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11935Gaps between twin prime pairs

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  • andrew_j_walker
    Mar 25, 2003
      Has anyone come across research on this subject? A quick check on the
      web didn't reveal anything.

      I modified the program in pi2e.zip at
      http://www.trnicely.net/index.html to look at the gaps between
      successive twin prime pairs, taking the distance to be the
      difference between the lower member of each pair. With this program
      I was only able to go up to ~ 4.29*10^9

      The maximal values found for the gaps are:
      (lowest member 1st pair, lowest member next pair, diff.)
      3 5 2
      5 11 6
      17 29 12
      41 59 18
      71 101 30
      311 347 36
      347 419 72
      659 809 150
      2381 2549 168
      5879 6089 210
      13397 13679 282
      18539 18911 372
      24419 24917 498
      62297 62927 630
      187907 188831 924
      687521 688451 930
      688451 689459 1008
      850349 851801 1452
      2868959 2870471 1512
      4869911 4871441 1530
      9923987 9925709 1722
      14656517 14658419 1902
      17382479 17384669 2190
      30752231 30754487 2256
      32822369 32825201 2832
      96894041 96896909 2868
      136283429 136286441 3012
      234966929 234970031 3102
      248641037 248644217 3180
      255949949 255953429 3480
      390817727 390821531 3804
      698542487 698547257 4770
      2466641069 2466646361 5292
      4289385521 4289391551 6030

      Also, the first multiple of 6 for which a gap
      of that size wasn't found was 3444. In all the first
      occurrence was found for 698 gap sizes between
      2 and 6030 inclusive.

      I'd like to take this higher, so if anyone has code
      that can be used for higher values than above and
      is faster please let me know! Also if this has already
      been done to higher values please let me know so
      I'm not wasting my time!

      Thanks,

      Andrew Walker
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