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求数列的通项公式

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 楼主| 发表于 2026-4-9 09:27 | 显示全部楼层
7999202243与8000202243之间的素数开头最多有公差为6469693230的8个连续素数:
/7999330307/14469023537/20938716767/27408409997/33878103227/40347796457/46817489687/53287182917
/7999389149/14469082379/20938775609/27408468839/33878162069/40347855299/46817548529/53287241759
/8000032511/14469725741/20939418971/27409112201/33878805431/40348498661/46818191891/53287885121
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 楼主| 发表于 2026-4-9 09:47 | 显示全部楼层
本帖最后由 ysr 于 2026-4-9 01:58 编辑

4026918759与4027918759之间的素数开头最多有公差为6469693230的9个连续素数:
/4027866383/10497559613/16967252843/23436946073/29906639303/36376332533/42846025763/49315718993/55785412223
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 楼主| 发表于 2026-4-9 10:12 | 显示全部楼层
7998202243与7999202243之间的素数开头最多有公差为6469693230的9个连续素数:
/7998799709/14468492939/20938186169/27407879399/33877572629/40347265859/46816959089/53286652319/59756345549
/7999089521/14468782751/20938475981/27408169211/33877862441/40347555671/46817248901/53286942131/59756635361
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 楼主| 发表于 2026-4-9 11:00 | 显示全部楼层
7997202243与7998202243之间的素数开头最多有公差为6469693230的9个连续素数:
/7997215997/14466909227/20936602457/27406295687/33875988917/40345682147
/7997232121/14466925351/20936618581/27406311811/33876005041/40345698271
/7997281517/14466974747/20936667977/27406361207/33876054437/40345747667
/7997290369/14466983599/20936676829/27406370059/33876063289/40345756519/46815449749/53285142979
/7997309083/14467002313/20936695543/27406388773/33876082003/40345775233/46815468463
/7997313101/14467006331/20936699561/27406392791/33876086021/40345779251/46815472481
/7997322077/14467015307/20936708537/27406401767/33876094997/40345788227
/7997338991/14467032221/20936725451/27406418681/33876111911/40345805141/46815498371
/7997384413/14467077643/20936770873/27406464103/33876157333/40345850563
/7997405237/14467098467/20936791697/27406484927/33876178157/40345871387/46815564617
/7997406121/14467099351/20936792581/27406485811/33876179041/40345872271
/7997429207/14467122437/20936815667/27406508897/33876202127/40345895357
/7997434787/14467128017/20936821247/27406514477/33876207707/40345900937
/7997475011/14467168241/20936861471/27406554701/33876247931/40345941161/46815634391
/7997476681/14467169911/20936863141/27406556371/33876249601/40345942831
/7997489419/14467182649/20936875879/27406569109/33876262339/40345955569/46815648799/53285342029/59755035259
/7997509343/14467202573/20936895803/27406589033/33876282263/40345975493
/7997521033/14467214263/20936907493/27406600723/33876293953/40345987183
/7997580469/14467273699/20936966929/27406660159/33876353389/40346046619
/7997581861/14467275091/20936968321/27406661551/33876354781/40346048011
/7997603197/14467296427/20936989657/27406682887/33876376117/40346069347/46815762577/53285455807/59755149037
/7997622361/14467315591/20937008821/27406702051/33876395281/40346088511/46815781741
/7997623597/14467316827/20937010057/27406703287/33876396517/40346089747
/7997637793/14467331023/20937024253/27406717483/33876410713/40346103943
/7997647243/14467340473/20937033703/27406726933/33876420163/40346113393
/7997660123/14467353353/20937046583/27406739813/33876433043/40346126273
/7997715403/14467408633/20937101863/27406795093/33876488323/40346181553
/7997721869/14467415099/20937108329/27406801559/33876494789/40346188019/46815881249
/7997726519/14467419749/20937112979/27406806209/33876499439/40346192669
/7997756323/14467449553/20937142783/27406836013/33876529243/40346222473
/7997760703/14467453933/20937147163/27406840393/33876533623/40346226853/46815920083/53285613313/59755306543
/7997790313/14467483543/20937176773/27406870003/33876563233/40346256463/46815949693
/7997826773/14467520003/20937213233/27406906463/33876599693/40346292923
/7997856973/14467550203/20937243433/27406936663/33876629893/40346323123
/7997891273/14467584503/20937277733/27406970963/33876664193/40346357423
/7997895431/14467588661/20937281891/27406975121/33876668351/40346361581/46816054811
/7997898253/14467591483/20937284713/27406977943/33876671173/40346364403/46816057633/53285750863/59755444093
/7997922601/14467615831/20937309061/27407002291/33876695521/40346388751
/7997948489/14467641719/20937334949/27407028179/33876721409/40346414639
/7997951581/14467644811/20937338041/27407031271/33876724501/40346417731
/7997955041/14467648271/20937341501/27407034731/33876727961/40346421191
/7997965039/14467658269/20937351499/27407044729/33876737959/40346431189
/7997989339/14467682569/20937375799/27407069029/33876762259/40346455489/46816148719
/7998005689/14467698919/20937392149/27407085379/33876778609/40346471839
/7998014287/14467707517/20937400747/27407093977/33876787207/40346480437
/7998036649/14467729879/20937423109/27407116339/33876809569/40346502799/46816196029
/7998040199/14467733429/20937426659/27407119889/33876813119/40346506349
/7998063131/14467756361/20937449591/27407142821/33876836051/40346529281/46816222511
/7998069661/14467762891/20937456121/27407149351/33876842581/40346535811
/7998110437/14467803667/20937496897/27407190127/33876883357/40346576587/46816269817/53285963047
/7998119651/14467812881/20937506111/27407199341/33876892571/40346585801
/7998128377/14467821607/20937514837/27407208067/33876901297/40346594527
/7998135421/14467828651/20937521881/27407215111/33876908341/40346601571
/7998146483/14467839713/20937532943/27407226173/33876919403/40346612633/46816305863
/7998155059/14467848289/20937541519/27407234749/33876927979/40346621209
/7998156823/14467850053/20937543283/27407236513/33876929743/40346622973/46816316203/53286009433
/7998166459/14467859689/20937552919/27407246149/33876939379/40346632609
/7998171703/14467864933/20937558163/27407251393/33876944623/40346637853
/7998182267/14467875497/20937568727/27407261957/33876955187/40346648417
/7998196439/14467889669/20937582899/27407276129/33876969359/40346662589
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 楼主| 发表于 2026-4-9 13:20 | 显示全部楼层
7995202243与7997202243之间的素数开头最多有公差为6469693230的9个连续素数:
/7995251071/14464944301/20934637531/27404330761/33874023991/40343717221/46813410451/53283103681/59752796911
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 楼主| 发表于 2026-4-9 14:40 | 显示全部楼层
本帖最后由 ysr 于 2026-4-9 06:43 编辑

由于这两个相邻素数的差p2-p1=4000101121-4000101059=62,所以,理论上在4000101121与2*4000101121+1=8,000,202,243之间,至少有一个素数打头,会形成62项公差为6469693230的素数数列。但是要从4000101121算到2*4000101121+1=8,000,202,243我的程序不知道需要多长时间,没法完成
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 楼主| 发表于 2026-4-9 15:11 | 显示全部楼层
现在开始从4047918759到7985202243看看,能否找到那个62项的等差素数数列
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 楼主| 发表于 2026-4-9 15:15 | 显示全部楼层
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 >= 0 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 > =10 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
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 楼主| 发表于 2026-4-9 18:40 | 显示全部楼层
4030918759与4034918759之间的素数开头最多有公差为6469693230的12个连续素数:
/4032381341/10502074571/16971767801/23441461031/29911154261/36380847491/42850540721/49320233951
/4032381511/10502074741/16971767971/23441461201
/4032384511/10502077741/16971770971/23441464201
/4032385733/10502078963/16971772193/23441465423
/4032386711/10502079941/16971773171/23441466401
/4032387089/10502080319/16971773549/23441466779
/4032387587/10502080817/16971774047/23441467277
/4032387673/10502080903/16971774133/23441467363/29911160593
/4032390251/10502083481/16971776711/23441469941
/4032393433/10502086663/16971779893/23441473123
/4032394343/10502087573/16971780803/23441474033
/4032395659/10502088889/16971782119/23441475349/29911168579
/4032397231/10502090461/16971783691/23441476921
/4032398171/10502091401/16971784631/23441477861/29911171091
/4032398371/10502091601/16971784831/23441478061/29911171291
/4032398627/10502091857/16971785087/23441478317
/4032398731/10502091961/16971785191/23441478421/29911171651
/4032399893/10502093123/16971786353/23441479583
/4032400103/10502093333/16971786563/23441479793
/4032400387/10502093617/16971786847/23441480077
/4032400649/10502093879/16971787109/23441480339/29911173569
/4032400927/10502094157/16971787387/23441480617
/4032401671/10502094901/16971788131/23441481361
/4032403883/10502097113/16971790343/23441483573
/4032404227/10502097457/16971790687/23441483917
/4032405107/10502098337/16971791567/23441484797
/4032407303/10502100533/16971793763/23441486993
/4032408157/10502101387/16971794617/23441487847/29911181077
/4032408227/10502101457/16971794687/23441487917/29911181147
/4032411319/10502104549/16971797779/23441491009
/4032412093/10502105323/16971798553/23441491783
/4032412183/10502105413/16971798643/23441491873/29911185103
/4032413309/10502106539/16971799769/23441492999
/4032415523/10502108753/16971801983/23441495213
/4032419707/10502112937/16971806167/23441499397
/4032421049/10502114279/16971807509/23441500739/29911193969/36380887199/42850580429
/4032422959/10502116189/16971809419/23441502649
/4032423023/10502116253/16971809483/23441502713/29911195943/36380889173
/4032424133/10502117363/16971810593/23441503823/29911197053
/4032425767/10502118997/16971812227
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 楼主| 发表于 2026-4-9 22:11 | 显示全部楼层
4032425767与4034918759之间的素数开头最多有公差为6469693230的12个连续素数:
/4033488713/10503181943/16972875173/23442568403/29912261633/36381954863/42851648093/49321341323/55791034553/62260727783/68730421013/75200114243
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