数论问题巅峰对决

ysr · 发表于 2020-8-9 11:22

无缝连接：
44058/44064/44070/44076/44082/44088/44094/44100/44106/44112/44118/44124/44130/44136/44142/44148/44154/44160/44166/44172/
44178/44184/44190/44196/44202/44208/44214/44220/44226/44232/44238/44244/44250/44256/44262/44268/44274/44280/44286/44292/
44298/44304/44310/44316/44322/44328/44334/44340/44346/44352/44358/44364/44370/44376/44382/44388/44394/44400/44406/44412/
44418/44424/44430/44436/44442/44448/44454/44460/44466/44472/44478/44484/44490/44496/44502/44508/44514/44520/44526/44532/
44538/44544/44550/44556/44562/44568/44574/44580/44586/44592/44598/44604/44610/44616/44622/44628/44634/44640/44646/44652/
44658/44664/44670/44676/44682/44688/44694/44700/44706/44712/44718/44724/44730/44736/44742/44748/44754/44760/44766/44772/
44778/44784/44790/44796/44802/44808/44814/44820/44826/44832/44838/44844/44850/44856/44862/44868/44874/44880/44886/44892/
44898/44904/44910/44916/44922/44928/44934/44940/44946/44952/44958/44964/44970/44976/44982/44988/44994/45000/45006/45012/
45018/45024/45030/45036/45042/45048/45054/45060/45066/45072/45078/45084/45090/45096/45102/45108/45114/45120/45126/45132/
45138/45144/45150/45156/45162/45168/45174/45180/45186/45192/45198/45204/45210/45216/45222/45228/45234/45240/45246/45252/
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45498/45504/45510/45516/45522/45528/45534/45540/45546/45552/45558/45564/45570/45576/45582/45588/45594/45600/45606/45612/
45618/45624/45630/45636/45642/45648/45654/45660/45666/45672/45678/45684/45690/45696/45702/45708/45714/45720/45726/45732/
45738/45744/45750/45756/45762/45768/45774/45780/45786/45792/45798/45804/45810/45816/45822/45828/45834/45840/45846/45852/
45858/45864/45870/45876/45882/45888/45894/45900/45906/45912/45918/45924/45930/45936/45942/45948/45954/45960/45966/45972/
45978/45984/45990/45996/46002/46008/46014/46020/46026/46032/46038/46044/46050/46056/46062/46068/46074/46080/46086/46092/
46098/46104/46110/46116/46122/46128/46134/46140/46146/46152/46158/46164/46170/46176/46182/46188/46194/46200/46206/46212/
46218/46224/46230/46236/46242/46248/46254/46260/46266/46272/46278/46284/46290/46296/46302/46308/46314/46320/46326/46332/
46338/46344/46350/46356/46362/46368/46374/46380/46386/46392/46398/46404/46410/46416/46422/46428/46434/46440/46446/46452/
46458/46464/46470/46476/46482/46488/46494/46500/46506/46512/46518/46524/46530/46536/46542/46548/46554/46560/46566/46572/
46578/46584/46590/46596/46602/46608/46614/46620/46626/46632/46638/46644/46650/46656/46662/46668/46674/46680/46686/46692/
46698/46704/46710/46716/46722/46728/46734/46740/46746/46752/46758/46764/46770/46776/46782/46788/46794/46800/46806/46812/
46818/46824/46830/46836/46842/46848/46854/46860/46866/46872/46878/46884/46890/46896/46902/46908/46914/46920/46926/46932/
46938/46944/46950/46956/46962/46968/46974/46980/46986/46992/46998/47004/47010/47016/47022/47028/47034/47040/47046/47052/
47058/47064/47070/47076/47082/47088/47094/47100/47106/47112/47118/47124/47130/47136/47142/47148/47154/47160/47166/47172/
47178/47184/47190/47196/47202/47208/47214/47220/47226/47232/47238/47244/47250/47256/47262/47268/47274/47280/47286/47292/
47298/47304/47310/47316/47322/47328/47334/47340/47346/47352/47358/47364/47370/47376/47382/47388/47394/47400/47406/47412/
47418/47424/47430/47436/47442/47448/47454/47460/47466/47472/47478/47484/47490/47496/47502/47508/47514/47520/47526/47532/
47538/47544/47550/47556/47562/47568/47574/47580/47586/47592/47598/47604/47610/47616/47622/47628/47634/47640/47646/47652/
47658/47664/47670/47676/47682/47688/47694/47700/47706/47712/47718/47724/47730/47736/47742/47748/47754/47760/47766/47772/
47778/47784/47790/47796/47802/47808/47814/47820/47826/47832/47838/47844/47850/47856/47862/47868/47874/47880/47886/47892/
47898/47904/47910/47916/47922/47928/47934/47940/47946/47952/47958/47964/47970/47976/47982/47988/47994/48000/48006/48012/
48018/48024/48030/48036/48042/48048/48054/48060/48066/48072/48078/48084/48090/48096/48102/48108/48114/48120/48126/48132/
48138/48144/48150/48156/48162/48168/48174/48180/48186/48192/48198/48204/48210/48216/48222/48228/48234/48240/48246/48252/
48258/48264/48270/48276/48282/48288/48294/48300/48306/48312/48318/48324/48330/48336/48342/48348/48354/48360/48366/48372/
48378/48384/48390/48396/48402/48408/48414/48420/48426/48432/48438/48444/48450/48456/48462/48468/48474/48480/48486/48492/
48498/48504/48510/48516/48522/48528/48534/48540/48546/48552/48558/48564/48570/48576/48582/48588/48594/48600/48606/48612/
48618/48624/48630/48636/48642/48648/48654/48660/48666/48672/48678/48684/48690/48696/48702/48708/48714/48720/48726/48732/
48738/48744/48750/48756/48762/48768/48774/48780/48786/48792/48798/48804/48810/48816/48822/48828/48834/48840/48846/48852/
48858/48864/48870/48876/48882/48888/48894/48900/48906/48912/48918/48924/48930/48936/48942/48948/48954/48960/48966/48972/
48978/48984/48990/48996/49002/49008/49014/49020/49026/49032/49038/49044/49050/49056/49062/49068/49074/49080/49086/49092/
49098/49104/49110/49116/49122/49128/49134/49140/49146/49152/49158/49164/49170/49176/49182/49188/49194/49200/49206/49212/
49218/49224/49230/49236/49242/49248/49254/49260/49266/49272/49278/49284/49290/49296/49302/49308/49314/49320/49326/49332/
49338/49344/49350/49356/49362/49368/49374/49380/49386/49392/49398/49404/49410/49416/49422/49428/49434/49440/49446/49452/
49458/49464/49470/49476/49482/49488/49494/49500/49506/49512/49518/49524/49530/49536/49542/49548/49554/49560/49566/49572/
49578/49584/49590/49596/49602/49608/49614/49620/49626/49632/49638/49644/49650/49656/49662/49668/49674/49680/49686/49692/
49698/49704/49710/49716/49722/49728/49734/49740/49746/49752/49758/49764/49770/49776/49782/49788/49794/49800/49806/49812/
49818/49824/49830/49836/49842/49848/49854/49860/49866/49872/49878/49884/49890/49896/49902/49908/49914/49920/49926/49932/
49938/49944/49950/49956/49962/49968/49974/49980/49986/49992/49998/50004/50010/50016/50022/50028/50034/50040/50046/50052/
50058/50064/50070/50076/50082/50088/50094/50100/50106/50112/50118/50124/50130/50136/50142/50148/50154/50160/50166/50172/
50178/50184/50190/50196/50202/50208/50214/50220/50226/50232/50238/50244/50250/50256/50262/50268/50274/50280/50286/50292/
50298/50304/50310/50316/50322/50328/50334/50340/50346/50352/50358/50364/50370/50376/50382/50388/50394/50400/50406/50412/
50418/50424/50430/50436/50442/50448/50454/50460/50466/50472/50478/50484/50490/50496/50502/50508/50514/50520/50526/50532/
50538/50544/50550/50556/50562/50568/50574/50580/50586/50592/50598/50604/50610/50616/50622/50628/50634/50640/50646/50652/

后面还很多不发了，而20000~40000内并没有实现偶数全覆盖。继续算也不可能实现到某数后偶数全覆盖了。能覆盖大于等于1122的差为6的全体偶数。

ysr · 发表于 2020-8-9 11:28

而孪中p+3的和，能覆盖大于等于8014的全体偶数。

ysr · 发表于 2020-8-9 11:50

额，您的命题成立，非常有趣，比哥德巴赫猜想和孪生素数猜想更厉害，虽然我证明不了我确信是成立的，佩服！

蔡家雄 · 发表于 2020-8-9 12:24

本帖最后由蔡家雄于 2020-8-9 16:14 编辑

再三谢谢 ysr，辛苦您了！

2生素数( p, p+6 )遍历覆盖对称4生连续素数15x±2, 15x±4, 及

2生素数( p, p+6 )遍历覆盖对称6生连续素数15x±2, 15x±4, 15x±8 ,

ysr · 发表于 2020-8-9 12:58

命题很好！感谢沟通探讨，不过我不懂啥是k生素数没有研究那个。

ysr · 发表于 2020-8-9 13:00

本帖最后由 ysr 于 2020-8-9 05:25 编辑

下面是改进版素数程序计算结果：（这个结果还是低于实际的）
10^5内的素数个数下限为 9571
10^6内的素数个数下限为 78415
10^7内的素数个数下限为 663567
10^8内的素数个数下限为 5749881
10^9内的素数个数下限为 50720963
10^10内的素数个数下限为 453678357
10^11内的素数个数下限为 4104048399
10^12内的素数个数下限为 37379740471
10^13内的素数个数下限为 339143631050
10^14内的素数个数下限为 3127108390065
10^15内的素数个数下限为 29161705875438
10^16内的素数个数下限为 273844893009129
10^17内的素数个数下限为 2.58444344177065E+15
10^18内的素数个数下限为 2.44905566203191E+16
10^19内的素数个数下限为 2.32899659565197E+17
10^20内的素数个数下限为 2.22186121705457E+18
10^21内的素数个数下限为 2.12577130696508E+19
10^22内的素数个数下限为 2.03921097636325E+20
10^23内的素数个数下限为 1.96093429480603E+21
10^24内的素数个数下限为 1.88990491098466E+22
10^25内的素数个数下限为 1.82525287620363E+23
10^26内的素数个数下限为 1.76624225909695E+24
10^27内的素数个数下限为 1.7122462099504E+25
10^28内的素数个数下限为 1.66272744579784E+26
10^29内的素数个数下限为 1.61722279682205E+27

程序代码如下：（仅发主程序）
Private Sub Command1_Click()
Dim a, b, c
a = Trim(Text1)
Do While Log(a) / Log(10) < 28
a = MbC(Trim(a), 10)
b = Sqr(a)
c = a / Log(a)
If a > 10 ^ 11 Then
s = 1
Do While Int(b ^ (2 ^ (1 - s))) > 1
b6 = b ^ (2 ^ (1 - s))
b7 = 2 ^ (s + 14) * b6 + b7
Print b7
s = s + 1
Loop
c = (a + b7) / Log(a)
ElseIf a > 10000000 Then
a1 = Log(a) / Log(10)
b2 = Exp(1.033 * a1)
B1 = 0.159 * b2
b4 = (1.74136140824861 ^ (1.8 * a1)) / 4.9
b5 = (B1 + b4) / 2
c = (a + (b5 + 4) * b) / Log(a)
ElseIf a >= 10000 Then
a1 = Log(a) / Log(10)
b3 = (56 * a1 ^ 3 - 741 * a1 ^ 2 + 3367 * a1 - 5142) / 6
c = (a + (b3 + 4) * b) / Log(a)
ElseIf a >= 1000 Then
c = (a + 4 * b) / Log(a)
ElseIf a > 500 Then
c = (a + 2 * b) / Log(a)
Else
c = c
End If
d = a / c
D1 = Int(c) * d
a1 = Log(a) / Log(10)
js = 0.0002 * a1 ^ 2 - 0.0035 * a1 + 1.0132
c = c * js
Text2 = Text2 & "10^" & Log(a) / Log(10) & "内的素数个数下限为 " & Int(c) & vbCrLf
Loop
Text3 = D1
End Sub

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

ysr · 发表于 2020-8-9 13:12

本帖最后由 ysr 于 2020-8-9 05:17 编辑

另一个素数个数程序计算结果：（这个结果大于实际了）
10^10内的素数个数下限为 459632260
10^11内的素数个数下限为 4124591238
10^12内的素数个数下限为 37057215852
10^13内的素数个数下限为 347036109068
10^14内的素数个数下限为 3307240726260
10^15内的素数个数下限为 32015266593043
10^16内的素数个数下限为 314225663596112
10^17内的素数个数下限为 3.12114619331356E+15
10^18内的素数个数下限为 3.13181093186547E+16
10^19内的素数个数下限为 3.16924208102884E+17
10^20内的素数个数下限为 3.22944115072979E+18
10^21内的素数个数下限为 3.30915725553855E+19
10^22内的素数个数下限为 3.4056927094738E+20
10^23内的素数个数下限为 3.51675616282711E+21
10^24内的素数个数下限为 3.64035167148443E+22
10^25内的素数个数下限为 3.77469845804351E+23
10^26内的素数个数下限为 3.91818032233073E+24
10^27内的素数个数下限为 4.06932547868719E+25
10^28内的素数个数下限为 4.22681649296179E+26
10^29内的素数个数下限为 4.38952570551729E+27

程序代码如下：（仅发主程序）
Private Sub Command1_Click()
Dim a, b, c
a = Trim(Text1)
Do While Log(a) / Log(10) < 28
a = MbC(Trim(a), 10)
b = Sqr(a)
c = a / Log(a)
If a > 10 ^ 11 Then
a1 = Log(a) / Log(10)
b3 = (1.74136140824861 ^ ((1.06415 * Exp(-0.00175 * (a1 - 0.65 * (a1 - 21)))) ^ a1)) ^ a1
c = (a + (b3 + 4) * b) / Log(a)
ElseIf a > 10000000 Then
a1 = Log(a) / Log(10)
b2 = Exp(1.033 * a1)
B1 = 0.159 * b2
b4 = (1.74136140824861 ^ (1.8 * a1)) / 4.9
b5 = (B1 + b4) / 2
c = (a + (b5 + 4) * b) / Log(a)
ElseIf a >= 10000 Then
a1 = Log(a) / Log(10)
b3 = (56 * a1 ^ 3 - 741 * a1 ^ 2 + 3367 * a1 - 5142) / 6
c = (a + (b3 + 4) * b) / Log(a)
ElseIf a >= 1000 Then
c = (a + 4 * b) / Log(a)
ElseIf a > 500 Then
c = (a + 2 * b) / Log(a)
Else
c = c
End If
d = a / c
D1 = Int(c) * d
a1 = Log(a) / Log(10)
js = 0.0059 * a1 ^ 2 - 0.1313 * a1 + 1.7343
c = c * js
Text2 = Text2 & "10^" & Log(a) / Log(10) & "内的素数个数下限为 " & Int(c) & vbCrLf
Loop
Text3 = D1
End Sub

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

蔡家雄 · 发表于 2020-8-9 13:15

请 ysr 编程寻找：对称6生连续素数15x±2, 15x±4, 15x±8 ,

注：15x 就是这6个连续素数的中项 ( 孪中数 )，分别：加减2，加减4，加减8，

ysr · 发表于 2020-8-9 13:29

抱歉！休息一会儿，下午去上班呢，明天下午再弄吧，抱歉啊！

ysr · 发表于 2020-8-10 19:23

“对称6生连续素数15x±2, 15x±4, 15x±8 ,”是指中间没有其他素数还是不用管中间是否有其他素数？其中15x+2,与15x+4是孪生素数吧就是说x相同？

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