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数论问题巅峰对决

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 楼主| 发表于 2020-8-14 20:22 | 显示全部楼层
1与31000之间有965对孪生(p,p+12)素数对,只显示孪中奇数:
/11/13/17/23/25/35/37/47/53/65/67/73/77/95/103/107/133/143/145/157/173/185/187/205/217/233/235/245/257/263/275/277/287/343/353/373/395/403/415/425/427/437/455/473/485/493/497/515/563/593/607/613/625/637/647/653/667/733/745/763/767/803/815/817/833/913/935/947/977/1003/1015/1025/1027/1045/1055/1057/1097/1103/1123/1157/1187/1207/1223/1243/1283/1285/1295/1297/1313/1367/1433/1445/1453/1465/1477/1487/1493/1505/1517/1537/1565/1573/1577/1603/1607/1613/1615/1663/1703/1715/1727/1747/1753/1783/1795/1817/1867/1873/1883/1895/1907/1993/2005/2023/2033/2075/2093/2105/2135/2137/2147/2245/2275/2287/2303/2345/2377/2383/2387/2405/2417/2453/2537/2545/2585/2615/2627/2653/2665/2677/2683/2693/2705/2713/2725/2735/2747/2783/2795/2797/2903/2933/2963/3005/3017/3043/3055/3073/3115/3175/3197/3215/3223/3265/3307/3313/3325/3337/3353/3365/3367/3455/3463/3505/3523/3533/3535/3553/3565/3577/3587/3637/3665/3703/3733/3773/3827/3857/3883/3913/3917/3923/3925/3937/3995/4007/4013/4085/4105/4133/4223/4225/4235/4237/4247/4265/4267/4277/4333/4343/4403/4415/4457/4487/4513/4555/4597/4643/4645/4657/4685/4697/4727/4793/4795/4807/4883/4925/4937/4963/4993/5005/5015/5017/5045/5093/5107/5113/5173/5203/5267/5303/5387/5393/5413/5425/5437/5443/5477/5513/5525/5563/5575/5645/5647/5653/5663/5695/5743/5785/5807/5833/5845/5855/5863/5873/5875/5933/6073/6085/6095/6107/6127/6137/6157/6205/6223/6263/6293/6305/6317/6323/6367/6373/6475/6557/6575/6613/6667/6685/6695/6697/6785/6787/6797/6835/6863/6877/6905/6953/6955/6965/6977/7007/7033/7063/7115/7213/7303/7315/7327/7483/7493/7523/7535/7543/7553/7555/7567/7583/7597/7675/7693/7697/7747/7823/7835/7847/7873/7913/7943/7957/8075/8087/8095/8117/8173/8185/8215/8225/8227/8237/8323/8383/8425/8437/8507/8533/8603/8635/8675/8683/8687/8713/8725/8747/8813/8825/8843/8855/8935/8957/9005/9007/9035/9097/9167/9193/9215/9233/9287/9317/9343/9397/9425/9427/9467/9473/9485/9527/9545/9607/9625/9637/9655/9683/9727/9775/9797/9823/9845/9865/9877/9935/10073/10085/10097/10105/10145/10157/10175/10187/10217/10253/10265/10295/10307/10327/10337/10363/10493/10507/10595/10607/10633/10645/10657/10717/10853/10897/10943/11053/11063/11065/11077/11125/11155/11165/11167/11245/11267/11293/11305/11323/11405/11417/11477/11497/11627/11683/11695/11725/11737/11783/11795/11807/11827/11833/11903/11933/11947/11965/11975/12043/12103/12107/12113/12155/12233/12245/12247/12257/12275/12283/12295/12385/12407/12415/12427/12485/12497/12533/12547/12583/12595/12607/12647/12653/12665/12815/12835/12847/12905/12913/12917/12947/12973/13043/13115/13153/13157/13165/13177/13223/13235/13303/13333/13405/13457/13463/13493/13675/13685/13687/13703/13715/13717/13757/13835/13907/13927/14003/14005/14077/14287/14395/14413/14417/14425/14443/14455/14543/14555/14557/14627/14633/14663/14747/14753/14765/14773/14777/14837/14873/14885/14945/14963/15067/15143/15155/15167/15193/15265/15283/15293/15313/15325/15355/15367/15407/15433/15445/15467/15575/15613/15635/15655/15673/15677/15733/15743/15755/15767/15797/15803/15883/15895/15907/15913/15965/16063/16067/16097/16133/16223/16355/16375/16427/16487/16567/16613/16625/16655/16667/16697/16735/16753/16817/16837/16877/16895/16937/16987/17027/17035/17047/17197/17327/17383/17395/17425/17437/17477/17483/17503/17545/17575/17603/17663/17675/17743/17755/17833/17845/17857/17897/17915/17917/17965/17983/18053/18055/18083/18125/18127/18137/18175/18205/18217/18223/18263/18295/18307/18335/18347/18373/18407/18433/18445/18487/18547/18685/18707/18725/18737/18905/18953/19007/19075/19213/19225/19243/19295/19385/19397/19423/19427/19435/19463/19477/19483/19495/19537/19547/19565/19577/19603/19693/19703/19733/19745/19757/19807/19847/19943/19955/19967/19985/20017/20057/20095/20107/20123/20155/20167/20225/20255/20347/20353/20363/20405/20437/20515/20527/20557/20605/20633/20687/20713/20725/20737/20753/20765/20893/20953/21007/21017/21025/21095/21163/21185/21385/21413/21487/21493/21497/21523/21563/21583/21593/21595/21605/21607/21655/21667/21707/21733/21745/21793/21845/21857/21865/21887/21997/22033/22045/22057/22073/22085/22117/22153/22165/22253/22265/22277/22285/22297/22375/22403/22447/22475/22537/22645/22685/22703/22715/22733/22745/22865/22967/23023/23033/23035/23047/23065/23093/23137/23195/23203/23285/23327/23333/23363/23453/23503/23543/23555/23587/23683/23747/23767/23795/23807/23825/23863/23893/23905/23923/23987/24013/24055/24077/24097/24103/24115/24127/24175/24245/24323/24365/24385/24413/24475/24617/24665/24677/24703/24787/24815/24853/24883/24913/24973/24983/25177/25315/25417/25463/25583/25595/25615/25627/25673/25753/25765/25925/25937/25945/25975/26023/26035/26047/26105/26113/26147/26177/26183/26243/26255/26257/26303/26315/26393/26443/26495/26507/26567/26675/26687/26693/26705/26707/26717/26723/26807/26827/26855/26885/26887/26897/26953/26987/27037/27067/27097/27185/27247/27265/27277/27403/27443/27533/27535/27545/27695/27743/27745/27757/27773/27785/27797/27947/28025/28063/28075/28093/28103/28105/28117/28157/28283/28303/28313/28543/28553/28565/28585/28597/28613/28625/28637/28655/28663/28717/28765/28865/28873/28915/28927/28955/29015/29027/29173/29185/29215/29237/29333/29393/29395/29405/29417/29575/29593/29605/29635/29677/29747/29857/29873/29953/30053/30065/30097/30103/30175/30217/30247/30265/30313/30397/30503/30523/30637/30643/30655/30683/30823/30835/30845/30847/30865/30875/30887/30943/30977
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 楼主| 发表于 2020-8-14 20:27 | 显示全部楼层
两两奇数孪中相加的结果一样,仍然没有19246:
19168/19170/19172/19174/19176/19178/19180/19182/19184/19186/19188/19190/19192/19194/19196/19198/19200/19202/19204/19206/
19208/19210/19212/19214/19216/19218/19220/19222/19224/19226/19228/19230/19232/19234/19236/19238/19240/19242/19244/19248/
19250/19252/19254/19256/19258/19260/19262/19264/19266/19268/19270/19272/19274/19276/19278/19280/19282/19284/19286/19288/

下面是末尾几行,仍然是一样的,没有显示完:
23250/23252/23254/23256/23258/23260/23262/23264/23266/23268/23270/23272/23274/23276/23278/23280/23282/23284/23286/23288/
23290/23292/23294/23296/23298/23300/23302/23304/23306/23308/23310/23312/23314/23316/23318/23320/23322/23324/23326/23328/
23330/23332/23334/23336/23338/23340/23342/23344/23346/23348/23350/23352/23354/23356/23358/23360/23362/23364/2336 (后面的照样没有显示,二者结果是一样的)
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 楼主| 发表于 2020-8-14 20:29 | 显示全部楼层
就是说奇数孪中p+6两两相加可以全覆盖大于等于19248的偶数。
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发表于 2020-8-14 20:47 | 显示全部楼层
本帖最后由 蔡家雄 于 2020-8-14 22:39 编辑

查了资料,在10^10内,

差 6 素数对数量 是 差2素数对数量的 1点8 倍,

差30素数对数量 是 差2素数对数量的 2点6 倍,

难道,孪中偶数( p+15 )两两相加的生命偶数不会很大?

若2X 无解,则显示小于2X的孪中数两两相加就可以了。
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 楼主| 发表于 2020-8-14 21:19 | 显示全部楼层
“难道,孪中偶数p+15 两两相加的生命偶数不会很大?”

嗯,可能不会很大,休息吧!明天验证一下。
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 楼主| 发表于 2020-8-15 12:08 | 显示全部楼层
本帖最后由 ysr 于 2020-8-15 04:11 编辑

验证能产生连续素数项的多项式的结果及程序:
以5与401之间的素数开头最多有40个连续素数:
/5/7/11/17
13
/17/19/23/29/37/47/59/73/89/107/127/149/173/199/227/257
29
37
/41/43/47/53/61/71/83/97/113/131/151/173/197/223/251/281/313/347/383/421
/461/503/547/593/641/691/743/797/853/911/971/1033/1097/1163/1231/1301/1373/1447/1523/1601

53
61
73
89
97
/101/103/107/113
109
113
137
149
157
173
181
193
197
229
233
241
257
269
277
281
293
313
317
337
349
353
373
389
397
401

程序代码如下:
Private Sub Command1_Click()
Dim a, b
a = Val(Text1) * 4 + 1
a1 = a
Q = Val(Text2) * 4 + 1
m = Sqr(Q)
If Right(a, 1) Mod 2 = 0 Then
a = a + 1
Else
a = a
End If

Do While InStr(fenjieyinzi0(Val(a)), "*") <> 0
a = a + 4
Loop

Do While a <= Q
b = a + s2
d = fenjieyinzi0(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 = a + s2
d = fenjieyinzi0(Val(b))
Loop
If s > 2 Then
Text3 = Text3 & s3 & vbCrLf
ElseIf InStr(fenjieyinzi0(Val(a)), "*") = 0 Then
Text3 = Text3 & a & vbCrLf
End If
s5 = s5 & "/" & s
Print s5
a = a + 4
s2 = 0
Loop
s6 = Mid(s5, 2)
     s7 = max(Trim(s6))
Combo1 = a1 & "与" & Q & "之间素数开头最多有" & s7 & "个连续素数:" & vbCrLf & Text3

     
Text4 = s5
End Sub

Private Sub Command2_Click()
Text1 = ""
Text2 = ""
Text3 = ""
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
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 楼主| 发表于 2020-8-15 12:14 | 显示全部楼层
本帖最后由 ysr 于 2020-8-15 04:15 编辑

401与4001之间的素数开头最多有7个连续素数:
401
409
421
433
449
457
/461/463/467
509
521
541
557
569
577
593
601
613
617
/641/643/647/653/661
653
661
673
677
701
709
733
757
761
769
773
797
809
/821/823/827
829
853
/857/859/863
877
/881/883/887
929
937
941
953
977
997
1009
1013
1021
1033
1049
1061
1069
1093
1097
1109
1117
1129
1153
1181
1193
1201
1213
1217
1229
1237
1249
/1277/1279/1283/1289/1297/1307/1319
1289
1297
/1301/1303/1307
1321
1361
1373
1381
1409
1429
1433
1453
/1481/1483/1487/1493
1489
1493
1549
1553
1597
1601
1609
1613
1621
1637
1657
1669
1693
1697
1709
1721
1733
1741
1753
1777
1789
1801
1861
1873
1877
1889
1901
1913
1933
1949
1973
1993
/1997/1999/2003
2017
2029
2053
2069
/2081/2083/2087
2089
2113
2129
2137
2141
2153
2161
2213
2221
/2237/2239/2243
2269
2273
2281
2293
2297
2309
2333
2341
2357
2377
2381
2389
2393
2417
2437
2441
2473
2477
2521
2549
2557
2593
2609
2617
2621
2633
/2657/2659/2663
2677
2689
2693
2713
2729
2741
2749
2753
2777
2789
2797
2801
2833
2837
2857
2861
2897
2909
2917
2953
2957
2969
3001
3037
3041
3049
3061
3089
3109
3121
3137
3169
3181
3209
3217
3221
3229
3253
3257
3301
3313
3329
3361
3373
3389
3413
3433
3449
3457
/3461/3463/3467
3469
3517
3529
3533
3541
3557
3581
3593
3613
3617
3637
3673
3677
3697
3701
3709
3733
3761
3769
3793
3797
3821
3833
3853
3877
3881
3889
/3917/3919/3923/3929
3929
3989
/4001/4003/4007/4013/4021
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 楼主| 发表于 2020-8-15 12:20 | 显示全部楼层
4001与40001之间的素数开头最多有8个连续素数:
/4001/4003/4007/4013/4021
4013
4021
4049
4057
4073
4093
4129
4133
4153
4157
4177
4201
4217
4229
4241
4253
4261
4273
4289
4297
4337
4349
4357
4373
4397
4409
4421
4441
4457
4481
4493
4513
/4517/4519/4523
4549
4561
4597
4621
/4637/4639/4643/4649/4657
4649
4657
4673
4721
4729
4733
4789
4793
4801
4813
4817
4861
4877
4889
4909
4933
4937
4957
4969
4973
4993
5009
5021
5077
5081
5101
5113
5153
5189
5197
5209
5233
5237
5261
5273
5281
5297
5309
5333
5381
5393
5413
5417
5437
5441
5449
/5477/5479/5483
/5501/5503/5507
5521
5557
5569
5573
5581
5641
5653
5657
5669
5689
5693
5701
5717
5737
5741
5749
5801
5813
5821
5849
5857
5861
5869
5881
5897
5953
5981
6029
6037
6053
6073
6089
6101
6113
6121
6133
6173
/6197/6199/6203
6217
6221
6229
6257
6269
6277
6301
6317
6329
6337
6353
6361
6373
6389
6397
6421
6449
6469
6473
6481
6521
6529
6553
6569
6577
6581
6637
6653
6661
6673
6689
6701
6709
6733
6737
6761
6781
6793
6829
6833
6841
6857
6869
6917
6949
6961
6977
6997
7001
7013
7057
7069
7109
7121
7129
7177
7193
7213
7229
7237
7253
7297
7309
7321
7333
7349
7369
7393
7417
7433
7457
7477
7481
7489
7517
7529
7537
7541
7549
7561
7573
7577
7589
7621
7649
7669
7673
7681
7717
7741
7753
7757
7789
7793
7817
7829
7841
7853
7873
/7877/7879/7883
7901
7933
7937
7949
7993
8009
8017
8053
8069
8081
8089
8093
8101
8117
8161
8209
8221
8233
8237
8269
8273
8293
8297
8317
8329
8353
8369
8377
8389
8429
8461
8501
8513
8521
/8537/8539/8543
8573
8581
8597
8609
8629
8641
8669
8677
8681
8689
8693
8713
8737
8741
8753
8761
8821
8837
8849
/8861/8863/8867
8893
8929
8933
8941
8969
9001
9013
9029
9041
9049
9109
9133
9137
9157
9161
9173
9181
9209
9221
9241
9257
9277
9281
9293
9337
9341
9349
9377
9397
9413
9421
9433
9437
/9461/9463/9467/9473
9473
9497
9521
9533
9601
9613
9629
9649
9661
9677
9689
9697
9721
9733
9749
9769
9781
9817
9829
9833
9857
9901
9929
9941
9949
9973
10009
10037
10061
10069
10093
10133
10141
10169
10177
10181
10193
10253
10273
10289
10301
10313
10321
10333
10337
10357
10369
10429
10433
10453
/10457/10459/10463
10477
10501
10513
10529
10589
10597
10601
10613
10657
10709
10729
10733
10753
10781
10789
10837
10853
10861
10889
10909
10937
10949
10957
10973
10993
11057
11069
11093
11113
11117
11149
11161
11173
11177
11197
11213
11257
11261
11273
11317
11321
11329
11353
11369
11393
11437
11489
11497
11549
11593
11597
11617
11621
11633
11657
11677
11681
11689
11701
11717
/11777/11779/11783/11789
11789
11801
11813
11821
11833
11897
11909
11933
11941
11953
11969
11981
12037
12041
12049
12073
12097
12101
12109
12113
12149
12157
12161
12197
12241
12253
12269
12277
12281
12289
12301
12329
12373
12377
12401
12409
12413
12421
12433
12437
12457
12473
12497
12517
12541
12553
12569
12577
12589
12601
12613
12637
12641
12653
12689
12697
12713
12721
12757
12781
12809
12821
12829
12841
12853
12889
12893
/12917/12919/12923
12941
12953
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 楼主| 发表于 2020-8-15 12:41 | 显示全部楼层
下面验证蔡兄的差为30的素数对的问题,输出孪中p+15.
先验证1~3000内的情况:(有220对)
1与3000之间有220对孪生(p,p+14)素数对:
/22/26/28/32/38/44/46/52/56/58/68/74/82/86/88/94/98/112/116/122/124/142/152/164/166/178/182/196/208/212/214/226/242/248/254/256/266/278/292/296/298/322/332/352/364/368/374/382/394/404/416/424/434/446/448/464/472/476/494/506/556/562/572/578/584/586/592/602/616/628/632/646/658/662/668/676/724/742/754/758/772/812/824/838/842/844/868/872/892/896/922/926/952/956/962/968/982/998/1006/1024/1034/1036/1046/1048/1054/1076/1078/1102/1108/1138/1166/1178/1186/1202/1208/1216/1244/1264/1274/1292/1304/1306/1312/1414/1424/1438/1444/1466/1468/1474/1496/1508/1538/1564/1568/1582/1586/1594/1598/1612/1622/1642/1652/1678/1682/1684/1708/1738/1762/1768/1774/1816/1846/1862/1886/1892/1916/1964/1988/2002/2012/2014/2054/2068/2084/2096/2098/2114/2126/2128/2146/2222/2228/2236/2252/2254/2258/2266/2282/2296/2324/2326/2356/2362/2366/2396/2408/2426/2432/2452/2462/2488/2536/2564/2594/2606/2632/2648/2662/2672/2674/2678/2692/2698/2704/2714/2726/2734/2782/2804/2818/2872/2894/2902/2912/2924/2942/2954/2984/2986。
下面是孪中p+15两辆相加的结果,分段发,篇幅超长了。
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 楼主| 发表于 2020-8-15 12:42 | 显示全部楼层
排序结果:
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