Quote:
Originally Posted by mart_r
Code:
gap: gap between the respective first members of the twin primes
F: first instance gap
M: maximal gap
R: record merit
merit: 2 * c_2 * gap / [log(p) * log(p + gap)] where c_2 = the twin prime constant = 0.6601618...
i: number of intermediate primes between the twins
k: initial twin p = 6 * k ± 1
gap/6 gap FMR discoverer year merit i k
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1 6 FMR R.Rathbun 1998 1.78 0 1
2 12 FM R.Rathbun 1998 1.61 1 3
3 18 FM R.Rathbun 1998 1.55 2 7
4 24 F R.Rathbun 1998 0.76 1 103
5 30 FMR R.Rathbun 1998 2.00 4 12
6 36 FM R.Rathbun 1998 1.41 3 52
7 42 F R.Rathbun 1998 0.93 5 378
8 48 F R.Rathbun 1998 1.60 4 87
9 54 F R.Rathbun 1998 1.25 4 313
10 60 F R R.Rathbun 1998 2.06 7 77
11 66 F R.Rathbun 1998 1.56 7 287
12 72 FMR R.Rathbun 1998 2.69 10 58
13 78 F R.Rathbun 1998 2.05 9 192
14 84 F R.Rathbun 1998 1.97 7 298
15 90 F R.Rathbun 1998 1.77 9 597
16 96 F R.Rathbun 1998 2.14 7 357
17 102 F R.Rathbun 1998 1.75 7 1075
18 108 F R R.Rathbun 1998 2.73 8 220
19 114 F R.Rathbun 1998 1.51 10 3563
20 120 F R R.Rathbun 1998 2.94 15 248
21 126 F R.Rathbun 1998 1.88 11 2042
22 132 F R.Rathbun 1998 2.42 10 800
23 138 F R R.Rathbun 1998 3.88 17 147
24 144 F R.Rathbun 1998 1.88 13 3843
25 150 FMR R.Rathbun 1998 4.56 18 110
26 156 F R.Rathbun 1998 2.11 11 3257
27 162 F R.Rathbun 1998 2.41 18 2063
28 168 FM R.Rathbun 1998 3.64 18 397
29 174 F R.Rathbun 1998 2.06 14 6458
30 180 F R.Rathbun 1998 2.77 16 1755
31 186 F R.Rathbun 1998 2.21 17 6227
32 192 F R.Rathbun 1998 3.08 22 1438
33 198 F R.Rathbun 1998 3.14 20 1507
34 204 F R.Rathbun 1998 2.47 15 5638
35 210 FM R.Rathbun 1998 3.67 18 980
36 216 F R.Rathbun 1998 2.24 16 13372
37 222 F R.Rathbun 1998 3.15 21 2560
38 228 F R.Rathbun 1998 2.61 17 7637
39 234 F R.Rathbun 1998 2.80 19 6018
40 240 F R.Rathbun 1998 3.44 27 2438
41 246 F R.Rathbun 1998 2.92 19 6332
42 252 F R.Rathbun 1998 3.01 25 6088
43 258 F R.Rathbun 1998 2.63 20 14542
44 264 F R.Rathbun 1998 2.79 21 11833
45 270 F R.Rathbun 1998 3.86 25 2478
46 276 F R.Rathbun 1998 3.24 19 6692
47 282 FM R.Rathbun 1998 4.11 25 2233
48 288 F R.Rathbun 1998 3.19 21 9105
49 294 F R.Rathbun 1998 3.44 25 6808
50 300 F R.Rathbun 1998 3.37 21 8432
51 306 F R.Rathbun 1998 2.88 24 23277
52 312 F R.Rathbun 1998 3.55 25 7968
53 318 F R.Rathbun 1998 3.75 26 6585
54 324 F R.Rathbun 1998 3.05 21 23133
55 330 F R.Rathbun 1998 3.40 22 13815
56 336 F R.Rathbun 1998 3.12 24 25347
57 342 F R.Rathbun 1998 3.51 24 13953
58 348 F R.Rathbun 1998 4.00 28 7462
59 354 F R.Rathbun 1998 3.10 20 35798
60 360 F R.Rathbun 1998 3.21 27 31972
61 366 F R.Rathbun 1998 3.39 23 25587
62 372 FMR R.Rathbun 1998 5.08 26 3090
63 378 F R.Rathbun 1998 3.73 25 17475
64 384 F R.Rathbun 1998 2.91 25 90423
65 390 F R.Rathbun 1998 4.33 29 9002
66 396 F R.Rathbun 1998 3.10 25 72942
67 402 F R.Rathbun 1998 3.91 28 19033
68 408 F R.Rathbun 1998 4.01 26 17850
69 414 F R.Rathbun 1998 3.69 23 32378
70 420 F R R.Rathbun 1998 5.35 36 4377
71 426 F R.Rathbun 1998 4.43 33 12952
72 432 F R.Rathbun 1998 4.05 32 23693
73 438 F R.Rathbun 1998 3.65 30 48785
74 444 F R.Rathbun 1998 3.87 29 37058
75 450 F R.Rathbun 1998 4.57 39 14845
76 456 F R.Rathbun 1998 3.70 30 58077
77 462 F R.Rathbun 1998 4.05 29 35368
78 468 F R.Rathbun 1998 3.63 30 77697
79 474 F R.Rathbun 1998 4.64 34 18308
80 480 F R.Rathbun 1998 3.92 35 55143
81 486 F R.Rathbun 1998 4.30 30 33397
82 492 F R.Rathbun 1998 3.84 28 74400
83 498 FMR R.Rathbun 1998 6.43 40 4070
84 504 F R.Rathbun 1998 4.71 39 24168
85 510 F R.Rathbun 1998 4.90 37 20478
86 516 F R.Rathbun 1998 3.67 29 138187
87 522 F R.Rathbun 1998 4.02 29 80868
88 528 F R.Rathbun 1998 4.98 42 22890
89 534 F R.Rathbun 1998 4.35 35 56523
90 540 F R.Rathbun 1998 4.41 34 55632
91 546 F R.Rathbun 1998 4.74 32 37942
92 552 F R.Rathbun 1998 4.25 41 81448
93 558 F R.Rathbun 1998 4.72 30 44660
94 564 F R.Rathbun 1998 3.77 40 213103
95 570 F R.Rathbun 1998 4.27 41 97545
96 576 F R.Rathbun 1998 3.58 39 354662
97 582 F R.Rathbun 1998 5.32 39 27620
98 588 F R.Rathbun 1998 5.36 41 27977
99 594 F R.Rathbun 1998 3.66 36 383148
100 600 F R.Rathbun 1998 5.07 40 44905
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The gap of 60 with merit 2.06 does not have record merit. The gap of 60 is between (461, 463) and (521, 523). There is a gap of 72 between (347, 349) and (419, 421) with merit 2.69 before it. Therefore, the R in column 3 for the gap of 60 should be removed. Similarly, every R in column 3 without an M should be removed. Just like regular prime gaps, all twin prime gaps with record merit are maximal twin prime gaps.