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Re: Gaps between twin prime pairs

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  • andrew_j_walker
    Using a newer version of this program by Thomas Nicely (uses GMP) with my own modifications, I m now extending this further, hopefully up to 10^12. New results
    Message 1 of 2 , Apr 30, 2003
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      Using a newer version of this program by Thomas Nicely (uses GMP)
      with my own modifications, I'm now extending this further, hopefully
      up to 10^12. New results are at the bottom.

      --- In primenumbers@yahoogroups.com, "andrew_j_walker" <ajw01@u...>
      wrote:
      >
      > 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

      19181736269 19181742551 6282
      24215097497 24215103971 6474
      24857578817 24857585369 6552

      > 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.
      >
      The first gap now not found is 4596. Now there are 940 first
      gaps found up to 6552.

      Andrew
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