/1570/1572/1574/1576/1578/1580/1582/1584/1586/1588
/1590/1592/1594/1596/1598/1600/1602/1604/1606/1610/1612/1614/1616/1618/1620/1622/1624/1626/1628/1630
/1632/1634/1636/1638/1640/1642/1644/1646/1648/1650/1652/1654/1656/1658/1660/1662/1666/1668/1672/1674
/1676/1678/1680/1682/1686/1690/1692/1694/1698/1702/1704/1710/1718/1722/1726/1728/1732/1734/1740/1744
/1746/1750/1752/1754/1762/1766/1776/1780/1806/1808/1830/1854/2000/3000/4000/6000/8888/66666/88888/100000
/123456

ysr

/1550/1552/1554/1556/1558/1560/1562/1564/1566/1568/1570/1572/1574/1576/1578/1580/1582/1584/1586/1588
/1590/1592/1594/1596/1598/1600/1602/1604/1606/1610/1612/1614/1616/1618/1620/1622/1624/1626/1628/1630
/1632/1634/1636/1638/1640/1642/1644/1646/1648/1650/1652/1654/1656/1658/1660/1662/1666/1668/1672/1674
/1676/1678/1680/1682/1686/1690/1692/1694/1698/1702/1704/1710/1718/1722/1726/1728/1732/1734/1740/1744
/1746/1750/1752/1754/1762/1766/1776/1780/1806/1808/1830/1854/2000/3000/4000/6000/8888/66666/88888/100000
/123456
这是 目前知道的最大的素数间距。
    缺少1608，1664，1670，1684，1688，1696，1700，1706，1708，1712~1716，1720，1724，1730，1736，1738，1742，1748，1756~1760，1764，1768~1774，1778，1782~1804，1810~18285，1832~1852，等

ysr

如何快速找到大间距呢？比如上面没有1608，要想找到1608间距的素数对，就要解下面这俩方程:
（（ln(x)）^2）/1.5=1608，其中的x的值应该是下限，
（（ln(x)）^2）/2.5=1608，其中的x的值应该是上限，
  解出来x，在这俩x的值中间找，
根据计算的结果找规律，可以进一步缩小范围，
能解这俩方程吗？可以利用网上的软件啊，请朋友们解一下这俩方程，谢谢！

ab.571016

楼主的问题，我早已给出了证明：
请查阅我发在“豆瓣”相关数学栏的文章：
《对数学结构实质的深度思考，及对费马大定理、比尔猜想等的新颖证明》最后部份对“平方差定理”的证明与应用。
不用费心力再去一个个举证。
(因数学符号转换的麻烦，所以未再发在该论坛)

ysr

ysr 发表于 2023-3-11 09:46
如何快速找到大间距呢？比如上面没有1608，要想找到1608间距的素数对，就要解下面这俩方程:
（（ln(x)）^2 ...

哈哈！这俩方程，可以利用电脑自带的计算器手工解决，用穷举法就可以，一个是22位的整数，一个是28位的整数。