基础理论中的两个重要定理的证明

ysr · 发表于 2026-4-3 08:50

本帖最后由 ysr 于 2026-4-3 02:34 编辑

在10000内的这样的素数组有1 组：
(1699 5689 9679 13669 17659 21649 25639 29629 33619 )
命题：公差为3990的9生素数组有且只有1组，中间可能还有其他素数。

ysr · 发表于 2026-4-3 08:57

本帖最后由 ysr 于 2026-4-3 02:36 编辑

在100000内的这样的素数组有3 组：
(30427 35257 40087 44917 49747 54577 59407 64237 69067 73897 )
命题：公差为4830的10生素数组有且只有1组，中间可能还有其他素数。

ysr · 发表于 2026-4-3 09:26

本帖最后由 ysr 于 2026-4-3 02:51 编辑

在500000内的这样的素数组有2 组：
(206191 212281 218371 224461 230551 236641 242731 248821 254911 )
(357661 363751 369841 375931 382021 388111 394201 400291 406381 )
命题：公差为6090的9生素数组有且只有2组，中间可能还有其他素数。

2*3*5*7*11*13*17*19*23*29=6469693230

ysr · 发表于 2026-4-3 13:35

127与300之间的素数开头最多有公差为210的10个连续素数:
/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

ysr · 发表于 2026-4-3 13:37

401与800之间的素数开头最多有公差为210的9个连续素数:
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

ysr · 发表于 2026-4-3 13:39

801与2000之间的素数开头最多有公差为210的8个连续素数:
/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
1009
/1013/1223/1433
/1019/1229/1439
1021
1031
1033
/1039/1249/1459/1669/1879/2089
1049
1051
1061
1063
/1069/1279/1489/1699
1087
/1091/1301/1511/1721/1931/2141/2351
1093
1097
1103
1109
1117
1123
1129
/1151/1361/1571
1153
/1163/1373/1583
1171
1181
1187
1193
1201
1213
/1217/1427/1637/1847
1223
1229
1231
/1237/1447/1657/1867
/1249/1459/1669/1879/2089
1259
/1277/1487/1697/1907
/1279/1489/1699
1283
/1289/1499/1709
1291
1297
/1301/1511/1721/1931/2141/2351
1303
1307
1319
/1321/1531/1741/1951/2161/2371
1327
1361
1367
1373
1381
1399
1409
1423
/1427/1637/1847
1429
1433
1439
/1447/1657/1867
1451
/1453/1663/1873/2083/2293/2503/2713
/1459/1669/1879/2089
1471
1481
1483
/1487/1697/1907
1489
1493
1499
/1511/1721/1931/2141/2351
1523
/1531/1741/1951/2161/2371
1543
1549
1553
1559
/1567/1777/1987
1571
/1579/1789/1999
1583
1597
1601
1607
1609
1613
1619
1621
1627
1637
1657
/1663/1873/2083/2293/2503/2713
/1667/1877/2087/2297
/1669/1879/2089
1693
1697
1699
1709
/1721/1931/2141/2351
/1723/1933/2143
1733
/1741/1951/2161/2371
1747
1753
1759
1777
/1783/1993/2203
/1787/1997/2207/2417
1789
/1801/2011/2221
1811
1823
1831
1847
1861
1867
1871
/1873/2083/2293/2503/2713
/1877/2087/2297
1879
/1889/2099/2309
1901
1907
1913
/1931/2141/2351
1933
1949
/1951/2161/2371
1973
1979
1987
1993
/1997/2207/2417
1999

ysr · 发表于 2026-4-3 13:46

30427与30527之间的素数开头最多有公差为4830的10个连续素数:
/30427/35257/40087/44917/49747/54577/59407/64237/69067/73897
30431
30449
30467
30469
30491
/30493/35323/40153/44983
30497
/30509/35339/40169
30517

ysr · 发表于 2026-4-3 13:50

30527与50527之间的素数开头最多有公差为4830的9个连续素数:
30529
30539
30553
30557
30559
/30577/35407/40237
/30593/35423/40253/45083
30631
30637
30643
30649
30661
30671
30677
30689
/30697/35527/40357
30703
30707
30713
30727
30757
/30763/35593/40423
/30773/35603/40433/45263/50093
30781
30803
30809
30817
30829
30839
30841
30851
30853
30859
30869
30871
30881
30893
30911
30931
30937
30941
30949
30971
30977
30983
31013
31019
/31033/35863/40693/45523
/31039/35869/40699
31051
31063
31069
31079
31081
31091
31121
31123
31139
31147
31151
/31153/35983/40813
31159
31177
/31181/36011/40841
31183
31189
31193
31219
31223
31231
/31237/36067/40897
31247
31249
31253
31259
/31267/36097/40927/45757/50587
31271
31277
31307
31319
31321
31327
31333
31337
/31357/36187/41017
/31379/36209/41039/45869
/31387/36217/41047
31391
31393
31397
31469
31477
31481
/31489/36319/41149/45979
31511
31513
31517
31531
31541
/31543/36373/41203
31547
31567
31573
31583
31601
31607
31627
31643
31649
31657
31663
31667
31687
31699
/31721/36551/41381
31723
31727
/31729/36559/41389/46219
31741
31751
31769
31771
31793
31799
31817
/31847/36677/41507/46337
31849
31859
31873
/31883/36713/41543
31891
31907
/31957/36787/41617/46447
31963
31973
31981
/31991/36821/41651
32003
32009
/32027/36857/41687
32029
32051
32057
32059
32063
/32069/36899/41729/46559
32077
32083
32089
/32099/36929/41759/46589/51419/56249
/32117/36947/41777
32119
32141
32143
32159
32173
/32183/37013/41843
/32189/37019/41849/46679
/32191/37021/41851/46681/51511
32203
32213
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32237
32251
32257
32261
32297
32299
32303
/32309/37139/41969
32321
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32353
/32359/37189/42019
32363
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/32413/37243/42073
/32423/37253/42083
32429
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/32479/37309/42139
32491
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/32533/37363/42193
32537
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/32579/37409/42239
32587
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/32633/37463/42293/47123
32647
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/32719/37549/42379
/32749/37579/42409
32771
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32801
/32803/37633/42463/47293
32831
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32869
32887
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/32917/37747/42577/47407/52237
32933
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/32983/37813/42643
32987
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/33023/37853/42683/47513
33029
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/33049/37879/42709
33053
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/33161/37991/42821
33179
/33181/38011/42841
33191
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/33353/38183/43013/47843/52673/57503
/33359/38189/43019
33377
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33413
33427
/33457/38287/43117/47947
33461
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/33547/38377/43207
/33563/38393/43223
33569
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/33601/38431/43261/48091
33613
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/33623/38453/43283
33629
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/33739/38569/43399
33749
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33851
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/33937/38767/43597
33941
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33997
34019
/34031/38861/43691
34033
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/34061/38891/43721
/34123/38953/43783
34127
/34129/38959/43789/48619
/34141/38971/43801
34147
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34211
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/34273/39103/43933
/34283/39113/43943
34297
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/34303/39133/43963
34313
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/34327/39157/43987/48817
34337
34351
/34361/39191/44021
34367
/34369/39199/44029/48859
34381
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/34471/39301/44131
34483
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/34511/39341/44171
34513
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/34543/39373/44203/49033
34549
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/34589/39419/44249
34591
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/34613/39443/44273/49103
34631
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/34721/39551/44381/49211
34729
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34819
/34841/39671/44501/49331
34843
34847
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34871
34877
34883
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34913
/34919/39749/44579/49409
34939
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/34961/39791/44621/49451
34963
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/35027/39857/44687
35051
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35107
35111
35117
35129
35141
/35149/39979/44809/49639/54469
35153
/35159/39989/44819
35171
35201
35221
35227
35251
/35257/40087/44917/49747/54577/59407/64237/69067/73897
35267
35279
35281
35291
35311
35317
/35323/40153/44983
35327
35339
35353
35363
35381
35393
/35401/40231/45061/49891/54721
35407
35419
/35423/40253/45083
35437
35447
35449
35461
35491
35507
35509
/35521/40351/45181
35527
/35531/40361/45191/50021/54851
35533
35537
35543
35569
35573
35591
35593
35597
/35603/40433/45263/50093
35617
35671
/35677/40507/45337
/35729/40559/45389
35731
35747
/35753/40583/45413
35759
35771
35797
35801
35803
35809
35831
35837
35839
35851
/35863/40693/45523
35869
35879
35897
35899
35911
35923
35933
35951
35963
35969
35977
35983
35993
/35999/40829/45659
36007
36011
36013
/36017/40847/45677
/36037/40867/45697/50527
36061
36067
36073
36083
/36097/40927/45757/50587
36107
36109
36131
36137
36151
36161
36187
36191
/36209/41039/45869
36217
36229
36241
36251
36263
36269
36277
36293
36299
36307
36313
/36319/41149/45979
36341
36343
36353
36373
36383
36389
/36433/41263/46093/50923
36451
36457
36467
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36479
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36523
/36527/41357/46187
36529
36541
36551
/36559/41389/46219
36563
36571
36583
36587
36599
36607
36629
36637
36643
36653
36671
/36677/41507/46337
36683
/36691/41521/46351
36697
36709
36713
36721
36739
36749
36761
36767
/36779/41609/46439
/36781/41611/46441
/36787/41617/46447
/36791/41621/46451
36793
36809
36821
36833
36847
36857
36871
36877
36887
/36899/41729/46559
36901
36913
36919
36923
/36929/41759/46589/51419/56249
/36931/41761/46591/51421
36943
36947
36973
/36979/41809/46639
36997
37003
37013
/37019/41849/46679
/37021/41851/46681/51511
37039
37049
37057
37061
37087
/37097/41927/46757
37117
37123
37139
37159
37171
37181
37189
37199
37201
37217
37223
37243
37253
37273
37277
37307
37309
37313
37321
37337
37339
/37357/42187/47017
37361
37363
37369
37379
/37397/42227/47057
37409
37423
37441
37447
/37463/42293/47123
37483
37489
37493
/37501/42331/47161/51991/56821/61651
37507
37511
37517
/37529/42359/47189
37537
37547
37549
/37561/42391/47221/52051
37567
37571
37573
37579
37589
37591
37607
37619
/37633/42463/47293
/37643/42473/47303
37649
/37657/42487/47317/52147
37663
37691
37693
37699
37717
/37747/42577/47407/52237
/37781/42611/47441
37783
37799
37811
37813
37831
/37847/42677/47507
/37853/42683/47513
37861
37871
37879
37889
37897
37907
37951
37957
/37963/42793/47623/52453/57283
37967
37987
37991
37993
37997
38011
38039
38047
38053
38069
38083
38113
38119
/38149/42979/47809/52639
38153
38167
38177
/38183/43013/47843/52673/57503
38189
38197
38201
38219
38231
38237
38239
38261
/38273/43103/47933
38281
/38287/43117/47947
38299
/38303/43133/47963
38317
/38321/43151/47981
38327
38329
38333
38351
38371
38377
38393
/38431/43261/48091
38447
38449
38453
38459
/38461/43291/48121/52951/57781
38501
38543
38557
/38561/43391/48221/53051/57881
38567
38569
38593
38603
38609
/38611/43441/48271/53101
38629
38639
/38651/43481/48311
38653
38669
38671
38677
38693
38699
38707
/38711/43541/48371/53201/58031/62861
38713
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38729
38737
/38747/43577/48407
/38749/43579/48409/53239
38767
38783
38791
/38803/43633/48463
/38821/43651/48481
38833
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38851
38861
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38891
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38953
/38959/43789/48619
38971
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/39139/43969/48799/53629
/39157/43987/48817
/39161/43991/48821
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/39199/44029/48859
39209
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/39229/44059/48889/53719/58549
39233
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/39293/44123/48953/53783/58613/63443
39301
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/39359/44189/49019/53849/58679
39367
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39799
/39821/44651/49481/54311/59141
39827
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39877
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39983
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/40009/44839/49669/54499
40013
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40039
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/40087/44917/49747/54577/59407/64237/69067/73897
40093
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/40123/44953/49783
40127
/40129/44959/49789
40151
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40213
/40231/45061/49891/54721
40237
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/40361/45191/50021/54851
40387
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/40433/45263/50093
/40459/45289/50119/54949/59779/64609/69439
40471
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/40487/45317/50147
40493
/40499/45329/50159
40507
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/40801/45631/50461/55291
40813
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/40867/45697/50527
40879
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/40933/45763/50593
40939
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/41011/45841/50671/55501/60331
41017
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41201
41203
41213
41221
41227
/41231/46061/50891/55721
41233
41243
41257
/41263/46093/50923
/41269/46099/50929
41281
41299
41333
/41341/46171/51001
41351
41357
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41387
41389
/41399/46229/51059/55889/60719
41411
41413
41443
41453
41467
41479
41491
41507
41513
41519
41521
41539
41543
41549
41579
41593
41597
41603
41609
41611
41617
41621
/41627/46457/51287
41641
/41647/46477/51307
41651
41659
/41669/46499/51329
/41681/46511/51341/56171/61001/65831
41687
41719
41729
41737
/41759/46589/51419/56249
/41761/46591/51421
/41771/46601/51431
41777
41801
41809
/41813/46643/51473
41843
41849
/41851/46681/51511
41863
41879
41887
41893
41897
41903
41911
41927
41941
41947
41953
41957
41959
41969
41981
41983
/41999/46829/51659/56489
42013
42017
42019
/42023/46853/51683
42043
42061
42071
42073
42083
/42089/46919/51749
42101
42131
42139
42157
42169
42179
42181
42187
42193
42197
42209
42221
42223
42227
42239
42257
/42281/47111/51941
42283
42293
42299
42307
42323
/42331/47161/51991/56821/61651
42337
42349
42359
42373
42379
/42391/47221/52051
42397
42403
/42407/47237/52067/56897
42409
42433
42437
42443
42451
42457
42461
42463
/42467/47297/52127/56957
42473
/42487/47317/52147
42491
42499
42509
42533
42557
42569
42571
/42577/47407/52237
/42589/47419/52249
42611
42641
42643
42649
42667
42677
42683
42689
42697
42701
/42703/47533/52363/57193
42709
42719
42727
42737
42743
42751
42767
42773
42787
/42793/47623/52453/57283
42797
42821
/42829/47659/52489
42839
42841
42853
42859
42863
42899
42901
42923
42929
42937
42943
42953
42961
/42967/47797/52627/57457
/42979/47809/52639
42989
43003
/43013/47843/52673/57503
43019
43037
43049
/43051/47881/52711
43063
43067
43093
43103
43117
43133
43151
43159
43177
43189
43201
43207
43223
43237
43261
43271
43283
/43291/48121/52951/57781
43313
43319
43321
43331
/43391/48221/53051/57881
43397
43399
43403
43411
43427
/43441/48271/53101
43451
43457
43481
43487
43499
43517
/43541/48371/53201/58031/62861
43543
43573
43577
/43579/48409/53239
43591
43597
/43607/48437/53267
43609
43613
43627
43633
/43649/48479/53309
43651
43661
43669
43691
43711
43717
43721
43753
/43759/48589/53419
43777
/43781/48611/53441/58271
43783
43787
43789
/43793/48623/53453
43801
43853
43867
43889
43891
43913
43933
43943
/43951/48781/53611/58441
43961
43963
/43969/48799/53629
43973
43987
43991
43997
44017
44021
44027
44029
44041
44053
/44059/48889/53719/58549
44071
44087
44089
44101
44111
44119
/44123/48953/53783/58613/63443
44129
44131
/44159/48989/53819
44171
44179
/44189/49019/53849/58679
/44201/49031/53861
44203
44207
44221
44249
44257
44263
44267
44269
44273
/44279/49109/53939
44281
44293
44351
44357
44371
44381
44383
44389
44417
44449
44453
44483
44491
44497
44501
44507
44519
44531
/44533/49363/54193/59023/63853/68683
44537
44543
44549
44563
44579
44587
44617
44621
44623
/44633/49463/54293/59123
44641
44647
/44651/49481/54311/59141
44657
44683
44687
44699
/44701/49531/54361
44711
44729
44741
44753
44771
44773
44777
44789
44797
/44809/49639/54469
44819
/44839/49669/54499
44843
44851
44867
44879
44887
44893
44909
/44917/49747/54577/59407/64237/69067/73897
44927
44939
44953
44959
44963
/44971/49801/54631
44983
44987
45007
/45013/49843/54673
45053
/45061/49891/54721
45077
45083
45119
45121
/45127/49957/54787/59617
45131
45137
45139
45161
45179
45181
/45191/50021/54851
45197
45233
/45247/50077/54907
45259
45263
/45281/50111/54941/59771/64601/69431
/45289/50119/54949/59779/64609/69439
45293
45307
45317
45319
45329
45337
45341
45343
45361
45377
45389
45403
45413
45427
45433
45439
45481
45491
45497
/45503/50333/55163
45523
45533
45541
/45553/50383/55213
/45557/50387/55217
45569
45587
45589
45599
45613
/45631/50461/55291
45641
45659
45667
/45673/50503/55333
45677
45691
45697
45707
45737
/45751/50581/55411
45757
45763
45767
45779
45817
45821
45823
45827
45833
/45841/50671/55501/60331
45853
45863
45869
45887
45893
/45943/50773/55603
45949
45953
/45959/50789/55619/60449
45971
45979
45989
46021
46027
46049
46051
/46061/50891/55721
46073
46091
46093
46099
46103
46133
46141
46147
46153
46171
46181
46183
46187
46199
46219
/46229/51059/55889/60719
46237
46261
46271
46273
46279
46301
/46307/51137/55967
46309
/46327/51157/55987
46337
46349
46351
46381
46399
46411
46439
46441
46447
46451
46457
46471
46477
46489
46499
46507
/46511/51341/56171/61001/65831
46523
46549
46559
46567
46573
/46589/51419/56249
46591
46601
46619
46633
46639
46643
46649
46663
46679
46681
46687
46691
46703
46723
46727
46747
46751
46757
46769
46771
/46807/51637/56467/61297
46811
/46817/51647/56477
46819
/46829/51659/56489
46831
46853
46861
46867
46877
46889
46901
46919
46933
46957
46993
46997
47017
/47041/51871/56701
47051
47057
47059
47087
47093
47111
/47119/51949/56779/61609
47123
47129
47137
47143
/47147/51977/56807/61637/66467
47149
/47161/51991/56821/61651
47189
47207
47221
/47237/52067/56897
/47251/52081/56911
47269
47279
47287
47293
/47297/52127/56957
47303
47309
47317
47339
47351
47353
47363
47381
47387
47389
47407
47417
47419
47431
47441
/47459/52289/57119/61949
47491
47497
47501
47507
47513
47521
47527
/47533/52363/57193
47543
47563
47569
47581
47591
47599
47609
/47623/52453/57283
47629
47639
47653
47657
47659
47681
47699
47701
47711
/47713/52543/57373
47717
/47737/52567/57397
47741
47743
47777
47779
47791
/47797/52627/57457
47807
47809
47819
47837
/47843/52673/57503
47857
47869
47881
47903
47911
47917
47933
47939
47947
47951
47963
47969
/47977/52807/57637/62467
47981
48017
48023
/48029/52859/57689
/48049/52879/57709/62539/67369
48073
48079
48091
48109
48119
/48121/52951/57781
48131
48157
48163
48179
/48187/53017/57847
48193
48197
/48221/53051/57881
/48239/53069/57899
48247
48259
48271
48281
48299
48311
48313
48337
48341
48353
/48371/53201/58031/62861
48383
48397
48407
48409
48413
48437
/48449/53279/58109/62939
48463
48473
48479
48481
48487
48491
48497
48523
48527
48533
48539
48541
48563
/48571/53401/58231
48589
48593
/48611/53441/58271
48619
48623
48647
/48649/53479/58309
48661
48673
/48677/53507/58337
48679
48731
48733
48751
48757
48761
/48767/53597/58427
/48779/53609/58439
/48781/53611/58441
48787
48799
48809
48817
48821
48823
48847
48857
48859
48869
48871
48883
/48889/53719/58549
48907
48947
/48953/53783/58613/63443
48973
48989
48991
49003
49009
/49019/53849/58679
49031
49033
49037
49043
49057
49069
49081
49103
49109
49117
49121
49123
49139
49157
49169
/49171/54001/58831
49177
49193
49199
49201
49207
49211
49223
/49253/54083/58913/63743
/49261/54091/58921
49277
49279
49297
49307
49331
49333
49339
/49363/54193/59023/63853/68683
49367
49369
49391
49393
49409
49411
49417
49429
49433
49451
49459
/49463/54293/59123
49477
/49481/54311/59141
49499
49523
49529
49531
/49537/54367/59197
/49547/54377/59207/64037
49549
49559
49597
49603
/49613/54443/59273
49627
49633
49639
49663
49667
49669
49681
49697
49711
49727
49739
49741
/49747/54577/59407/64237/69067/73897
49757
49783
/49787/54617/59447
49789
49801
49807
49811
49823
49831
49843
49853
49871
49877
49891
49919
/49921/54751/59581
49927
49937
49939
49943
/49957/54787/59617
49991
49993
/49999/54829/59659/64489
50021
50023
50033
/50047/54877/59707
50051
50053
50069
50077
/50087/54917/59747/64577
50093
50101
/50111/54941/59771/64601/69431
/50119/54949/59779/64609/69439
50123
50129
50131
50147
50153
50159
50177
50207
50221
/50227/55057/59887/64717
50231
50261
50263
50273
50287
50291
50311
50321
50329
50333
50341
50359
50363
/50377/55207/60037
50383
50387
50411
50417
50423
50441
50459
50461
50497
50503
50513
50527

ysr · 发表于 2026-4-3 13:56

1000001与1001001之间的素数开头最多有公差为6469693230的5个连续素数:
1000003
1000033
1000037
1000039
1000081
1000099
1000117
1000121
1000133
1000151
1000159
1000171
1000183
1000187
1000193
1000199
/1000211/6470693441/12940386671
1000213
1000231
1000249
1000253
1000273
1000289
1000291
1000303
1000313
/1000333/6470693563/12940386793
1000357
1000367
/1000381/6470693611/12940386841/19410080071/25879773301
1000393
1000397
1000403
1000409
1000423
1000427
1000429
1000453
1000457
1000507
1000537
1000541
1000547
1000577
1000579
1000589
1000609
1000619
1000621
1000639
1000651
/1000667/6470693897/12940387127
1000669
1000679
1000691
1000697
1000721
1000723
1000763
1000777
1000793
1000829
1000847
1000849
1000859
1000861
1000889
1000907
1000919
1000921
/1000931/6470694161/12940387391/19410080621/25879773851
1000969
1000973
1000981
1000999

ysr · 发表于 2026-4-3 13:57

1001001与1002001之间的素数开头最多有公差为6469693230的4个连续素数:
1001003
1001017
1001023
1001027
1001041
1001069
1001081
1001087
1001089
1001093
1001107
1001123
1001153
1001159
1001173
1001177
1001191
1001197
1001219
1001237
1001267
1001279
1001291
1001303
1001311
1001321
1001323
1001327
1001347
1001353
/1001369/6470694599/12940387829/19410081059
1001381
1001387
1001389
1001401
1001411
1001431
1001447
1001459
1001467
1001491
1001501
1001527
1001531
1001549
1001551
1001563
1001569
1001587
1001593
1001621
1001629
1001639
1001659
1001669
1001683
/1001687/6470694917/12940388147
1001713
1001723
/1001743/6470694973/12940388203
1001783
1001797
1001801
1001807
1001809
1001821
1001831
1001839
1001911
1001933
1001941
1001947
1001953
1001977
1001981
1001983
1001989

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