根据素数周期循环分布规律及其特有的48条素数位缺带可以证明，以210m及210+X为公差的素数等差级数无穷多，并给出一些素数等差级数实例。
（1）240内的素数等差级数实例：
公差——素数等差数列（不计少于4个元素的）
6——（11,17,23,29），（61,67,73,79）
12——（17,29,41,53），（127,139,151,163）
30——（11,41,71,101,131），（107,137,167,197,227,257），（7，37,67,97），（37,67,97,127,157）
60——（11,71,131,191,251,311）
150——（7,157,307,457,607,757,907）
240——（107,347,587,827）

举几百个例子，对电脑来说不值一提。
2024-02-01 10:16:03
公差：6
1 [5, 11, 17, 23, 29]
2 [11, 17, 23, 29]
3 [41, 47, 53, 59]
4 [61, 67, 73, 79]
5 [251, 257, 263, 269]
6 [601, 607, 613, 619]
7 [641, 647, 653, 659]
8 [1091, 1097, 1103, 1109]
9 [1481, 1487, 1493, 1499]
10 [1601, 1607, 1613, 1619]
11 [1741, 1747, 1753, 1759]
12 [1861, 1867, 1873, 1879]
13 [2371, 2377, 2383, 2389]
14 [2671, 2677, 2683, 2689]
15 [3301, 3307, 3313, 3319]
16 [3911, 3917, 3923, 3929]
17 [4001, 4007, 4013, 4019]
18 [5101, 5107, 5113, 5119]
19 [5381, 5387, 5393, 5399]
20 [5431, 5437, 5443, 5449]
21 [5641, 5647, 5653, 5659]
22 [6311, 6317, 6323, 6329]
23 [6361, 6367, 6373, 6379]
24 [9461, 9467, 9473, 9479]
公差：12
1 [5, 17, 29, 41, 53]
2 [7, 19, 31, 43]
3 [17, 29, 41, 53]
4 [47, 59, 71, 83]
5 [127, 139, 151, 163]
6 [227, 239, 251, 263]
7 [257, 269, 281, 293]
8 [397, 409, 421, 433]
9 [467, 479, 491, 503]
10 [607, 619, 631, 643]
11 [997, 1009, 1021, 1033]
12 [1447, 1459, 1471, 1483]
13 [1487, 1499, 1511, 1523]
14 [1697, 1709, 1721, 1733]
15 [1877, 1889, 1901, 1913]
16 [2647, 2659, 2671, 2683]
17 [3307, 3319, 3331, 3343]
18 [3547, 3559, 3571, 3583]
19 [3907, 3919, 3931, 3943]
20 [4217, 4229, 4241, 4253]
21 [4987, 4999, 5011, 5023]
22 [5407, 5419, 5431, 5443]
23 [6287, 6299, 6311, 6323]
24 [6947, 6959, 6971, 6983]
25 [7297, 7309, 7321, 7333]
26 [7537, 7549, 7561, 7573]
27 [7817, 7829, 7841, 7853]
公差：18
1 [5, 23, 41, 59]
2 [43, 61, 79, 97]
3 [53, 71, 89, 107]
4 [113, 131, 149, 167]
5 [313, 331, 349, 367]
6 [673, 691, 709, 727]
7 [733, 751, 769, 787]
8 [1033, 1051, 1069, 1087]
9 [1583, 1601, 1619, 1637]
10 [1723, 1741, 1759, 1777]
11 [2423, 2441, 2459, 2477]
12 [2503, 2521, 2539, 2557]
13 [2713, 2731, 2749, 2767]
14 [2843, 2861, 2879, 2897]
15 [3673, 3691, 3709, 3727]
16 [4603, 4621, 4639, 4657]
17 [4933, 4951, 4969, 4987]
18 [5843, 5861, 5879, 5897]
19 [6343, 6361, 6379, 6397]
20 [7193, 7211, 7229, 7247]
21 [7523, 7541, 7559, 7577]
22 [7883, 7901, 7919, 7937]
23 [9203, 9221, 9239, 9257]
24 [9643, 9661, 9679, 9697]
公差：24
1 [59, 83, 107, 131]
2 [79, 103, 127, 151]
3 [349, 373, 397, 421]
4 [419, 443, 467, 491]
5 [499, 523, 547, 571]
6 [569, 593, 617, 641]
7 [839, 863, 887, 911]
8 [1399, 1423, 1447, 1471]
9 [2039, 2063, 2087, 2111]
10 [2089, 2113, 2137, 2161]
11 [2309, 2333, 2357, 2381]
12 [2659, 2683, 2707, 2731]
13 [2729, 2753, 2777, 2801]
14 [3299, 3323, 3347, 3371]
15 [3559, 3583, 3607, 3631]
16 [4129, 4153, 4177, 4201]
17 [4349, 4373, 4397, 4421]
18 [5669, 5693, 5717, 5741]
19 [7079, 7103, 7127, 7151]
20 [7829, 7853, 7877, 7901]
21 [8689, 8713, 8737, 8761]
22 [9109, 9133, 9157, 9181]
23 [9719, 9743, 9767, 9791]
24 [9859, 9883, 9907, 9931]
公差：30
1 [7, 37, 67, 97, 127, 157]
2 [11, 41, 71, 101, 131]
3 [13, 43, 73, 103]
4 [23, 53, 83, 113]
5 [37, 67, 97, 127, 157]
6 [41, 71, 101, 131]
7 [67, 97, 127, 157]
8 [107, 137, 167, 197, 227, 257]
9 [137, 167, 197, 227, 257]
10 [151, 181, 211, 241, 271]
11 [167, 197, 227, 257]
12 [181, 211, 241, 271]
13 [277, 307, 337, 367, 397]
14 [307, 337, 367, 397]
15 [349, 379, 409, 439]
16 [359, 389, 419, 449, 479, 509]
17 [389, 419, 449, 479, 509]
18 [401, 431, 461, 491, 521]
19 [419, 449, 479, 509]
20 [431, 461, 491, 521]
21 [541, 571, 601, 631, 661, 691]
22 [557, 587, 617, 647, 677]
23 [571, 601, 631, 661, 691]
24 [587, 617, 647, 677]
25 [601, 631, 661, 691]
26 [797, 827, 857, 887]
27 [877, 907, 937, 967, 997]
28 [881, 911, 941, 971]
29 [907, 937, 967, 997]
30 [1033, 1063, 1093, 1123, 1153]
31 [1063, 1093, 1123, 1153]
32 [1229, 1259, 1289, 1319]
33 [1399, 1429, 1459, 1489]
34 [1493, 1523, 1553, 1583, 1613]
35 [1523, 1553, 1583, 1613]
36 [1567, 1597, 1627, 1657]
37 [1607, 1637, 1667, 1697]
38 [1663, 1693, 1723, 1753, 1783]
39 [1693, 1723, 1753, 1783]
40 [2039, 2069, 2099, 2129]
41 [2053, 2083, 2113, 2143]
42 [2207, 2237, 2267, 2297]
43 [2221, 2251, 2281, 2311, 2341, 2371]
44 [2251, 2281, 2311, 2341, 2371]
45 [2281, 2311, 2341, 2371]
46 [2351, 2381, 2411, 2441]
47 [2617, 2647, 2677, 2707]
48 [2659, 2689, 2719, 2749]
49 [2879, 2909, 2939, 2969, 2999]
50 [2909, 2939, 2969, 2999]
51 [3019, 3049, 3079, 3109]
52 [3271, 3301, 3331, 3361, 3391]
53 [3299, 3329, 3359, 3389]
54 [3301, 3331, 3361, 3391]
55 [3469, 3499, 3529, 3559]
56 [3583, 3613, 3643, 3673]
57 [3821, 3851, 3881, 3911]
58 [3989, 4019, 4049, 4079]
59 [4391, 4421, 4451, 4481]
60 [4561, 4591, 4621, 4651]
61 [4643, 4673, 4703, 4733]
62 [5441, 5471, 5501, 5531]
63 [5791, 5821, 5851, 5881]
64 [6113, 6143, 6173, 6203]
65 [6269, 6299, 6329, 6359, 6389]
66 [6299, 6329, 6359, 6389]
67 [6337, 6367, 6397, 6427]
68 [6491, 6521, 6551, 6581]
69 [6547, 6577, 6607, 6637]
70 [6673, 6703, 6733, 6763, 6793, 6823]
71 [6703, 6733, 6763, 6793, 6823]
72 [6733, 6763, 6793, 6823]
73 [6967, 6997, 7027, 7057]
74 [7457, 7487, 7517, 7547, 7577, 7607]
75 [7487, 7517, 7547, 7577, 7607]
76 [7499, 7529, 7559, 7589]
77 [7517, 7547, 7577, 7607]
78 [7793, 7823, 7853, 7883]
79 [8647, 8677, 8707, 8737]
80 [8969, 8999, 9029, 9059]
81 [9281, 9311, 9341, 9371]
82 [9431, 9461, 9491, 9521, 9551]
83 [9461, 9491, 9521, 9551]
公差：60
1 [11, 71, 131, 191, 251, 311]
2 [19, 79, 139, 199]
3 [43, 103, 163, 223, 283]
4 [47, 107, 167, 227]
5 [53, 113, 173, 233, 293, 353]
6 [71, 131, 191, 251, 311]
7 [103, 163, 223, 283]
8 [113, 173, 233, 293, 353]
9 [131, 191, 251, 311]
10 [137, 197, 257, 317]
11 [151, 211, 271, 331]
12 [173, 233, 293, 353]
13 [277, 337, 397, 457]
14 [383, 443, 503, 563]
15 [389, 449, 509, 569]
16 [571, 631, 691, 751, 811]
17 [631, 691, 751, 811]
18 [641, 701, 761, 821, 881, 941]
19 [701, 761, 821, 881, 941]
20 [761, 821, 881, 941]
21 [911, 971, 1031, 1091, 1151]
22 [971, 1031, 1091, 1151]
23 [1033, 1093, 1153, 1213]
24 [1103, 1163, 1223, 1283]
25 [1307, 1367, 1427, 1487]
26 [1373, 1433, 1493, 1553, 1613]
27 [1429, 1489, 1549, 1609, 1669]
28 [1433, 1493, 1553, 1613]
29 [1439, 1499, 1559, 1619]
30 [1489, 1549, 1609, 1669]
31 [1873, 1933, 1993, 2053, 2113]
32 [1933, 1993, 2053, 2113]
33 [2153, 2213, 2273, 2333, 2393]
34 [2161, 2221, 2281, 2341]
35 [2213, 2273, 2333, 2393]
36 [2237, 2297, 2357, 2417, 2477]
37 [2297, 2357, 2417, 2477]
38 [2671, 2731, 2791, 2851]
39 [2777, 2837, 2897, 2957]
40 [2819, 2879, 2939, 2999]
41 [2843, 2903, 2963, 3023, 3083]
42 [2903, 2963, 3023, 3083]
43 [3001, 3061, 3121, 3181]
44 [3049, 3109, 3169, 3229]
45 [3253, 3313, 3373, 3433]
46 [3347, 3407, 3467, 3527]
47 [3511, 3571, 3631, 3691]
48 [3613, 3673, 3733, 3793, 3853]
49 [3673, 3733, 3793, 3853]
50 [3701, 3761, 3821, 3881]
51 [3847, 3907, 3967, 4027]
52 [4229, 4289, 4349, 4409]
53 [4337, 4397, 4457, 4517]
54 [4463, 4523, 4583, 4643, 4703]
55 [4523, 4583, 4643, 4703]
56 [4603, 4663, 4723, 4783]
57 [4999, 5059, 5119, 5179]
58 [5443, 5503, 5563, 5623, 5683, 5743]
59 [5471, 5531, 5591, 5651, 5711]
60 [5503, 5563, 5623, 5683, 5743]
61 [5521, 5581, 5641, 5701]
62 [5531, 5591, 5651, 5711]
63 [5563, 5623, 5683, 5743]
64 [5807, 5867, 5927, 5987, 6047]
65 [5867, 5927, 5987, 6047]
66 [6091, 6151, 6211, 6271]
67 [6143, 6203, 6263, 6323]
68 [6217, 6277, 6337, 6397]
69 [6269, 6329, 6389, 6449]
70 [6301, 6361, 6421, 6481]
71 [6599, 6659, 6719, 6779]
72 [6703, 6763, 6823, 6883]
73 [6899, 6959, 7019, 7079]
74 [7127, 7187, 7247, 7307]
75 [7523, 7583, 7643, 7703]
76 [7561, 7621, 7681, 7741]
77 [7757, 7817, 7877, 7937]
78 [7873, 7933, 7993, 8053]
79 [8111, 8171, 8231, 8291]
80 [8209, 8269, 8329, 8389]
81 [8461, 8521, 8581, 8641]
82 [9007, 9067, 9127, 9187]
83 [9161, 9221, 9281, 9341]
84 [9283, 9343, 9403, 9463]
85 [9311, 9371, 9431, 9491, 9551]
86 [9371, 9431, 9491, 9551]
87 [9601, 9661, 9721, 9781]

公差：90
1 [11, 101, 191, 281]
2 [13, 103, 193, 283, 373, 463]
3 [47, 137, 227, 317]
4 [61, 151, 241, 331, 421]
5 [83, 173, 263, 353, 443]
6 [89, 179, 269, 359, 449]
7 [103, 193, 283, 373, 463]
8 [151, 241, 331, 421]
9 [173, 263, 353, 443]
10 [179, 269, 359, 449]
11 [193, 283, 373, 463]
12 [277, 367, 457, 547]
13 [307, 397, 487, 577]
14 [389, 479, 569, 659]
15 [503, 593, 683, 773, 863, 953]
16 [593, 683, 773, 863, 953]
17 [683, 773, 863, 953]
18 [739, 829, 919, 1009]
19 [839, 929, 1019, 1109]
20 [881, 971, 1061, 1151]
21 [1013, 1103, 1193, 1283, 1373]
22 [1033, 1123, 1213, 1303]
23 [1097, 1187, 1277, 1367]
24 [1103, 1193, 1283, 1373]
25 [1201, 1291, 1381, 1471]
26 [1229, 1319, 1409, 1499]
27 [1399, 1489, 1579, 1669, 1759]
28 [1489, 1579, 1669, 1759]
29 [1607, 1697, 1787, 1877]
30 [1609, 1699, 1789, 1879]
31 [1733, 1823, 1913, 2003]
32 [1973, 2063, 2153, 2243, 2333, 2423]
33 [1999, 2089, 2179, 2269]
34 [2063, 2153, 2243, 2333, 2423]
35 [2113, 2203, 2293, 2383, 2473]
36 [2153, 2243, 2333, 2423]
37 [2203, 2293, 2383, 2473]
38 [2287, 2377, 2467, 2557, 2647]
39 [2351, 2441, 2531, 2621, 2711, 2801]
40 [2377, 2467, 2557, 2647]
41 [2441, 2531, 2621, 2711, 2801]
42 [2531, 2621, 2711, 2801]
43 [2609, 2699, 2789, 2879, 2969]
44 [2617, 2707, 2797, 2887]
45 [2699, 2789, 2879, 2969]
46 [2729, 2819, 2909, 2999, 3089]
47 [2819, 2909, 2999, 3089]
48 [3119, 3209, 3299, 3389]
49 [3163, 3253, 3343, 3433]
50 [3457, 3547, 3637, 3727]
51 [3491, 3581, 3671, 3761, 3851]
52 [3581, 3671, 3761, 3851]
53 [3821, 3911, 4001, 4091]
54 [3931, 4021, 4111, 4201]
55 [4723, 4813, 4903, 4993]
56 [4919, 5009, 5099, 5189, 5279]
57 [5009, 5099, 5189, 5279]
58 [5081, 5171, 5261, 5351, 5441, 5531]
59 [5171, 5261, 5351, 5441, 5531]
60 [5233, 5323, 5413, 5503]
61 [5261, 5351, 5441, 5531]
62 [5303, 5393, 5483, 5573]
63 [5479, 5569, 5659, 5749, 5839]
64 [5557, 5647, 5737, 5827]
65 [5569, 5659, 5749, 5839]
66 [5717, 5807, 5897, 5987]
67 [6599, 6689, 6779, 6869, 6959]
68 [6689, 6779, 6869, 6959]
69 [6691, 6781, 6871, 6961]
70 [6949, 7039, 7129, 7219, 7309]
71 [7013, 7103, 7193, 7283]
72 [7039, 7129, 7219, 7309]
73 [7369, 7459, 7549, 7639]
74 [8623, 8713, 8803, 8893]
75 [9281, 9371, 9461, 9551]
76 [9497, 9587, 9677, 9767, 9857]
77 [9587, 9677, 9767, 9857]
78 [9631, 9721, 9811, 9901]
79 [9679, 9769, 9859, 9949, 10039]
80 [9769, 9859, 9949, 10039]
公差：120
1 [29, 149, 269, 389, 509]
2 [37, 157, 277, 397]
3 [71, 191, 311, 431]
4 [73, 193, 313, 433]
5 [107, 227, 347, 467, 587]
6 [149, 269, 389, 509]
7 [227, 347, 467, 587]
8 [239, 359, 479, 599, 719, 839]
9 [281, 401, 521, 641, 761, 881]
10 [359, 479, 599, 719, 839]
11 [367, 487, 607, 727]
12 [379, 499, 619, 739, 859]
13 [401, 521, 641, 761, 881]
14 [479, 599, 719, 839]
15 [499, 619, 739, 859]
16 [521, 641, 761, 881]
17 [701, 821, 941, 1061, 1181, 1301]
18 [743, 863, 983, 1103, 1223]
19 [757, 877, 997, 1117, 1237]
20 [821, 941, 1061, 1181, 1301]
21 [857, 977, 1097, 1217]
22 [863, 983, 1103, 1223]
23 [877, 997, 1117, 1237]
24 [941, 1061, 1181, 1301]
25 [1303, 1423, 1543, 1663, 1783]
26 [1361, 1481, 1601, 1721]
27 [1373, 1493, 1613, 1733]
28 [1423, 1543, 1663, 1783]
29 [1429, 1549, 1669, 1789]
30 [1627, 1747, 1867, 1987]
31 [1667, 1787, 1907, 2027]
32 [1753, 1873, 1993, 2113]
33 [2011, 2131, 2251, 2371]
34 [2339, 2459, 2579, 2699, 2819, 2939]
35 [2437, 2557, 2677, 2797, 2917, 3037]
36 [2459, 2579, 2699, 2819, 2939]
37 [2473, 2593, 2713, 2833, 2953]
38 [2557, 2677, 2797, 2917, 3037]
39 [2579, 2699, 2819, 2939]
40 [2593, 2713, 2833, 2953]
41 [2677, 2797, 2917, 3037]
42 [2843, 2963, 3083, 3203, 3323]
43 [2963, 3083, 3203, 3323]
44 [2969, 3089, 3209, 3329, 3449]
45 [3089, 3209, 3329, 3449]
46 [3271, 3391, 3511, 3631]
47 [3461, 3581, 3701, 3821]
48 [3557, 3677, 3797, 3917]
49 [3607, 3727, 3847, 3967]
50 [4013, 4133, 4253, 4373, 4493]
51 [4133, 4253, 4373, 4493]
52 [4243, 4363, 4483, 4603, 4723]
53 [4363, 4483, 4603, 4723]
54 [4663, 4783, 4903, 5023]
55 [4679, 4799, 4919, 5039]
56 [4987, 5107, 5227, 5347]
57 [5231, 5351, 5471, 5591, 5711]
58 [5279, 5399, 5519, 5639]
59 [5323, 5443, 5563, 5683]
60 [5351, 5471, 5591, 5711]
61 [5741, 5861, 5981, 6101, 6221]
62 [5861, 5981, 6101, 6221]
63 [6329, 6449, 6569, 6689]
64 [6659, 6779, 6899, 7019]
65 [6709, 6829, 6949, 7069]
66 [7057, 7177, 7297, 7417, 7537]
67 [7177, 7297, 7417, 7537]
68 [8423, 8543, 8663, 8783]
69 [9137, 9257, 9377, 9497]
70 [9173, 9293, 9413, 9533]
71 [9941, 10061, 10181, 10301]
公差：150
1 [7, 157, 307, 457, 607, 757, 907]
2 [13, 163, 313, 463, 613]
3 [17, 167, 317, 467, 617]
4 [73, 223, 373, 523, 673, 823]
5 [157, 307, 457, 607, 757, 907]
6 [163, 313, 463, 613]
7 [167, 317, 467, 617]
8 [223, 373, 523, 673, 823]
9 [269, 419, 569, 719]
10 [293, 443, 593, 743]
11 [307, 457, 607, 757, 907]
12 [359, 509, 659, 809]
13 [373, 523, 673, 823]
14 [457, 607, 757, 907]
15 [619, 769, 919, 1069]
16 [647, 797, 947, 1097]
17 [787, 937, 1087, 1237]
18 [1021, 1171, 1321, 1471, 1621]
19 [1109, 1259, 1409, 1559, 1709]
20 [1129, 1279, 1429, 1579]
21 [1151, 1301, 1451, 1601]
22 [1171, 1321, 1471, 1621]
23 [1249, 1399, 1549, 1699]
24 [1259, 1409, 1559, 1709]
25 [1283, 1433, 1583, 1733]
26 [1297, 1447, 1597, 1747]
27 [1861, 2011, 2161, 2311]
28 [1987, 2137, 2287, 2437]
29 [2089, 2239, 2389, 2539, 2689]
30 [2221, 2371, 2521, 2671]
31 [2239, 2389, 2539, 2689]
32 [2243, 2393, 2543, 2693, 2843]
33 [2393, 2543, 2693, 2843]
34 [2467, 2617, 2767, 2917, 3067, 3217]
35 [2617, 2767, 2917, 3067, 3217]
36 [2767, 2917, 3067, 3217]
37 [3019, 3169, 3319, 3469]
38 [3163, 3313, 3463, 3613]
39 [3467, 3617, 3767, 3917]
40 [3643, 3793, 3943, 4093, 4243]
41 [3727, 3877, 4027, 4177, 4327]
42 [3779, 3929, 4079, 4229]
43 [3793, 3943, 4093, 4243]
44 [3877, 4027, 4177, 4327]
45 [4363, 4513, 4663, 4813]
46 [4493, 4643, 4793, 4943]
47 [4637, 4787, 4937, 5087, 5237, 5387]
48 [4651, 4801, 4951, 5101]
49 [4721, 4871, 5021, 5171]
50 [4759, 4909, 5059, 5209]
51 [4787, 4937, 5087, 5237, 5387]
52 [4931, 5081, 5231, 5381, 5531]
53 [4937, 5087, 5237, 5387]
54 [5081, 5231, 5381, 5531]
55 [5351, 5501, 5651, 5801]
56 [5903, 6053, 6203, 6353]
57 [6079, 6229, 6379, 6529, 6679, 6829]
58 [6121, 6271, 6421, 6571]
59 [6229, 6379, 6529, 6679, 6829]
60 [6379, 6529, 6679, 6829]
61 [6569, 6719, 6869, 7019]
62 [7307, 7457, 7607, 7757, 7907]
63 [7457, 7607, 7757, 7907]
64 [7717, 7867, 8017, 8167, 8317, 8467]
65 [7867, 8017, 8167, 8317, 8467]
66 [7919, 8069, 8219, 8369]
67 [7937, 8087, 8237, 8387, 8537]
68 [8011, 8161, 8311, 8461]
69 [8017, 8167, 8317, 8467]
70 [8087, 8237, 8387, 8537]
71 [8123, 8273, 8423, 8573]
72 [8147, 8297, 8447, 8597, 8747]
73 [8297, 8447, 8597, 8747]
74 [8389, 8539, 8689, 8839]
75 [8563, 8713, 8863, 9013]
76 [8861, 9011, 9161, 9311, 9461]
77 [8941, 9091, 9241, 9391]
78 [9011, 9161, 9311, 9461]
79 [9173, 9323, 9473, 9623]
公差：180
1 [59, 239, 419, 599]
2 [61, 241, 421, 601]
3 [101, 281, 461, 641, 821]
4 [103, 283, 463, 643, 823]
5 [281, 461, 641, 821]
6 [283, 463, 643, 823]
7 [367, 547, 727, 907, 1087]
8 [397, 577, 757, 937, 1117, 1297]
9 [479, 659, 839, 1019]
10 [521, 701, 881, 1061]
11 [547, 727, 907, 1087]
12 [577, 757, 937, 1117, 1297]
13 [631, 811, 991, 1171]
14 [673, 853, 1033, 1213]
15 [757, 937, 1117, 1297]
16 [1013, 1193, 1373, 1553, 1733, 1913]
17 [1069, 1249, 1429, 1609, 1789]
18 [1123, 1303, 1483, 1663]
19 [1193, 1373, 1553, 1733, 1913]
20 [1249, 1429, 1609, 1789]
21 [1307, 1487, 1667, 1847, 2027, 2207]
22 [1373, 1553, 1733, 1913]
23 [1487, 1667, 1847, 2027, 2207]
24 [1667, 1847, 2027, 2207]
25 [1753, 1933, 2113, 2293, 2473]
26 [1907, 2087, 2267, 2447]
27 [1933, 2113, 2293, 2473]
28 [2297, 2477, 2657, 2837]
29 [2549, 2729, 2909, 3089]
30 [2663, 2843, 3023, 3203]
31 [2677, 2857, 3037, 3217]
32 [3001, 3181, 3361, 3541]
33 [3253, 3433, 3613, 3793]
34 [3463, 3643, 3823, 4003]
35 [3517, 3697, 3877, 4057]
36 [3559, 3739, 3919, 4099]
37 [3911, 4091, 4271, 4451]
38 [4243, 4423, 4603, 4783]
39 [4261, 4441, 4621, 4801]
40 [4691, 4871, 5051, 5231]
41 [4793, 4973, 5153, 5333]
42 [4987, 5167, 5347, 5527]
43 [5171, 5351, 5531, 5711]
44 [5857, 6037, 6217, 6397, 6577]
45 [6037, 6217, 6397, 6577]
46 [6067, 6247, 6427, 6607]
47 [6121, 6301, 6481, 6661, 6841]
48 [6301, 6481, 6661, 6841]
49 [6473, 6653, 6833, 7013, 7193]
50 [6653, 6833, 7013, 7193]
51 [6791, 6971, 7151, 7331]
52 [6947, 7127, 7307, 7487]
53 [6949, 7129, 7309, 7489, 7669]
54 [7129, 7309, 7489, 7669]
55 [7213, 7393, 7573, 7753, 7933]
56 [7393, 7573, 7753, 7933]
57 [7547, 7727, 7907, 8087]
58 [7577, 7757, 7937, 8117, 8297]
59 [7757, 7937, 8117, 8297]
60 [8263, 8443, 8623, 8803]
61 [8461, 8641, 8821, 9001, 9181]
62 [8501, 8681, 8861, 9041, 9221]
63 [8527, 8707, 8887, 9067]
64 [8641, 8821, 9001, 9181]
65 [8669, 8849, 9029, 9209]
66 [8681, 8861, 9041, 9221]
67 [8923, 9103, 9283, 9463, 9643]
68 [9103, 9283, 9463, 9643]
69 [9241, 9421, 9601, 9781]
70 [9497, 9677, 9857, 10037]
71 [9887, 10067, 10247, 10427, 10607]

（2）以210m为公差的素数等差级数：
公差——素数等差数列
210——（221,421,631），（2311,2521,2731），（4001,4211,4421）
210——（13,223,433,643），（2953,3163,3373,3583,3793,4003）
210——（1277,1487,1697,1907），（3797,4007,4217）
210——（19,229,430），（859，1069,1279,1489,1699）
210——（23,233,443,653,863），（2333,2543,2753,2963），（3593,3803,4013）
210——（29,239,449,659），（1289,1499,1709），（2129,2339,2549）
210——（2131,2341,2551），（2791,3181,3391,），（4021，4231,4441,4651,4861
210——（877,1087,1297），（2137,2347,2557,2767）
以上仅仅是一点点实例，待续。

公差：210
1 [13, 223, 433, 643, 853, 1063]
2 [23, 233, 443, 653, 863]
3 [29, 239, 449, 659]
4 [47, 257, 467, 677, 887, 1097, 1307]
5 [71, 281, 491, 701, 911]
6 [103, 313, 523, 733]
7 [127, 337, 547, 757, 967]
8 [157, 367, 577, 787, 997]
9 [179, 389, 599, 809, 1019, 1229, 1439]
10 [199, 409, 619, 829, 1039, 1249, 1459, 1669, 1879, 2089]
11 [223, 433, 643, 853, 1063]
12 [233, 443, 653, 863]
13 [257, 467, 677, 887, 1097, 1307]
14 [281, 491, 701, 911]
15 [337, 547, 757, 967]
16 [353, 563, 773, 983, 1193]
17 [367, 577, 787, 997]
18 [389, 599, 809, 1019, 1229, 1439]
19 [409, 619, 829, 1039, 1249, 1459, 1669, 1879, 2089]
20 [433, 643, 853, 1063]
21 [463, 673, 883, 1093, 1303]
22 [467, 677, 887, 1097, 1307]
23 [499, 709, 919, 1129]
24 [563, 773, 983, 1193]
25 [599, 809, 1019, 1229, 1439]
26 [601, 811, 1021, 1231]
27 [619, 829, 1039, 1249, 1459, 1669, 1879, 2089]
28 [673, 883, 1093, 1303]
29 [677, 887, 1097, 1307]
30 [743, 953, 1163, 1373, 1583]
31 [809, 1019, 1229, 1439]
32 [829, 1039, 1249, 1459, 1669, 1879, 2089]
33 [859, 1069, 1279, 1489, 1699]
34 [881, 1091, 1301, 1511, 1721, 1931, 2141, 2351]
35 [941, 1151, 1361, 1571]
36 [953, 1163, 1373, 1583]
37 [1039, 1249, 1459, 1669, 1879, 2089]
38 [1069, 1279, 1489, 1699]
39 [1091, 1301, 1511, 1721, 1931, 2141, 2351]
40 [1217, 1427, 1637, 1847]
41 [1237, 1447, 1657, 1867]
42 [1249, 1459, 1669, 1879, 2089]
43 [1277, 1487, 1697, 1907]
44 [1301, 1511, 1721, 1931, 2141, 2351]
45 [1321, 1531, 1741, 1951, 2161, 2371]
46 [1453, 1663, 1873, 2083, 2293, 2503, 2713]
47 [1459, 1669, 1879, 2089]
48 [1511, 1721, 1931, 2141, 2351]
49 [1531, 1741, 1951, 2161, 2371]
50 [1663, 1873, 2083, 2293, 2503, 2713]
51 [1667, 1877, 2087, 2297]
52 [1721, 1931, 2141, 2351]
53 [1741, 1951, 2161, 2371]
54 [1787, 1997, 2207, 2417]
55 [1873, 2083, 2293, 2503, 2713]
56 [2003, 2213, 2423, 2633, 2843]
57 [2027, 2237, 2447, 2657]
58 [2083, 2293, 2503, 2713]
59 [2137, 2347, 2557, 2767]
60 [2213, 2423, 2633, 2843]
61 [2267, 2477, 2687, 2897]
62 [2333, 2543, 2753, 2963]
63 [2381, 2591, 2801, 3011, 3221]
64 [2437, 2647, 2857, 3067]
65 [2579, 2789, 2999, 3209]
66 [2591, 2801, 3011, 3221]
67 [2699, 2909, 3119, 3329, 3539]
68 [2909, 3119, 3329, 3539]
69 [2927, 3137, 3347, 3557, 3767]
70 [2953, 3163, 3373, 3583, 3793, 4003]
71 [3041, 3251, 3461, 3671, 3881, 4091]
72 [3109, 3319, 3529, 3739]
73 [3137, 3347, 3557, 3767]
74 [3163, 3373, 3583, 3793, 4003]
75 [3203, 3413, 3623, 3833]
76 [3251, 3461, 3671, 3881, 4091]
77 [3373, 3583, 3793, 4003]
78 [3461, 3671, 3881, 4091]
79 [3499, 3709, 3919, 4129, 4339, 4549, 4759, 4969, 5179]
80 [3709, 3919, 4129, 4339, 4549, 4759, 4969, 5179]
81 [3719, 3929, 4139, 4349]
82 [3733, 3943, 4153, 4363]
83 [3863, 4073, 4283, 4493, 4703]
84 [3917, 4127, 4337, 4547]
85 [3919, 4129, 4339, 4549, 4759, 4969, 5179]
86 [4021, 4231, 4441, 4651, 4861]
87 [4073, 4283, 4493, 4703]
88 [4129, 4339, 4549, 4759, 4969, 5179]
89 [4231, 4441, 4651, 4861]
90 [4339, 4549, 4759, 4969, 5179]
91 [4373, 4583, 4793, 5003]
92 [4523, 4733, 4943, 5153]
93 [4549, 4759, 4969, 5179]
94 [4603, 4813, 5023, 5233, 5443, 5653]
95 [4679, 4889, 5099, 5309, 5519]
96 [4789, 4999, 5209, 5419]
97 [4813, 5023, 5233, 5443, 5653]
98 [4877, 5087, 5297, 5507, 5717, 5927]
99 [4889, 5099, 5309, 5519]
100 [5021, 5231, 5441, 5651, 5861]
101 [5023, 5233, 5443, 5653]
102 [5087, 5297, 5507, 5717, 5927]
103 [5171, 5381, 5591, 5801, 6011, 6221]
104 [5227, 5437, 5647, 5857, 6067, 6277]
105 [5231, 5441, 5651, 5861]
106 [5273, 5483, 5693, 5903, 6113, 6323]
107 [5297, 5507, 5717, 5927]
108 [5381, 5591, 5801, 6011, 6221]
109 [5437, 5647, 5857, 6067, 6277]
110 [5449, 5659, 5869, 6079]
111 [5483, 5693, 5903, 6113, 6323]
112 [5591, 5801, 6011, 6221]
113 [5647, 5857, 6067, 6277]
114 [5669, 5879, 6089, 6299]
115 [5693, 5903, 6113, 6323]
116 [5743, 5953, 6163, 6373]
117 [5843, 6053, 6263, 6473]
118 [5923, 6133, 6343, 6553, 6763]
119 [6007, 6217, 6427, 6637]
120 [6133, 6343, 6553, 6763]
121 [6151, 6361, 6571, 6781, 6991]
122 [6361, 6571, 6781, 6991]
123 [6449, 6659, 6869, 7079]
124 [6491, 6701, 6911, 7121, 7331, 7541]
125 [6581, 6791, 7001, 7211]
126 [6701, 6911, 7121, 7331, 7541]
127 [6911, 7121, 7331, 7541]
128 [7297, 7507, 7717, 7927]
129 [7307, 7517, 7727, 7937, 8147]
130 [7459, 7669, 7879, 8089]
131 [7481, 7691, 7901, 8111]
132 [7517, 7727, 7937, 8147]
133 [8011, 8221, 8431, 8641]
134 [8101, 8311, 8521, 8731, 8941, 9151]
135 [8209, 8419, 8629, 8839, 9049]
136 [8311, 8521, 8731, 8941, 9151]
137 [8419, 8629, 8839, 9049]
138 [8521, 8731, 8941, 9151]
139 [8543, 8753, 8963, 9173]
140 [8609, 8819, 9029, 9239]
141 [8713, 8923, 9133, 9343]
142 [8741, 8951, 9161, 9371]
143 [8761, 8971, 9181, 9391, 9601, 9811]
144 [8971, 9181, 9391, 9601, 9811]
145 [8999, 9209, 9419, 9629, 9839]
146 [9181, 9391, 9601, 9811]
147 [9203, 9413, 9623, 9833]
148 [9209, 9419, 9629, 9839]
149 [9257, 9467, 9677, 9887]
150 [9439, 9649, 9859, 10069]
151 [9511, 9721, 9931, 10141]
152 [9739, 9949, 10159, 10369]
153 [9883, 10093, 10303, 10513, 10723]
154 [9901, 10111, 10321, 10531]

公差：420
1 [19, 439, 859, 1279, 1699]
2 [23, 443, 863, 1283]
3 [37, 457, 877, 1297]
4 [41, 461, 881, 1301, 1721, 2141]
5 [43, 463, 883, 1303, 1723, 2143]
6 [47, 467, 887, 1307]
7 [67, 487, 907, 1327, 1747]
8 [101, 521, 941, 1361]
9 [173, 593, 1013, 1433]
10 [179, 599, 1019, 1439]
11 [193, 613, 1033, 1453, 1873, 2293, 2713]
12 [199, 619, 1039, 1459, 1879]
13 [211, 631, 1051, 1471]
14 [223, 643, 1063, 1483]
15 [263, 683, 1103, 1523]
16 [353, 773, 1193, 1613]
17 [409, 829, 1249, 1669, 2089]
18 [439, 859, 1279, 1699]
19 [461, 881, 1301, 1721, 2141]
20 [463, 883, 1303, 1723, 2143]
21 [487, 907, 1327, 1747]
22 [613, 1033, 1453, 1873, 2293, 2713]
23 [619, 1039, 1459, 1879]
24 [641, 1061, 1481, 1901]
25 [743, 1163, 1583, 2003, 2423, 2843]
26 [829, 1249, 1669, 2089]
27 [881, 1301, 1721, 2141]
28 [883, 1303, 1723, 2143]
29 [947, 1367, 1787, 2207]
30 [1033, 1453, 1873, 2293, 2713]
31 [1091, 1511, 1931, 2351]
32 [1163, 1583, 2003, 2423, 2843]
33 [1187, 1607, 2027, 2447]
34 [1289, 1709, 2129, 2549, 2969, 3389]
35 [1427, 1847, 2267, 2687]
36 [1447, 1867, 2287, 2707]
37 [1453, 1873, 2293, 2713]
38 [1493, 1913, 2333, 2753]
39 [1531, 1951, 2371, 2791]
40 [1559, 1979, 2399, 2819]
41 [1583, 2003, 2423, 2843]
42 [1597, 2017, 2437, 2857]
43 [1619, 2039, 2459, 2879, 3299, 3719, 4139]
44 [1709, 2129, 2549, 2969, 3389]
45 [1823, 2243, 2663, 3083]
46 [1997, 2417, 2837, 3257, 3677]
47 [2039, 2459, 2879, 3299, 3719, 4139]
48 [2129, 2549, 2969, 3389]
49 [2131, 2551, 2971, 3391]
50 [2239, 2659, 3079, 3499, 3919, 4339, 4759, 5179]
51 [2269, 2689, 3109, 3529]
52 [2347, 2767, 3187, 3607, 4027, 4447]
53 [2377, 2797, 3217, 3637, 4057]
54 [2417, 2837, 3257, 3677]
55 [2459, 2879, 3299, 3719, 4139]
56 [2467, 2887, 3307, 3727]
57 [2617, 3037, 3457, 3877, 4297]
58 [2621, 3041, 3461, 3881]
59 [2659, 3079, 3499, 3919, 4339, 4759, 5179]
60 [2767, 3187, 3607, 4027, 4447]
61 [2797, 3217, 3637, 4057]
62 [2833, 3253, 3673, 4093, 4513, 4933]
63 [2851, 3271, 3691, 4111]
64 [2879, 3299, 3719, 4139]
65 [3037, 3457, 3877, 4297]
66 [3079, 3499, 3919, 4339, 4759, 5179]
67 [3163, 3583, 4003, 4423]
68 [3187, 3607, 4027, 4447]
69 [3253, 3673, 4093, 4513, 4933]
70 [3413, 3833, 4253, 4673]
71 [3499, 3919, 4339, 4759, 5179]
72 [3673, 4093, 4513, 4933]
73 [3709, 4129, 4549, 4969]
74 [3919, 4339, 4759, 5179]
75 [4021, 4441, 4861, 5281, 5701, 6121]
76 [4127, 4547, 4967, 5387, 5807]
77 [4219, 4639, 5059, 5479]
78 [4259, 4679, 5099, 5519, 5939, 6359, 6779]
79 [4397, 4817, 5237, 5657]
80 [4441, 4861, 5281, 5701, 6121]
81 [4457, 4877, 5297, 5717]
82 [4483, 4903, 5323, 5743, 6163]
83 [4547, 4967, 5387, 5807]
84 [4567, 4987, 5407, 5827, 6247]
85 [4591, 5011, 5431, 5851, 6271, 6691]
86 [4679, 5099, 5519, 5939, 6359, 6779]
87 [4751, 5171, 5591, 6011]
88 [4813, 5233, 5653, 6073]
89 [4861, 5281, 5701, 6121]
90 [4903, 5323, 5743, 6163]
91 [4987, 5407, 5827, 6247]
92 [5011, 5431, 5851, 6271, 6691]
93 [5099, 5519, 5939, 6359, 6779]
94 [5431, 5851, 6271, 6691]
95 [5477, 5897, 6317, 6737]
96 [5503, 5923, 6343, 6763]
97 [5519, 5939, 6359, 6779]
98 [5711, 6131, 6551, 6971]
99 [5779, 6199, 6619, 7039, 7459, 7879]
100 [5849, 6269, 6689, 7109, 7529, 7949, 8369]
101 [5953, 6373, 6793, 7213]
102 [6151, 6571, 6991, 7411]
103 [6199, 6619, 7039, 7459, 7879]
104 [6217, 6637, 7057, 7477]
105 [6269, 6689, 7109, 7529, 7949, 8369]
106 [6529, 6949, 7369, 7789, 8209, 8629, 9049]
107 [6619, 7039, 7459, 7879]
108 [6659, 7079, 7499, 7919]
109 [6689, 7109, 7529, 7949, 8369]
110 [6833, 7253, 7673, 8093, 8513, 8933]
111 [6863, 7283, 7703, 8123, 8543, 8963]
112 [6949, 7369, 7789, 8209, 8629, 9049]
113 [7013, 7433, 7853, 8273, 8693]
114 [7109, 7529, 7949, 8369]
115 [7253, 7673, 8093, 8513, 8933]
116 [7283, 7703, 8123, 8543, 8963]
117 [7321, 7741, 8161, 8581, 9001, 9421]
118 [7369, 7789, 8209, 8629, 9049]
119 [7433, 7853, 8273, 8693]
120 [7589, 8009, 8429, 8849]
121 [7673, 8093, 8513, 8933]
122 [7681, 8101, 8521, 8941]
123 [7703, 8123, 8543, 8963]
124 [7741, 8161, 8581, 9001, 9421]
125 [7789, 8209, 8629, 9049]
126 [7867, 8287, 8707, 9127, 9547, 9967]
127 [7873, 8293, 8713, 9133]
128 [8161, 8581, 9001, 9421]
129 [8287, 8707, 9127, 9547, 9967]
130 [8363, 8783, 9203, 9623]
131 [8623, 9043, 9463, 9883, 10303, 10723]
132 [8707, 9127, 9547, 9967]
133 [8779, 9199, 9619, 10039, 10459]
134 [8951, 9371, 9791, 10211, 10631]
135 [8999, 9419, 9839, 10259]
136 [9011, 9431, 9851, 10271, 10691]
137 [9043, 9463, 9883, 10303, 10723]
138 [9199, 9619, 10039, 10459]
139 [9371, 9791, 10211, 10631]
140 [9431, 9851, 10271, 10691]
141 [9463, 9883, 10303, 10723]
142 [9587, 10007, 10427, 10847]
143 [9719, 10139, 10559, 10979, 11399]

公差：630
1 [17, 647, 1277, 1907]
2 [23, 653, 1283, 1913, 2543]
3 [43, 673, 1303, 1933]
4 [61, 691, 1321, 1951]
5 [113, 743, 1373, 2003, 2633]
6 [139, 769, 1399, 2029, 2659]
7 [179, 809, 1439, 2069, 2699, 3329]
8 [191, 821, 1451, 2081, 2711]
9 [193, 823, 1453, 2083, 2713, 3343]
10 [199, 829, 1459, 2089, 2719]
11 [223, 853, 1483, 2113]
12 [251, 881, 1511, 2141]
13 [347, 977, 1607, 2237]
14 [353, 983, 1613, 2243]
15 [461, 1091, 1721, 2351]
16 [487, 1117, 1747, 2377]
17 [499, 1129, 1759, 2389, 3019]
18 [587, 1217, 1847, 2477]
19 [653, 1283, 1913, 2543]
20 [743, 1373, 2003, 2633]
21 [769, 1399, 2029, 2659]
22 [809, 1439, 2069, 2699, 3329]
23 [821, 1451, 2081, 2711]
24 [823, 1453, 2083, 2713, 3343]
25 [829, 1459, 2089, 2719]
26 [953, 1583, 2213, 2843]
27 [1129, 1759, 2389, 3019]
28 [1319, 1949, 2579, 3209]
29 [1423, 2053, 2683, 3313, 3943]
30 [1433, 2063, 2693, 3323]
31 [1439, 2069, 2699, 3329]
32 [1453, 2083, 2713, 3343]
33 [1481, 2111, 2741, 3371, 4001]
34 [1637, 2267, 2897, 3527, 4157, 4787, 5417, 6047]
35 [1657, 2287, 2917, 3547, 4177]
36 [1667, 2297, 2927, 3557]
37 [1741, 2371, 3001, 3631, 4261]
38 [2053, 2683, 3313, 3943]
39 [2099, 2729, 3359, 3989]
40 [2111, 2741, 3371, 4001]
41 [2203, 2833, 3463, 4093, 4723]
42 [2267, 2897, 3527, 4157, 4787, 5417, 6047]
43 [2287, 2917, 3547, 4177]
44 [2371, 3001, 3631, 4261]
45 [2437, 3067, 3697, 4327, 4957]
46 [2459, 3089, 3719, 4349]
47 [2591, 3221, 3851, 4481]
48 [2671, 3301, 3931, 4561]
49 [2833, 3463, 4093, 4723]
50 [2897, 3527, 4157, 4787, 5417, 6047]
51 [3067, 3697, 4327, 4957]
52 [3079, 3709, 4339, 4969]
53 [3191, 3821, 4451, 5081, 5711]
54 [3389, 4019, 4649, 5279]
55 [3391, 4021, 4651, 5281]
56 [3461, 4091, 4721, 5351, 5981]
57 [3527, 4157, 4787, 5417, 6047]
58 [3529, 4159, 4789, 5419]
59 [3733, 4363, 4993, 5623]
60 [3761, 4391, 5021, 5651]
61 [3779, 4409, 5039, 5669, 6299]
62 [3821, 4451, 5081, 5711]
63 [3853, 4483, 5113, 5743, 6373]
64 [3967, 4597, 5227, 5857]
65 [4013, 4643, 5273, 5903]
66 [4049, 4679, 5309, 5939, 6569]
67 [4091, 4721, 5351, 5981]
68 [4153, 4783, 5413, 6043, 6673]
69 [4157, 4787, 5417, 6047]
70 [4241, 4871, 5501, 6131, 6761]
71 [4409, 5039, 5669, 6299]
72 [4483, 5113, 5743, 6373]
73 [4679, 5309, 5939, 6569]
74 [4783, 5413, 6043, 6673]
75 [4813, 5443, 6073, 6703, 7333, 7963]
76 [4871, 5501, 6131, 6761]
77 [4943, 5573, 6203, 6833]
78 [4951, 5581, 6211, 6841]
79 [5009, 5639, 6269, 6899, 7529]
80 [5107, 5737, 6367, 6997]
81 [5231, 5861, 6491, 7121]
82 [5443, 6073, 6703, 7333, 7963]
83 [5503, 6133, 6763, 7393]
84 [5521, 6151, 6781, 7411]
85 [5569, 6199, 6829, 7459, 8089, 8719, 9349]
86 [5639, 6269, 6899, 7529]
87 [5647, 6277, 6907, 7537, 8167]
88 [5657, 6287, 6917, 7547]
89 [6073, 6703, 7333, 7963]
90 [6197, 6827, 7457, 8087]
91 [6199, 6829, 7459, 8089, 8719, 9349]
92 [6277, 6907, 7537, 8167]
93 [6329, 6959, 7589, 8219, 8849, 9479]
94 [6427, 7057, 7687, 8317]
95 [6529, 7159, 7789, 8419, 9049, 9679]
96 [6691, 7321, 7951, 8581]
97 [6829, 7459, 8089, 8719, 9349]
98 [6857, 7487, 8117, 8747, 9377, 10007]
99 [6959, 7589, 8219, 8849, 9479]
100 [6977, 7607, 8237, 8867, 9497]
101 [7159, 7789, 8419, 9049, 9679]
102 [7459, 8089, 8719, 9349]
103 [7481, 8111, 8741, 9371]
104 [7487, 8117, 8747, 9377, 10007]
105 [7589, 8219, 8849, 9479]
106 [7607, 8237, 8867, 9497]
107 [7789, 8419, 9049, 9679]
108 [8017, 8647, 9277, 9907]
109 [8059, 8689, 9319, 9949]
110 [8117, 8747, 9377, 10007]
111 [8369, 8999, 9629, 10259, 10889, 11519, 12149]
112 [8543, 9173, 9803, 10433]
113 [8573, 9203, 9833, 10463, 11093]
114 [8597, 9227, 9857, 10487, 11117]
115 [8707, 9337, 9967, 10597]
116 [8999, 9629, 10259, 10889, 11519, 12149]
117 [9013, 9643, 10273, 10903]
118 [9203, 9833, 10463, 11093]
119 [9227, 9857, 10487, 11117]
120 [9241, 9871, 10501, 11131]
121 [9431, 10061, 10691, 11321]
122 [9463, 10093, 10723, 11353]
123 [9521, 10151, 10781, 11411, 12041, 12671]
124 [9629, 10259, 10889, 11519, 12149]
公差：840
1 [19, 859, 1699, 2539]
2 [97, 937, 1777, 2617, 3457, 4297]
3 [151, 991, 1831, 2671, 3511]
4 [191, 1031, 1871, 2711]
5 [193, 1033, 1873, 2713]
6 [199, 1039, 1879, 2719, 3559]
7 [269, 1109, 1949, 2789]
8 [313, 1153, 1993, 2833, 3673, 4513]
9 [331, 1171, 2011, 2851, 3691]
10 [383, 1223, 2063, 2903]
11 [389, 1229, 2069, 2909]
12 [419, 1259, 2099, 2939, 3779]
13 [449, 1289, 2129, 2969]
14 [541, 1381, 2221, 3061]
15 [709, 1549, 2389, 3229]
16 [787, 1627, 2467, 3307]
17 [823, 1663, 2503, 3343]
18 [937, 1777, 2617, 3457, 4297]
19 [991, 1831, 2671, 3511]
20 [1039, 1879, 2719, 3559]
21 [1061, 1901, 2741, 3581, 4421, 5261, 6101]
22 [1153, 1993, 2833, 3673, 4513]
23 [1171, 2011, 2851, 3691]
24 [1259, 2099, 2939, 3779]
25 [1399, 2239, 3079, 3919, 4759]
26 [1571, 2411, 3251, 4091, 4931]
27 [1619, 2459, 3299, 4139]
28 [1709, 2549, 3389, 4229]
29 [1753, 2593, 3433, 4273, 5113, 5953, 6793]
30 [1777, 2617, 3457, 4297]
31 [1901, 2741, 3581, 4421, 5261, 6101]
32 [1993, 2833, 3673, 4513]
33 [1997, 2837, 3677, 4517]
34 [2239, 3079, 3919, 4759]
35 [2341, 3181, 4021, 4861, 5701]
36 [2411, 3251, 4091, 4931]
37 [2473, 3313, 4153, 4993]
38 [2531, 3371, 4211, 5051]
39 [2593, 3433, 4273, 5113, 5953, 6793]
40 [2659, 3499, 4339, 5179]
41 [2677, 3517, 4357, 5197, 6037]
42 [2741, 3581, 4421, 5261, 6101]
43 [2777, 3617, 4457, 5297]
44 [2803, 3643, 4483, 5323, 6163]
45 [2887, 3727, 4567, 5407, 6247]
46 [2957, 3797, 4637, 5477, 6317]
47 [2963, 3803, 4643, 5483, 6323]
48 [3011, 3851, 4691, 5531]
49 [3049, 3889, 4729, 5569]
50 [3181, 4021, 4861, 5701]
51 [3271, 4111, 4951, 5791]
52 [3319, 4159, 4999, 5839, 6679]
53 [3433, 4273, 5113, 5953, 6793]
54 [3517, 4357, 5197, 6037]
55 [3581, 4421, 5261, 6101]
56 [3623, 4463, 5303, 6143, 6983, 7823, 8663]
57 [3643, 4483, 5323, 6163]
58 [3727, 4567, 5407, 6247]
59 [3797, 4637, 5477, 6317]
60 [3803, 4643, 5483, 6323]
61 [3823, 4663, 5503, 6343]
62 [4133, 4973, 5813, 6653]
63 [4159, 4999, 5839, 6679]
64 [4259, 5099, 5939, 6779]
65 [4273, 5113, 5953, 6793]
66 [4349, 5189, 6029, 6869]
67 [4441, 5281, 6121, 6961]
68 [4463, 5303, 6143, 6983, 7823, 8663]
69 [4493, 5333, 6173, 7013, 7853, 8693, 9533]
70 [4801, 5641, 6481, 7321, 8161, 9001]
71 [5009, 5849, 6689, 7529, 8369, 9209]
72 [5021, 5861, 6701, 7541]
73 [5039, 5879, 6719, 7559]
74 [5303, 6143, 6983, 7823, 8663]
75 [5333, 6173, 7013, 7853, 8693, 9533]
76 [5641, 6481, 7321, 8161, 9001]
77 [5651, 6491, 7331, 8171, 9011, 9851, 10691]
78 [5689, 6529, 7369, 8209, 9049]
79 [5849, 6689, 7529, 8369, 9209]
80 [5869, 6709, 7549, 8389]
81 [5923, 6763, 7603, 8443, 9283]
82 [6043, 6883, 7723, 8563, 9403, 10243, 11083, 11923, 12763]
83 [6143, 6983, 7823, 8663]
84 [6173, 7013, 7853, 8693, 9533]
85 [6199, 7039, 7879, 8719]
86 [6373, 7213, 8053, 8893, 9733]
87 [6481, 7321, 8161, 9001]
88 [6491, 7331, 8171, 9011, 9851, 10691]
89 [6529, 7369, 8209, 9049]
90 [6637, 7477, 8317, 9157]
91 [6689, 7529, 8369, 9209]
92 [6763, 7603, 8443, 9283]
93 [6883, 7723, 8563, 9403, 10243, 11083, 11923, 12763]
94 [6917, 7757, 8597, 9437]
95 [7001, 7841, 8681, 9521]
96 [7013, 7853, 8693, 9533]
97 [7027, 7867, 8707, 9547]
98 [7213, 8053, 8893, 9733]
99 [7283, 8123, 8963, 9803]
100 [7331, 8171, 9011, 9851, 10691]
101 [7547, 8387, 9227, 10067]
102 [7723, 8563, 9403, 10243, 11083, 11923, 12763]
103 [7907, 8747, 9587, 10427]
104 [8009, 8849, 9689, 10529, 11369]
105 [8111, 8951, 9791, 10631, 11471]
106 [8171, 9011, 9851, 10691]
107 [8269, 9109, 9949, 10789]
108 [8563, 9403, 10243, 11083, 11923, 12763]
109 [8573, 9413, 10253, 11093, 11933]
110 [8779, 9619, 10459, 11299]
111 [8849, 9689, 10529, 11369]
112 [8951, 9791, 10631, 11471]
113 [8971, 9811, 10651, 11491]
114 [9293, 10133, 10973, 11813, 12653]
115 [9403, 10243, 11083, 11923, 12763]
116 [9413, 10253, 11093, 11933]
117 [9433, 10273, 11113, 11953]
118 [9491, 10331, 11171, 12011]
119 [9719, 10559, 11399, 12239]
120 [9871, 10711, 11551, 12391]
用时 0.04684 秒

【以210m为级差，长度大于3的等差级数无穷多。】这是更强于陶哲轩等人的研究成果！
请问：
（1）这里的长度大于3，指的是什么？
（2）陶哲轩等人的研究成果，指的是什么？

（3）以210m+x为公差的素数等差级数：
公差——素数等差数列
210-6——（23,227,431）
210+6——（11,227,443）
210+6——（17,233,449）
210+6——（251,467,683）
210+6——（1061,1277,1493）

概念：播报编辑2004年，格林和陶哲轩证明存在任意长的素数等差数列。
2004年4月18日，两人宣布：他们证明了“存在任意长度的素数等差数列”，也就是说，对于任意值K，存在K个成等差级数的素数。
例如 K=3，有素数序列3, 5, 7 （每两个差2）……
K=10，有素数序列 199, 409, 619, 829, 1039, 1249, 1459, 1669, 1879, 2089 （每两个差210）。
对于长度为k的素数等差数列，它们的公差能被小于k的所有素数整除。
他们将长达50页的论文——《素数含有任意长度的等差数列》——张贴在当日的预印本网站上，并向《美国数学年鉴》（Annals of Mathematics）投稿 [1]。

以下是一些长度10以上的素数等差数列。
2024-02-02 09:59:49
公差：30030
1 [6007, 36037, 66067, 96097, 126127, 156157, 186187, 216217, 246247, 276277]
2 [23143, 53173, 83203, 113233, 143263, 173293, 203323, 233353, 263383, 293413, 323443, 353473]
3 [53173, 83203, 113233, 143263, 173293, 203323, 233353, 263383, 293413, 323443, 353473]
4 [75307, 105337, 135367, 165397, 195427, 225457, 255487, 285517, 315547, 345577, 375607]
5 [83203, 113233, 143263, 173293, 203323, 233353, 263383, 293413, 323443, 353473]
6 [105337, 135367, 165397, 195427, 225457, 255487, 285517, 315547, 345577, 375607]
7 [516449, 546479, 576509, 606539, 636569, 666599, 696629, 726659, 756689, 786719]
8 [667673, 697703, 727733, 757763, 787793, 817823, 847853, 877883, 907913, 937943]
9 [820793, 850823, 880853, 910883, 940913, 970943, 1000973, 1031003, 1061033, 1091063, 1121093]
10 [850823, 880853, 910883, 940913, 970943, 1000973, 1031003, 1061033, 1091063, 1121093]
11 [1123739, 1153769, 1183799, 1213829, 1243859, 1273889, 1303919, 1333949, 1363979, 1394009]
12 [1195123, 1225153, 1255183, 1285213, 1315243, 1345273, 1375303, 1405333, 1435363, 1465393]
13 [1337431, 1367461, 1397491, 1427521, 1457551, 1487581, 1517611, 1547641, 1577671, 1607701]
14 [1498141, 1528171, 1558201, 1588231, 1618261, 1648291, 1678321, 1708351, 1738381, 1768411, 1798441, 1828471]
15 [1528171, 1558201, 1588231, 1618261, 1648291, 1678321, 1708351, 1738381, 1768411, 1798441, 1828471]
16 [1558201, 1588231, 1618261, 1648291, 1678321, 1708351, 1738381, 1768411, 1798441, 1828471]
17 [1955957, 1985987, 2016017, 2046047, 2076077, 2106107, 2136137, 2166167, 2196197, 2226227]
18 [2562619, 2592649, 2622679, 2652709, 2682739, 2712769, 2742799, 2772829, 2802859, 2832889]
19 [2626837, 2656867, 2686897, 2716927, 2746957, 2776987, 2807017, 2837047, 2867077, 2897107]
20 [2841557, 2871587, 2901617, 2931647, 2961677, 2991707, 3021737, 3051767, 3081797, 3111827]
21 [3199051, 3229081, 3259111, 3289141, 3319171, 3349201, 3379231, 3409261, 3439291, 3469321, 3499351]
22 [3229081, 3259111, 3289141, 3319171, 3349201, 3379231, 3409261, 3439291, 3469321, 3499351]
23 [4113419, 4143449, 4173479, 4203509, 4233539, 4263569, 4293599, 4323629, 4353659, 4383689]
24 [4468339, 4498369, 4528399, 4558429, 4588459, 4618489, 4648519, 4678549, 4708579, 4738609]
25 [4811713, 4841743, 4871773, 4901803, 4931833, 4961863, 4991893, 5021923, 5051953, 5081983]
26 [6904727, 6934757, 6964787, 6994817, 7024847, 7054877, 7084907, 7114937, 7144967, 7174997]
27 [7015627, 7045657, 7075687, 7105717, 7135747, 7165777, 7195807, 7225837, 7255867, 7285897]
28 [7026821, 7056851, 7086881, 7116911, 7146941, 7176971, 7207001, 7237031, 7267061, 7297091, 7327121]
29 [7056851, 7086881, 7116911, 7146941, 7176971, 7207001, 7237031, 7267061, 7297091, 7327121]
30 [7654411, 7684441, 7714471, 7744501, 7774531, 7804561, 7834591, 7864621, 7894651, 7924681]
31 [7909919, 7939949, 7969979, 8000009, 8030039, 8060069, 8090099, 8120129, 8150159, 8180189]
32 [8081737, 8111767, 8141797, 8171827, 8201857, 8231887, 8261917, 8291947, 8321977, 8352007]
公差：60060
1 [4943, 65003, 125063, 185123, 245183, 305243, 365303, 425363, 485423, 545483, 605543, 665603, 725663]
2 [65003, 125063, 185123, 245183, 305243, 365303, 425363, 485423, 545483, 605543, 665603, 725663]
3 [125063, 185123, 245183, 305243, 365303, 425363, 485423, 545483, 605543, 665603, 725663]
4 [167429, 227489, 287549, 347609, 407669, 467729, 527789, 587849, 647909, 707969, 768029]
5 [185123, 245183, 305243, 365303, 425363, 485423, 545483, 605543, 665603, 725663]
6 [227489, 287549, 347609, 407669, 467729, 527789, 587849, 647909, 707969, 768029]
7 [264637, 324697, 384757, 444817, 504877, 564937, 624997, 685057, 745117, 805177]
8 [465523, 525583, 585643, 645703, 705763, 765823, 825883, 885943, 946003, 1006063]
9 [500119, 560179, 620239, 680299, 740359, 800419, 860479, 920539, 980599, 1040659]
10 [765169, 825229, 885289, 945349, 1005409, 1065469, 1125529, 1185589, 1245649, 1305709]
11 [1154177, 1214237, 1274297, 1334357, 1394417, 1454477, 1514537, 1574597, 1634657, 1694717]
12 [2320699, 2380759, 2440819, 2500879, 2560939, 2620999, 2681059, 2741119, 2801179, 2861239]
13 [2356553, 2416613, 2476673, 2536733, 2596793, 2656853, 2716913, 2776973, 2837033, 2897093]
14 [2562097, 2622157, 2682217, 2742277, 2802337, 2862397, 2922457, 2982517, 3042577, 3102637]
15 [3093011, 3153071, 3213131, 3273191, 3333251, 3393311, 3453371, 3513431, 3573491, 3633551]
16 [4856083, 4916143, 4976203, 5036263, 5096323, 5156383, 5216443, 5276503, 5336563, 5396623, 5456683]
17 [4916143, 4976203, 5036263, 5096323, 5156383, 5216443, 5276503, 5336563, 5396623, 5456683]
18 [5610763, 5670823, 5730883, 5790943, 5851003, 5911063, 5971123, 6031183, 6091243, 6151303]
19 [5984453, 6044513, 6104573, 6164633, 6224693, 6284753, 6344813, 6404873, 6464933, 6524993, 6585053]
20 [6044513, 6104573, 6164633, 6224693, 6284753, 6344813, 6404873, 6464933, 6524993, 6585053]
21 [7081871, 7141931, 7201991, 7262051, 7322111, 7382171, 7442231, 7502291, 7562351, 7622411, 7682471]
22 [7141931, 7201991, 7262051, 7322111, 7382171, 7442231, 7502291, 7562351, 7622411, 7682471]
23 [7306933, 7366993, 7427053, 7487113, 7547173, 7607233, 7667293, 7727353, 7787413, 7847473]
24 [7562141, 7622201, 7682261, 7742321, 7802381, 7862441, 7922501, 7982561, 8042621, 8102681]
25 [8066717, 8126777, 8186837, 8246897, 8306957, 8367017, 8427077, 8487137, 8547197, 8607257]
26 [8473831, 8533891, 8593951, 8654011, 8714071, 8774131, 8834191, 8894251, 8954311, 9014371]
27 [9488377, 9548437, 9608497, 9668557, 9728617, 9788677, 9848737, 9908797, 9968857, 10028917]
公差：90090
1 [218723, 308813, 398903, 488993, 579083, 669173, 759263, 849353, 939443, 1029533, 1119623]
2 [308813, 398903, 488993, 579083, 669173, 759263, 849353, 939443, 1029533, 1119623]
3 [409027, 499117, 589207, 679297, 769387, 859477, 949567, 1039657, 1129747, 1219837, 1309927, 1400017]
4 [499117, 589207, 679297, 769387, 859477, 949567, 1039657, 1129747, 1219837, 1309927, 1400017]
5 [589207, 679297, 769387, 859477, 949567, 1039657, 1129747, 1219837, 1309927, 1400017]
6 [802951, 893041, 983131, 1073221, 1163311, 1253401, 1343491, 1433581, 1523671, 1613761, 1703851, 1793941]
7 [862397, 952487, 1042577, 1132667, 1222757, 1312847, 1402937, 1493027, 1583117, 1673207, 1763297, 1853387]
8 [893041, 983131, 1073221, 1163311, 1253401, 1343491, 1433581, 1523671, 1613761, 1703851, 1793941]
9 [952487, 1042577, 1132667, 1222757, 1312847, 1402937, 1493027, 1583117, 1673207, 1763297, 1853387]
10 [983131, 1073221, 1163311, 1253401, 1343491, 1433581, 1523671, 1613761, 1703851, 1793941]
11 [1042577, 1132667, 1222757, 1312847, 1402937, 1493027, 1583117, 1673207, 1763297, 1853387]
12 [3217537, 3307627, 3397717, 3487807, 3577897, 3667987, 3758077, 3848167, 3938257, 4028347]
13 [3657289, 3747379, 3837469, 3927559, 4017649, 4107739, 4197829, 4287919, 4378009, 4468099]
14 [3780509, 3870599, 3960689, 4050779, 4140869, 4230959, 4321049, 4411139, 4501229, 4591319]
15 [4072949, 4163039, 4253129, 4343219, 4433309, 4523399, 4613489, 4703579, 4793669, 4883759]
16 [4116353, 4206443, 4296533, 4386623, 4476713, 4566803, 4656893, 4746983, 4837073, 4927163, 5017253]
17 [4206443, 4296533, 4386623, 4476713, 4566803, 4656893, 4746983, 4837073, 4927163, 5017253]
18 [5052823, 5142913, 5233003, 5323093, 5413183, 5503273, 5593363, 5683453, 5773543, 5863633]
19 [5323027, 5413117, 5503207, 5593297, 5683387, 5773477, 5863567, 5953657, 6043747, 6133837]
20 [5510353, 5600443, 5690533, 5780623, 5870713, 5960803, 6050893, 6140983, 6231073, 6321163]
21 [5959799, 6049889, 6139979, 6230069, 6320159, 6410249, 6500339, 6590429, 6680519, 6770609]
22 [7912181, 8002271, 8092361, 8182451, 8272541, 8362631, 8452721, 8542811, 8632901, 8722991, 8813081]
23 [8002271, 8092361, 8182451, 8272541, 8362631, 8452721, 8542811, 8632901, 8722991, 8813081]
公差：120120
1 [410621, 530741, 650861, 770981, 891101, 1011221, 1131341, 1251461, 1371581, 1491701]
2 [1521809, 1641929, 1762049, 1882169, 2002289, 2122409, 2242529, 2362649, 2482769, 2602889]
3 [2424619, 2544739, 2664859, 2784979, 2905099, 3025219, 3145339, 3265459, 3385579, 3505699]
4 [3294097, 3414217, 3534337, 3654457, 3774577, 3894697, 4014817, 4134937, 4255057, 4375177, 4495297]
5 [3295321, 3415441, 3535561, 3655681, 3775801, 3895921, 4016041, 4136161, 4256281, 4376401]
6 [3414217, 3534337, 3654457, 3774577, 3894697, 4014817, 4134937, 4255057, 4375177, 4495297]
7 [3819709, 3939829, 4059949, 4180069, 4300189, 4420309, 4540429, 4660549, 4780669, 4900789, 5020909]
8 [3939829, 4059949, 4180069, 4300189, 4420309, 4540429, 4660549, 4780669, 4900789, 5020909]
9 [4406821, 4526941, 4647061, 4767181, 4887301, 5007421, 5127541, 5247661, 5367781, 5487901]
10 [4539011, 4659131, 4779251, 4899371, 5019491, 5139611, 5259731, 5379851, 5499971, 5620091]
11 [5275451, 5395571, 5515691, 5635811, 5755931, 5876051, 5996171, 6116291, 6236411, 6356531, 6476651, 6596771, 6716891]
12 [5395571, 5515691, 5635811, 5755931, 5876051, 5996171, 6116291, 6236411, 6356531, 6476651, 6596771, 6716891]
13 [5515691, 5635811, 5755931, 5876051, 5996171, 6116291, 6236411, 6356531, 6476651, 6596771, 6716891]
14 [5635811, 5755931, 5876051, 5996171, 6116291, 6236411, 6356531, 6476651, 6596771, 6716891]
用时 26.21253 秒

7#=210 长度7以上的素数等差数列，公差一定是210的倍数；长度23的素数等差数列的公差一定是23
#的倍数，比如44546738095860。

2024-02-03 11:25:19
公差30030
[100000000000303811753, 100000000000303841783, 100000000000303871813, 100000000000303901843, 100000000000303931873, 100000000000303961903, 100000000000303991933, 100000000000304021963]
[100000000000450235467, 100000000000450265497, 100000000000450295527, 100000000000450325557, 100000000000450355587, 100000000000450385617, 100000000000450415647, 100000000000450445677]
[100000000000532872127, 100000000000532902157, 100000000000532932187, 100000000000532962217, 100000000000532992247, 100000000000533022277, 100000000000533052307, 100000000000533082337]
[100000000001199819473, 100000000001199849503, 100000000001199879533, 100000000001199909563, 100000000001199939593, 100000000001199969623, 100000000001199999653, 100000000001200029683]
[100000000001320770709, 100000000001320800739, 100000000001320830769, 100000000001320860799, 100000000001320890829, 100000000001320920859, 100000000001320950889, 100000000001320980919, 100000000001321010949]
[100000000001714530777, 100000000001714560807, 100000000001714590837, 100000000001714620867, 100000000001714650897, 100000000001714680927, 100000000001714710957, 100000000001714740987]
[100000000001738578619, 100000000001738608649, 100000000001738638679, 100000000001738668709, 100000000001738698739, 100000000001738728769, 100000000001738758799, 100000000001738788829]
[100000000001851945757, 100000000001851975787, 100000000001852005817, 100000000001852035847, 100000000001852065877, 100000000001852095907, 100000000001852125937, 100000000001852155967]
[100000000001921129023, 100000000001921159053, 100000000001921189083, 100000000001921219113, 100000000001921249143, 100000000001921279173, 100000000001921309203, 100000000001921339233]
[100000000002086909761, 100000000002086939791, 100000000002086969821, 100000000002086999851, 100000000002087029881, 100000000002087059911, 100000000002087089941, 100000000002087119971]
用时 15238.40439 秒

时间取决于搜索的区间跨度。
2024-02-03 20:29:47
公差60060
[100000000000127728793, 100000000000127788853, 100000000000127848913, 100000000000127908973, 100000000000127969033, 100000000000128029093, 100000000000128089153, 100000000000128149213]
[100000000000542401819, 100000000000542461879, 100000000000542521939, 100000000000542581999, 100000000000542642059, 100000000000542702119, 100000000000542762179, 100000000000542822239]
[100000000001683102703, 100000000001683162763, 100000000001683222823, 100000000001683282883, 100000000001683342943, 100000000001683403003, 100000000001683463063, 100000000001683523123]
[100000000001750561749, 100000000001750621809, 100000000001750681869, 100000000001750741929, 100000000001750801989, 100000000001750862049, 100000000001750922109, 100000000001750982169]
[100000000002227539999, 100000000002227600059, 100000000002227660119, 100000000002227720179, 100000000002227780239, 100000000002227840299, 100000000002227900359, 100000000002227960419]
[100000000003220332343, 100000000003220392403, 100000000003220452463, 100000000003220512523, 100000000003220572583, 100000000003220632643, 100000000003220692703, 100000000003220752763]
[100000000003281425401, 100000000003281485461, 100000000003281545521, 100000000003281605581, 100000000003281665641, 100000000003281725701, 100000000003281785761, 100000000003281845821]
[100000000003716524449, 100000000003716584509, 100000000003716644569, 100000000003716704629, 100000000003716764689, 100000000003716824749, 100000000003716884809, 100000000003716944869]
[100000000004051256701, 100000000004051316761, 100000000004051376821, 100000000004051436881, 100000000004051496941, 100000000004051557001, 100000000004051617061, 100000000004051677121]
[100000000004146725947, 100000000004146786007, 100000000004146846067, 100000000004146906127, 100000000004146966187, 100000000004147026247, 100000000004147086307, 100000000004147146367]
用时 51513.22745 秒