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Old 2020-01-07, 23:29   #154
rudy235
 
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Jun 2015
Vallejo, CA/.

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I like it. Dr Nicely format was very suscinct and highly informative. I believe you have managed to do the same here!

Quote:
Originally Posted by mart_r View Post
I was digging through half of the web to track down the sources for this table. I tried to make it look more like the tables from T. R. Nicely.

The earliest mention of a search explicitly for gaps between prime twins was from a NMBRTHRY letter on Nov 23, 1998 by Randall L. Rathbun.
If you know of any earlier work from anyone who was studying gaps between prime twins, please let me know so I can update the table.

I can only give the first few lines here, as the whole table exceeds 65536 characters.
See attachment for the whole table.

Attached is also a more spreadsheet-friendly version in the format used earlier.
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
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