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Old 2020-01-07, 18:40   #153
Bobby Jacobs
 
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May 2018

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Quote:
Originally Posted by mart_r View Post
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
-----------------------------------------------------------------
    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
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.
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