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Re: [PrimeNumbers] AP19, AP20 with difference 19#

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  • Jaroslaw Wroblewski
    I have changed my program searching for AP with difference 19# from AP19 exhaustive to AP21 exhaustive, which allowed me to move much faster. I have found:
    Message 1 of 4 , Dec 2, 2008
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      I have changed my program searching for AP with difference 19# from
      AP19 exhaustive to AP21 exhaustive, which allowed me to move much
      faster.

      I have found:

      AP21: 28112131522731197609+19#*n, n=0..20

      This is:
      The smallest EXISTING AP21 with difference 19#.
      The first KNOWN case of 21 simultaneous primes according to JKA rules.
      The first KNOWN AP21 with any difference and terms above 2^64.

      I have used 42 computers yesterday during the day and total of 58
      overnight, making something like 50 computers on average times 24
      hours since the program was restarted after change.

      After the restart I found one AP19, and the above AP21 was the second AP19+.

      With 5 AP18 (for a total of 7 AP18+) I think I fully deserved to find
      one AP19, perhaps two with some luck. I shouldn't really expect any
      AP20, so AP21 is a miracle.

      Jarek
    • Jens Kruse Andersen
      ... Big congratulations! An AP21 with the minimal difference 19# is amazing. http://hjem.get2net.dk/jka/math/aprecords.htm and
      Message 2 of 4 , Dec 3, 2008
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        Jaroslaw Wroblewski wrote:
        > AP21: 28112131522731197609+19#*n, n=0..20
        >
        > This is:
        > The smallest EXISTING AP21 with difference 19#.
        > The first KNOWN case of 21 simultaneous primes according to JKA rules.
        > The first KNOWN AP21 with any difference and terms above 2^64.

        Big congratulations!
        An AP21 with the minimal difference 19# is amazing.

        http://hjem.get2net.dk/jka/math/aprecords.htm and
        http://hjem.get2net.dk/jka/math/simultprime.htm are updated.

        --
        Jens Kruse Andersen
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