基础理论中的两个重要定理的证明

ysr

在126与200之间的10项公差为210的素数组有1 组：
(199   409   619   829   1039   1249   1459   1669   1879   2089 )  

代码如下：

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)
r = Val(Text3)
p1 = Val(Text4)
If Right(p1, 1) Mod 2 = 0 Then
p1 = p1 + 1
End If

Do While p1 <= a
p1 = p1: p2 = p1 + r: p3 = p2 + r
p4 = p3 + r: p5 = p4 + r: p6 = p5 + r: p7 = p6 + r
p8 = p7 + r: p9 = p8 + r: p10 = p9 + r
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" & Text4 & "与" & Text1 & "之间的10项公差为" & r & "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 = ""
Text4 = ""
Combo1 = ""
Form1.Cls
End Sub

ysr

640943与641143之间的素数开头最多有公差为6469693230的10个连续素数:
/640943/6470334173/12940027403/19409720633/25879413863/32349107093/38818800323/45288493553/51758186783/58227880013

代码如下：

Private Sub Command1_Click()
Dim a, b
a = Val(Text1)
a1 = a
Q = Val(Text2)
r = Val(Text4)
m = Sqr(Q)
If Right(a, 1) Mod 2 = 0 Then
a = a + 1
Else
a = a
End If

Do While InStr(fenjieyinzi(Val(a)), "*") <> 0
a = a + 2
Loop

Do While a <= Q
b = a
d = fenjieyinzi(Val(b))
s = 0
s3 = ""
Do While s < 40 And InStr(d, "*") = 0
s4 = s + 1
If s4 Mod 20 = 0 Then
s3 = s3 & "/" & b & vbCrLf
Else
s3 = s3 & "/" & b
End If
s = s + 1
s2 = s * (s + 1)
b = b + r
d = fenjieyinzi(Val(b))
Loop
If s > 5 Then
Text3 = Text3 & s3 & vbCrLf
End If
If s > 1 Then
s5 = s5 & "/" & s
Else
s5 = s5
End If
Print s5
a = a + 2
s2 = 0
Loop
s6 = Mid(s5, 2)
     s7 = max(Trim(s6))
Combo1 = a1 & "与" & Q & "之间的素数开头最多有公差为" & r & "的" & s7 & "个连续素数:" & vbCrLf & Text3

     

End Sub

Private Sub Command2_Click()
Text1 = ""
Text2 = ""
Text3 = ""
Text4 = ""
Combo1 = ""
Form1.Cls
End Sub
Private Function max(ByVal lists As String) As String
Dim temp As Long
Dim a() As String
a = Split(lists, "/")
Dim b As Long

For b = 0 To UBound(a)
If temp < a(b) Then temp = a(b)
Next
max = temp
End Function

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

ysr

640943与641143之间的素数开头最多有公差为6469693230的10个连续素数:
/640943/6470334173/12940027403/19409720633/25879413863/32349107093/38818800323/45288493553/51758186783/58227880013
/640963/6470334193/12940027423/19409720653/25879413883
/641093/6470334323/12940027553
/641131/6470334361/12940027591

代码如下：

Private Sub Command1_Click()
Dim a, b
a = Val(Text1)
a1 = a
Q = Val(Text2)
r = Val(Text4)
m = Sqr(Q)
If Right(a, 1) Mod 2 = 0 Then
a = a + 1
Else
a = a
End If

Do While InStr(fenjieyinzi(Val(a)), "*") <> 0
a = a + 2
Loop

Do While a <= Q
b = a
d = fenjieyinzi(Val(b))
s = 0
s3 = ""
Do While s < 40 And InStr(d, "*") = 0
s4 = s + 1
If s4 Mod 20 = 0 Then
s3 = s3 & "/" & b & vbCrLf
Else
s3 = s3 & "/" & b
End If
s = s + 1
s2 = s * (s + 1)
b = b + r
d = fenjieyinzi(Val(b))
Loop
If s > 2 Then
Text3 = Text3 & s3 & vbCrLf
End If
If s > 1 Then
s5 = s5 & "/" & s
Else
s5 = s5
End If
Print s5
a = a + 2
s2 = 0
Loop
s6 = Mid(s5, 2)
     s7 = max(Trim(s6))
Combo1 = a1 & "与" & Q & "之间的素数开头最多有公差为" & r & "的" & s7 & "个连续素数:" & vbCrLf & Text3

     

End Sub

Private Sub Command2_Click()
Text1 = ""
Text2 = ""
Text3 = ""
Text4 = ""
Combo1 = ""
Form1.Cls
End Sub
Private Function max(ByVal lists As String) As String
Dim temp As Long
Dim a() As String
a = Split(lists, "/")
Dim b As Long

For b = 0 To UBound(a)
If temp < a(b) Then temp = a(b)
Next
max = temp
End Function

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

ysr

春蚕到死丝方尽，蜡炬成灰泪始干。昨天停电了，今天10:000才能来电，幸亏手机还有电。不敢多用了。

ysr

641143与649143之间的素数开头最多有公差为6469693230的5个连续素数:
/641279/6470334509/12940027739/19409720969
/641833/6470335063/12940028293
/641981/6470335211/12940028441
/642977/6470336207/12940029437
/643099/6470336329/12940029559
/643213/6470336443/12940029673/19409722903
/643403/6470336633/12940029863
/643619/6470336849/12940030079
/643703/6470336933/12940030163
/644009/6470337239/12940030469
/644431/6470337661/12940030891
/644653/6470337883/12940031113/19409724343/25879417573
/644837/6470338067/12940031297
/644923/6470338153/12940031383
/645049/6470338279/12940031509
/645233/6470338463/12940031693
/645497/6470338727/12940031957
/645683/6470338913/12940032143/19409725373
/645941/6470339171/12940032401
/646003/6470339233/12940032463
/646099/6470339329/12940032559
/646609/6470339839/12940033069
/646883/6470340113/12940033343/19409726573/25879419803
/647219/6470340449/12940033679
/647303/6470340533/12940033763
/647371/6470340601/12940033831
/647399/6470340629/12940033859
/647609/6470340839/12940034069
/647783/6470341013/12940034243
/647909/6470341139/12940034369
/648101/6470341331/12940034561
/648317/6470341547/12940034777
/648341/6470341571/12940034801
/648481/6470341711/12940034941

ysr

649143与699143之间的素数开头最多有公差为6469693230的6个连续素数:
/650873/6470344103/12940037333/19409730563/25879423793
/653153/6470346383/12940039613/19409732843/25879426073
/654371/6470347601/12940040831/19409734061/25879427291
/655657/6470348887/12940042117/19409735347/25879428577
/657413/6470350643/12940043873/19409737103/25879430333
/659761/6470352991/12940046221/19409739451/25879432681
/659873/6470353103/12940046333/19409739563/25879432793
/663977/6470357207/12940050437/19409743667/25879436897/32349130127
/665801/6470359031/12940052261/19409745491/25879438721
/666301/6470359531/12940052761/19409745991/25879439221
/667417/6470360647/12940053877/19409747107/25879440337
/667883/6470361113/12940054343/19409747573/25879440803/32349134033
/668029/6470361259/12940054489/19409747719/25879440949
/669077/6470362307/12940055537/19409748767/25879441997
/677471/6470370701/12940063931/19409757161/25879450391
/685793/6470379023/12940072253/19409765483/25879458713/32349151943
/686423/6470379653/12940072883/19409766113/25879459343
/686449/6470379679/12940072909/19409766139/25879459369
/686989/6470380219/12940073449/19409766679/25879459909
/693701/6470386931/12940080161/19409773391/25879466621/32349159851

ysr

699143与799143之间的素数开头最多有公差为6469693230的8个连续素数:
/700877/6470394107/12940087337/19409780567/25879473797
/703243/6470396473/12940089703/19409782933/25879476163/32349169393
/710441/6470403671/12940096901/19409790131/25879483361
/710641/6470403871/12940097101/19409790331/25879483561
/712093/6470405323/12940098553/19409791783/25879485013
/715417/6470408647/12940101877/19409795107/25879488337
/716249/6470409479/12940102709/19409795939/25879489169
/717151/6470410381/12940103611/19409796841/25879490071/32349183301/38818876531/45288569761
/718633/6470411863/12940105093/19409798323/25879491553
/719573/6470412803/12940106033/19409799263/25879492493
/721529/6470414759/12940107989/19409801219/25879494449
/721891/6470415121/12940108351/19409801581/25879494811/32349188041
/725161/6470418391/12940111621/19409804851/25879498081
/730637/6470423867/12940117097/19409810327/25879503557
/731851/6470425081/12940118311/19409811541/25879504771
/731869/6470425099/12940118329/19409811559/25879504789
/732293/6470425523/12940118753/19409811983/25879505213
/734869/6470428099/12940121329/19409814559/25879507789
/736867/6470430097/12940123327/19409816557/25879509787
/739327/6470432557/12940125787/19409819017/25879512247/32349205477
/740603/6470433833/12940127063/19409820293/25879513523/32349206753
/740989/6470434219/12940127449/19409820679/25879513909
/741547/6470434777/12940128007/19409821237/25879514467
/742151/6470435381/12940128611/19409821841/25879515071
/743279/6470436509/12940129739/19409822969/25879516199
/745517/6470438747/12940131977/19409825207/25879518437
/751307/6470444537/12940137767/19409830997/25879524227/32349217457
/753139/6470446369/12940139599/19409832829/25879526059/32349219289
/754703/6470447933/12940141163/19409834393/25879527623
/761119/6470454349/12940147579/19409840809/25879534039
/763339/6470456569/12940149799/19409843029/25879536259
/770909/6470464139/12940157369/19409850599/25879543829/32349237059
/773837/6470467067/12940160297/19409853527/25879546757/32349239987
/775987/6470469217/12940162447/19409855677/25879548907
/781967/6470475197/12940168427/19409861657/25879554887
/787993/6470481223/12940174453/19409867683/25879560913/32349254143
/788027/6470481257/12940174487/19409867717/25879560947/32349254177
/792641/6470485871/12940179101/19409872331/25879565561

ysr

799143与999143之间的素数开头最多有公差为6469693230的7个连续素数:
/800117/6470493347/12940186577/19409879807/25879573037
/801179/6470494409/12940187639/19409880869/25879574099
/816649/6470509879/12940203109/19409896339/25879589569
/819811/6470513041/12940206271/19409899501/25879592731/32349285961
/822131/6470515361/12940208591/19409901821/25879595051/32349288281/38818981511
/824981/6470518211/12940211441/19409904671/25879597901
/825203/6470518433/12940211663/19409904893/25879598123
/825403/6470518633/12940211863/19409905093/25879598323
/826907/6470520137/12940213367/19409906597/25879599827
/827927/6470521157/12940214387/19409907617/25879600847
/831191/6470524421/12940217651/19409910881/25879604111
/832121/6470525351/12940218581/19409911811/25879605041
/832123/6470525353/12940218583/19409911813/25879605043/32349298273
/832969/6470526199/12940219429/19409912659/25879605889
/833201/6470526431/12940219661/19409912891/25879606121
/836317/6470529547/12940222777/19409916007/25879609237/32349302467/38818995697
/838949/6470532179/12940225409/19409918639/25879611869
/839669/6470532899/12940226129/19409919359/25879612589
/842701/6470535931/12940229161/19409922391/25879615621
/848461/6470541691/12940234921/19409928151/25879621381
/850711/6470543941/12940237171/19409930401/25879623631
/852427/6470545657/12940238887/19409932117/25879625347
/856441/6470549671/12940242901/19409936131/25879629361
/859513/6470552743/12940245973/19409939203/25879632433
/860381/6470553611/12940246841/19409940071/25879633301
/860929/6470554159/12940247389/19409940619/25879633849/32349327079
/865957/6470559187/12940252417/19409945647/25879638877
/874477/6470567707/12940260937/19409954167/25879647397
/879961/6470573191/12940266421/19409959651/25879652881
/881173/6470574403/12940267633/19409960863/25879654093
/881611/6470574841/12940268071/19409961301/25879654531
/883781/6470577011/12940270241/19409963471/25879656701
/891439/6470584669/12940277899/19409971129/25879664359
/893479/6470586709/12940279939/19409973169/25879666399
/895309/6470588539/12940281769/19409974999/25879668229
/897053/6470590283/12940283513/19409976743/25879669973
/897499/6470590729/12940283959/19409977189/25879670419
/899263/6470592493/12940285723/19409978953/25879672183/32349365413/38819058643
/902789/6470596019/12940289249/19409982479/25879675709
/913259/6470606489/12940299719/19409992949/25879686179
/915611/6470608841/12940302071/19409995301/25879688531
/922223/6470615453/12940308683/19410001913/25879695143
/922451/6470615681/12940308911/19410002141/25879695371
/923177/6470616407/12940309637/19410002867/25879696097
/923333/6470616563/12940309793/19410003023/25879696253
/923551/6470616781/12940310011/19410003241/25879696471
/923833/6470617063/12940310293/19410003523/25879696753/32349389983
/924383/6470617613/12940310843/19410004073/25879697303/32349390533
/924907/6470618137/12940311367/19410004597/25879697827
/925741/6470618971/12940312201/19410005431/25879698661/32349391891/38819085121
/925783/6470619013/12940312243/19410005473/25879698703
/931981/6470625211/12940318441/19410011671/25879704901
/938243/6470631473/12940324703/19410017933/25879711163/32349404393
/941737/6470634967/12940328197/19410021427/25879714657
/943219/6470636449/12940329679/19410022909/25879716139/32349409369/38819102599
/943567/6470636797/12940330027/19410023257/25879716487
/943871/6470637101/12940330331/19410023561/25879716791/32349410021
/946489/6470639719/12940332949/19410026179/25879719409/32349412639
/950483/6470643713/12940336943/19410030173/25879723403
/956353/6470649583/12940342813/19410036043/25879729273/32349422503/38819115733
/959921/6470653151/12940346381/19410039611/25879732841
/961703/6470654933/12940348163/19410041393/25879734623
/961739/6470654969/12940348199/19410041429/25879734659
/964213/6470657443/12940350673/19410043903/25879737133/32349430363/38819123593
/964571/6470657801/12940351031/19410044261/25879737491
/974443/6470667673/12940360903/19410054133/25879747363
/976211/6470669441/12940362671/19410055901/25879749131
/977791/6470671021/12940364251/19410057481/25879750711
/978001/6470671231/12940364461/19410057691/25879750921/32349444151
/979037/6470672267/12940365497/19410058727/25879751957
/986411/6470679641/12940372871/19410066101/25879759331/32349452561
/986477/6470679707/12940372937/19410066167/25879759397
/987607/6470680837/12940374067/19410067297/25879760527
/989239/6470682469/12940375699/19410068929/25879762159
/989347/6470682577/12940375807/19410069037/25879762267/32349455497
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/998947/6470692177/12940385407/19410078637/25879771867/32349465097/38819158327

ysr

999143与1999143之间的素数开头最多有公差为6469693230的10个连续素数:
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/1939169/6471632399/12941325629/19411018859/25880712089
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/1946761/6471639991/12941333221/19411026451/25880719681
/1957117/6471650347/12941343577/19411036807/25880730037/32350423267
/1961249/6471654479/12941347709/19411040939/25880734169
/1965449/6471658679/12941351909/19411045139/25880738369/32350431599
/1970719/6471663949/12941357179/19411050409/25880743639
/1974887/6471668117/12941361347/19411054577/25880747807
/1975147/6471668377/12941361607/19411054837/25880748067
/1986253/6471679483/12941372713/19411065943/25880759173
/1990981/6471684211/12941377441/19411070671/25880763901
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/1994777/6471688007/12941381237/19411074467/25880767697
/1997911/6471691141/12941384371/19411077601/25880770831
/1998343/6471691573/12941384803/19411078033/25880771263/32350464493

ysr

1999143与2999143之间的素数开头最多有公差为6469693230的8个连续素数:
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