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求数列的通项公式

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 楼主| 发表于 2020-9-1 20:53 | 显示全部楼层
下面是连续输出差为210的素数数列的程序结果:
/199/409/619/829/1039/1249/1459/1669/1879/2089
1与1000之间的素数开头最多有10个连续素数:
3
5
7
11
/13/223/433/643/853/1063
17
/19/229/439
/23/233/443/653/863
/29/239/449/659
31
37
/41/251/461
43
/47/257/467/677/887/1097/1307
53
/59/269/479
61
/67/277/487
/71/281/491/701/911
73
79
/83/293/503
89
97
/101/311/521
/103/313/523/733
107
109
113
/127/337/547/757/967
131
/137/347/557
139
/149/359/569
151
/157/367/577/787/997
163
167
/173/383/593
/179/389/599/809/1019/1229/1439
181
191
193
197
/199/409/619/829/1039/1249/1459/1669/1879/2089
/211/421/631
/223/433/643/853/1063
227
229
/233/443/653/863
/239/449/659
241
251
/257/467/677/887/1097/1307
263
269
271
277
/281/491/701/911
283
293
307
311
/313/523/733
317
/331/541/751
/337/547/757/967
347
349
/353/563/773/983/1193
359
/367/577/787/997
373
379
383
/389/599/809/1019/1229/1439
397
401
/409/619/829/1039/1249/1459/1669/1879/2089
419
421
431
/433/643/853/1063
439
/443/653/863
449
457
461
/463/673/883/1093/1303
/467/677/887/1097/1307
479
487
/491/701/911
/499/709/919/1129
503
/509/719/929
521
523
541
/547/757/967
557
/563/773/983/1193
569
571
/577/787/997
587
593
/599/809/1019/1229/1439
/601/811/1021/1231
607
/613/823/1033
617
/619/829/1039/1249/1459/1669/1879/2089
631
641
/643/853/1063
647
653
659
661
/673/883/1093/1303
/677/887/1097/1307
683
691
701
/709/919/1129
719
727
733
739
/743/953/1163/1373/1583
751
757
/761/971/1181
769
/773/983/1193
787
797
/809/1019/1229/1439
/811/1021/1231
821
823
827
/829/1039/1249/1459/1669/1879/2089
/839/1049/1259
853
857
/859/1069/1279/1489/1699
863
/877/1087/1297
/881/1091/1301/1511/1721/1931/2141/2351
/883/1093/1303
/887/1097/1307
/907/1117/1327
911
919
929
937
/941/1151/1361/1571
947
/953/1163/1373/1583
967
971
977
983
991
997
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 楼主| 发表于 2020-9-1 20:55 | 显示全部楼层
代码如下:(只发主程序)
Private Sub Command1_Click()
Dim a, b
a = Val(Text1)
a1 = a
Q = Val(Text2)
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 + 2
Loop

Do While a <= Q
b = a
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 = b + 210
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
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" & 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 2020-9-3 17:21 | 显示全部楼层
3000与4000之间的素数开头差为223092870最多有8个连续素数:
3001
3011
3019
3023
/3037/223095907/446188777/669281647
3041
/3049/223095919/446188789/669281659/892374529/1115467399/1338560269/1561653139
/3061/223095931/446188801/669281671
/3067/223095937/446188807/669281677
3079
3083
3089
3109
3119
3121
3137
3163
3167
3169
3181
3187
3191
/3203/223096073/446188943
3209
3217
/3221/223096091/446188961
3229
3251
3253
3257
3259
3271
3299
3301
3307
3313
/3319/223096189/446189059/669281929
3323
3329
3331
3343
3347
3359
3361
3371
3373
3389
3391
3407
3413
3433
3449
3457
3461
3463
3467
3469
3491
/3499/223096369/446189239
3511
3517
3527
3529
3533
/3539/223096409/446189279
3541
3547
3557
3559
3571
3581
3583
3593
3607
/3613/223096483/446189353
/3617/223096487/446189357
3623
3631
3637
3643
3659
3671
3673
3677
3691
3697
3701
3709
3719
3727
/3733/223096603/446189473
3739
3761
3767
3769
3779
3793
3797
3803
3821
3823
3833
3847
/3851/223096721/446189591
3853
3863
/3877/223096747/446189617
3881
3889
3907
3911
3917
3919
3923
3929
3931
3943
3947
3967
3989
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 楼主| 发表于 2020-9-3 17:28 | 显示全部楼层
5000与10000之间的素数开头差为9699690最多有8个连续素数:
5003
5009
5011
5021
5023
5039
5051
5059
5077
5081
5087
5099
5101
5107
5113
/5119/9704809/19404499
5147
5153
5167
/5171/9704861/19404551/29104241
5179
5189
/5197/9704887/19404577
/5209/9704899/19404589/29104279
5227
5231
5233
5237
5261
5273
5279
5281
5297
5303
5309
/5323/9705013/19404703
5333
/5347/9705037/19404727
5351
5381
5387
5393
/5399/9705089/19404779
5407
5413
5417
5419
5431
5437
5441
5443
5449
5471
5477
5479
5483
5501
/5503/9705193/19404883/29104573
5507
5519
5521
5527
5531
5557
5563
/5569/9705259/19404949
5573
/5581/9705271/19404961/29104651/38804341/48504031
5591
5623
/5639/9705329/19405019
5641
5647
5651
5653
5657
5659
5669
5683
5689
5693
5701
5711
5717
5737
/5741/9705431/19405121
5743
5749
5779
5783
/5791/9705481/19405171
5801
5807
/5813/9705503/19405193
5821
5827
5839
5843
5849
5851
5857
5861
5867
5869
5879
5881
5897
5903
5923
5927
5939
5953
/5981/9705671/19405361
5987
6007
6011
6029
/6037/9705727/19405417
6043
6047
6053
6067
6073
6079
6089
6091
6101
6113
6121
6131
6133
6143
6151
6163
6173
6197
6199
6203
6211
6217
/6221/9705911/19405601
6229
6247
6257
6263
6269
6271
6277
6287
6299
/6301/9705991/19405681
6311
6317
6323
6329
6337
6343
/6353/9706043/19405733/29105423
6359
6361
6367
/6373/9706063/19405753
6379
6389
6397
6421
6427
6449
6451
/6469/9706159/19405849
6473
/6481/9706171/19405861
6491
6521
6529
6547
/6551/9706241/19405931
6553
6563
6569
6571
6577
6581
/6599/9706289/19405979
/6607/9706297/19405987/29105677/38805367/48505057
/6619/9706309/19405999/29105689/38805379
6637
6653
6659
6661
/6673/9706363/19406053/29105743/38805433
6679
6689
6691
6701
6703
6709
/6719/9706409/19406099/29105789
6733
/6737/9706427/19406117
6761
6763
6779
6781
6791
6793
6803
/6823/9706513/19406203
6827
6829
/6833/9706523/19406213
6841
6857
6863
6869
6871
6883
6899
6907
6911
6917
6947
6949
6959
6961
6967
/6971/9706661/19406351/29106041
6977
6983
/6991/9706681/19406371
/6997/9706687/19406377
7001
7013
7019
7027
7039
7043
7057
7069
7079
7103
7109
7121
7127
7129
7151
7159
/7177/9706867/19406557
7187
7193
7207
7211
7213
7219
7229
7237
7243
7247
7253
7283
7297
7307
7309
7321
7331
7333
7349
/7351/9707041/19406731
7369
7393
7411
7417
7433
7451
7457
/7459/9707149/19406839
7477
7481
/7487/9707177/19406867/29106557
/7489/9707179/19406869/29106559/38806249
7499
7507
7517
7523
7529
7537
7541
7547
7549
7559
/7561/9707251/19406941/29106631
7573
7577
7583
7589
7591
7603
/7607/9707297/19406987
7621
7639
7643
7649
7669
7673
7681
7687
/7691/9707381/19407071
7699
/7703/9707393/19407083/29106773/38806463/48506153/58205843/67905533
/7717/9707407/19407097
7723
7727
7741
7753
7757
7759
7789
7793
7817
7823
7829
/7841/9707531/19407221
7853
7867
7873
7877
7879
7883
7901
7907
7919
7927
7933
/7937/9707627/19407317
7949
7951
7963
7993
/8009/9707699/19407389
8011
8017
8039
8053
8059
8069
8081
8087
8089
8093
8101
8111
/8117/9707807/19407497
/8123/9707813/19407503/29107193/38806883/48506573/58206263
8147
8161
8167
8171
8179
8191
8209
8219
8221
8231
8233
8237
/8243/9707933/19407623
8263
8269
8273
8287
8291
8293
8297
8311
8317
8329
8353
8363
8369
8377
8387
8389
8419
/8423/9708113/19407803
8429
/8431/9708121/19407811
8443
8447
8461
8467
/8501/9708191/19407881
8513
8521
8527
8537
/8539/9708229/19407919
8543
8563
8573
8581
/8597/9708287/19407977
8599
8609
/8623/9708313/19408003
8627
8629
8641
8647
8663
8669
8677
8681
8689
8693
8699
8707
8713
8719
/8731/9708421/19408111
8737
8741
8747
8753
8761
8779
8783
8803
8807
8819
8821
8831
8837
/8839/9708529/19408219
8849
/8861/9708551/19408241
8863
8867
8887
8893
8923
8929
8933
8941
8951
8963
8969
8971
8999
9001
9007
9011
9013
9029
/9041/9708731/19408421/29108111
9043
9049
9059
9067
9091
9103
9109
9127
9133
9137
9151
9157
9161
9173
9181
9187
9199
9203
9209
9221
9227
9239
9241
9257
9277
/9281/9708971/19408661
/9283/9708973/19408663
9293
9311
9319
9323
/9337/9709027/19408717
9341
9343
9349
9371
9377
/9391/9709081/19408771
9397
9403
9413
9419
9421
9431
9433
9437
9439
9461
9463
9467
9473
9479
/9491/9709181/19408871/29108561
9497
9511
9521
9533
9539
9547
9551
9587
/9601/9709291/19408981
9613
9619
/9623/9709313/19409003/29108693
9629
9631
9643
9649
9661
9677
/9679/9709369/19409059/29108749
9689
9697
9719
/9721/9709411/19409101
9733
9739
9743
9749
9767
9769
9781
9787
9791
9803
9811
9817
9829
9833
9839
9851
9857
9859
9871
9883
9887
9901
/9907/9709597/19409287/29108977
9923
9929
9931
/9941/9709631/19409321
/9949/9709639/19409329/29109019/38808709/48508399/58208089
9967
9973
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 楼主| 发表于 2020-9-3 17:29 | 显示全部楼层
15000与20000之间的素数开头差为9699690最多有7个连续素数:
/15013/9714703/19414393
15017
15031
/15053/9714743/19414433/29114123
15061
15073
15077
15083
15091
15101
15107
15121
15131
15137
15139
15149
15161
15173
15187
15193
15199
15217
15227
15233
15241
15259
15263
15269
/15271/9714961/19414651
15277
15287
15289
15299
15307
15313
15319
15329
15331
15349
/15359/9715049/19414739
15361
15373
15377
15383
15391
15401
15413
15427
15439
15443
15451
15461
15467
15473
15493
15497
15511
15527
15541
/15551/9715241/19414931/29114621
15559
15569
15581
15583
15601
15607
/15619/9715309/19414999
15629
15641
15643
15647
/15649/9715339/19415029
15661
15667
15671
15679
15683
15727
15731
15733
15737
15739
15749
15761
15767
15773
15787
15791
/15797/9715487/19415177
15803
15809
15817
15823
15859
15877
15881
15887
15889
15901
15907
15913
15919
15923
15937
15959
15971
15973
15991
16001
16007
16033
16057
16061
16063
16067
16069
/16073/9715763/19415453
16087
16091
16097
16103
16111
16127
16139
/16141/9715831/19415521
/16183/9715873/19415563
16187
16189
/16193/9715883/19415573
16217
16223
16229
16231
16249
16253
16267
16273
16301
16319
16333
16339
16349
16361
16363
16369
16381
16411
16417
/16421/9716111/19415801
/16427/9716117/19415807
16433
16447
16451
16453
/16477/9716167/19415857/29115547
16481
16487
16493
16519
16529
16547
16553
16561
16567
16573
/16603/9716293/19415983/29115673/38815363/48515053/58214743
16607
16619
/16631/9716321/19416011
16633
16649
16651
16657
16661
16673
16691
16693
16699
16703
16729
16741
16747
16759
16763
16787
/16811/9716501/19416191/29115881/38815571
16823
16829
16831
16843
16871
/16879/9716569/19416259
16883
/16889/9716579/19416269/29115959/38815649/48515339/58215029
16901
16903
16921
/16927/9716617/19416307
16931
/16937/9716627/19416317
16943
16963
16979
16981
16987
16993
17011
17021
/17027/9716717/19416407/29116097/38815787/48515477
17029
17033
/17041/9716731/19416421
17047
17053
17077
17093
/17099/9716789/19416479
17107
17117
17123
17137
17159
17167
17183
17189
17191
17203
17207
17209
17231
/17239/9716929/19416619/29116309
17257
17291
17293
17299
17317
17321
17327
17333
17341
17351
17359
17377
17383
17387
17389
17393
17401
/17417/9717107/19416797/29116487/38816177/48515867
17419
17431
17443
17449
17467
17471
17477
17483
17489
17491
17497
17509
17519
17539
17551
/17569/9717259/19416949
/17573/9717263/19416953
17579
17581
17597
17599
/17609/9717299/19416989
/17623/9717313/19417003/29116693
17627
17657
17659
17669
17681
17683
17707
17713
17729
17737
17747
17749
17761
17783
17789
/17791/9717481/19417171/29116861/38816551
17807
/17827/9717517/19417207
17837
17839
17851
17863
17881
17891
/17903/9717593/19417283
17909
17911
17921
17923
17929
17939
17957
/17959/9717649/19417339
17971
17977
17981
17987
17989
18013
18041
18043
18047
18049
18059
18061
18077
18089
18097
18119
18121
18127
18131
18133
18143
/18149/9717839/19417529/29117219/38816909
18169
18181
18191
18199
18211
18217
18223
/18229/9717919/19417609
/18233/9717923/19417613
18251
18253
18257
/18269/9717959/19417649
18287
18289
18301
18307
18311
18313
18329
18341
18353
/18367/9718057/19417747
18371
18379
18397
18401
18413
18427
18433
18439
18443
18451
/18457/9718147/19417837/29117527/38817217/48516907
18461
18481
18493
18503
18517
/18521/9718211/19417901/29117591
18523
18539
18541
18553
18583
18587
18593
18617
/18637/9718327/19418017/29117707
18661
18671
18679
/18691/9718381/19418071/29117761
18701
18713
18719
18731
18743
18749
18757
18773
18787
18793
18797
18803
18839
18859
18869
18899
18911
18913
18917
18919
18947
18959
18973
/18979/9718669/19418359
19001
19009
19013
19031
19037
19051
19069
19073
19079
19081
19087
19121
/19139/9718829/19418519/29118209
19141
19157
19163
19181
19183
19207
19211
19213
19219
19231
19237
/19249/9718939/19418629
19259
19267
19273
19289
19301
/19309/9718999/19418689
19319
19333
19373
19379
/19381/9719071/19418761
19387
19391
19403
/19417/9719107/19418797
19421
19423
19427
19429
19433
19441
/19447/9719137/19418827
19457
19463
19469
19471
/19477/9719167/19418857/29118547
19483
19489
19501
19507
19531
/19541/9719231/19418921
19543
19553
/19559/9719249/19418939
19571
/19577/9719267/19418957/29118647
19583
19597
19603
19609
19661
19681
19687
19697
19699
19709
/19717/9719407/19419097/29118787
19727
/19739/9719429/19419119
19751
19753
19759
/19763/9719453/19419143
19777
19793
19801
19813
19819
/19841/9719531/19419221/29118911/38818601
19843
19853
19861
19867
19889
/19891/9719581/19419271/29118961
/19913/9719603/19419293/29118983/38818673
19919
19927
19937
19949
19961
19963
19973
19979
19991
19993
19997
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 楼主| 发表于 2020-9-3 17:31 | 显示全部楼层
本帖最后由 ysr 于 2020-9-3 09:33 编辑

35000与40000之间的素数开头差为9699690最多有10个连续素数:
35023
35027
35051
35053
35059
35069
35081
35083
35089
35099
/35107/9734797/19434487
35111
35117
35129
35141
35149
35153
35159
35171
35201
35221
35227
35251
35257
35267
35279
35281
35291
35311
35317
35323
35327
/35339/9735029/19434719
/35353/9735043/19434733/29134423/38834113
35363
35381
35393
35401
35407
35419
35423
35437
/35447/9735137/19434827
35449
35461
35491
/35507/9735197/19434887
35509
35521
35527
35531
/35533/9735223/19434913/29134603
35537
35543
35569
35573
35591
/35593/9735283/19434973
35597
35603
35617
/35671/9735361/19435051/29134741
35677
35729
35731
35747
35753
35759
35771
35797
35801
35803
35809
35831
35837
35839
35851
35863
35869
35879
35897
/35899/9735589/19435279
35911
35923
35933
35951
35963
/35969/9735659/19435349/29135039/38834729/48534419/58234109/67933799/77633489/87333179
35977
35983
35993
35999
36007
36011
36013
36017
36037
36061
36067
/36073/9735763/19435453
36083
36097
36107
36109
36131
36137
36151
36161
36187
36191
/36209/9735899/19435589
36217
36229
36241
36251
36263
36269
36277
36293
36299
36307
36313
36319
36341
/36343/9736033/19435723
36353
36373
36383
36389
/36433/9736123/19435813
36451
36457
36467
36469
36473
/36479/9736169/19435859
36493
/36497/9736187/19435877
36523
36527
36529
36541
36551
36559
36563
/36571/9736261/19435951
36583
36587
/36599/9736289/19435979
36607
36629
/36637/9736327/19436017
36643
/36653/9736343/19436033
36671
36677
36683
36691
36697
36709
36713
36721
36739
36749
/36761/9736451/19436141/29135831
/36767/9736457/19436147/29135837
36779
36781
36787
36791
36793
/36809/9736499/19436189
36821
36833
36847
36857
/36871/9736561/19436251/29135941
36877
36887
/36899/9736589/19436279/29135969
36901
36913
/36919/9736609/19436299
36923
36929
36931
36943
36947
36973
36979
36997
37003
37013
37019
37021
37039
37049
/37057/9736747/19436437
37061
37087
37097
/37117/9736807/19436497
37123
37139
37159
37171
37181
37189
37199
37201
37217
37223
37243
37253
37273
37277
37307
37309
37313
37321
37337
/37339/9737029/19436719/29136409
/37357/9737047/19436737
37361
37363
37369
37379
37397
37409
37423
37441
/37447/9737137/19436827
37463
37483
37489
37493
37501
/37507/9737197/19436887
37511
37517
37529
37537
37547
/37549/9737239/19436929
37561
37567
37571
37573
37579
37589
/37591/9737281/19436971/29136661
37607
37619
37633
37643
/37649/9737339/19437029/29136719
37657
37663
37691
37693
/37699/9737389/19437079
/37717/9737407/19437097/29136787
37747
37781
37783
37799
/37811/9737501/19437191/29136881
37813
37831
37847
37853
37861
/37871/9737561/19437251
/37879/9737569/19437259
37889
37897
37907
37951
37957
37963
37967
37987
37991
37993
37997
/38011/9737701/19437391
38039
38047
38053
38069
38083
38113
38119
38149
38153
38167
38177
38183
38189
/38197/9737887/19437577
38201
38219
/38231/9737921/19437611/29137301/38836991/48536681
38237
38239
38261
38273
/38281/9737971/19437661/29137351
38287
/38299/9737989/19437679/29137369/38837059
38303
38317
38321
/38327/9738017/19437707
38329
38333
38351
38371
38377
38393
38431
38447
38449
38453
38459
38461
/38501/9738191/19437881
38543
38557
38561
38567
38569
38593
38603
38609
38611
38629
38639
38651
38653
38669
38671
38677
38693
38699
/38707/9738397/19438087/29137777
38711
38713
38723
38729
/38737/9738427/19438117
38747
38749
38767
38783
38791
/38803/9738493/19438183/29137873/38837563/48537253
38821
38833
/38839/9738529/19438219
38851
38861
38867
38873
38891
38903
38917
38921
38923
38933
38953
38959
38971
38977
38993
39019
39023
39041
39043
39047
39079
39089
/39097/9738787/19438477
/39103/9738793/19438483/29138173
/39107/9738797/19438487
39113
39119
39133
39139
39157
/39161/9738851/19438541
39163
39181
39191
39199
39209
/39217/9738907/19438597
39227
39229
39233
39239
39241
39251
39293
39301
39313
39317
39323
39341
39343
39359
39367
/39371/9739061/19438751/29138441
/39373/9739063/19438753/29138443
39383
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39409
39419
39439
/39443/9739133/19438823/29138513
39451
39461
39499
39503
39509
39511
39521
39541
39551
39563
39569
39581
39607
/39619/9739309/19438999
39623
39631
39659
39667
39671
39679
39703
39709
39719
39727
39733
39749
39761
39769
39779
39791
39799
39821
39827
39829
39839
39841
39847
39857
39863
39869
39877
39883
39887
39901
39929
39937
39953
39971
39979
39983
39989
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 楼主| 发表于 2020-9-3 18:51 | 显示全部楼层
5000与10000之间的素数开头差为200560490130最多有5个连续素数:
/5323/200560495453/401120985583/601681475713/802241965843
/5477/200560495607/401120985737/601681475867/802241965997
/6043/200560496173/401120986303/601681476433/802241966563
/6143/200560496273/401120986403/601681476533/802241966663

行间差依次为154,566,100
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 楼主| 发表于 2020-9-3 20:00 | 显示全部楼层
30000与40000之间的素数开头差为200560490130最多有7个连续素数:
/34313/200560524443/401121014573/601681504703/802241994833/1002802484963/1203362975093

/31181/200560521311/401121011441
/31183/200560521313/401121011443

后面这两行行间距是2,所以,有3对孪生素数。
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 楼主| 发表于 2020-9-5 20:38 | 显示全部楼层
275087与375087之间的素数开头差为200560490130最多有8个连续素数:

/282851/200560772981/401121263111/601681753241/802242243371/1002802733501/1203363223631/1403923713761
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 楼主| 发表于 2020-9-5 23:01 | 显示全部楼层
对应项差为6(首项是相邻素数对):
/404693/200560894823/401121384953/601681875083
/404699/200560894829/401121384959
对应项差为32(首项是相邻素数对):
/403901/200560894031/401121384161/601681874291
/403933/200560894063/401121384193
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