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Re: [PrimeNumbers] 4-Brilliant results

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  • Phil Carmody
    ... [SNIP] Grand work, Jim! Do we yet have a heuristic for the delta from the power of ten for each of the brilliant types. It appears that with the increased
    Message 1 of 4 , Jun 2, 2002
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      --- jim_fougeron <jfoug@...> wrote:
      > These are minimal 4 brilliant numbers:
      [SNIP]

      Grand work, Jim!

      Do we yet have a heuristic for the delta from the power of ten for
      each of the brilliant types. It appears that with the increased
      choice of primes, there's a limited growth of the delta, and
      sometimes it almost looks like it's hardly growing at all. However,
      any formal attack evades me. Probably the 2 factor type is the most
      attackable.

      Phil

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    • alpertron
      ... [snip] It appears that your computer worked a lot. Thanks a lot, Jim. I ve just uploaded you results to: http://www.alpertron.com.ar/BRILLIANT.HTM Best
      Message 2 of 4 , Jun 2, 2002
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        --- In primenumbers@y..., "jim_fougeron" <jfoug@k...> wrote:
        > These are minimal 4 brilliant numbers:

        [snip]

        It appears that your computer worked a lot. Thanks a lot, Jim.

        I've just uploaded you results to:

        http://www.alpertron.com.ar/BRILLIANT.HTM

        Best regards,

        Dario Alejandro Alpern
        Buenos Aires - Argentina
        http://www.alpertron.com.ar/ENGLISH.HTM
      • jim_fougeron
        ... Actually no. I worked more than my computer (for the larger numbers at least). When starting out, I used this technique: (for 10^29+ and 10^30+) 1. trial
        Message 3 of 4 , Jun 3, 2002
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          --- In primenumbers@y..., "alpertron" <alpertron@h...> wrote:
          >--- In primenumbers@y..., "jim_fougeron" <jfoug@k...> wrote:
          >> These are minimal 4 brilliant numbers:
          >
          >[snip]
          >
          >It appears that your computer worked a lot. Thanks a lot, Jim.

          Actually no. I worked more than my computer (for the larger numbers
          at least).

          When starting out, I used this technique: (for 10^29+ and 10^30+)
          1. trial factor a 5000000 range with CPAPSieve up to prime 10000000
          2. compute ceil((10^29)^.25) (17782795)
          3. trial factor the values left over up to this point.
          4. Whatever items factored out on step 2 (not too many) are the only
          candidates which can be brilliant-4.
          5. Check each of these by fully factoring until a brilliant was found
          6. For 10^30+ step 2 is ceil((10^30)^.25) which is 31622776

          For the larger numbers (where I show a lot of additional brilliants,
          and "large enough" 4 factor results), I used this method: (10^35+)

          1. trial factor a 5000000 range with CPAPSieve up to prime 100000000
          2. modified CPAPSieve to not eliminate candidates, but to count how
          many factors each had seen. Then simply run it to prime 1000000000
          and output all candidates which 4 factors were found.

          Method 2 is a constant time method, however, each time you increase
          the size of the brilliant factors by 1 digit, this method take 10
          times as long to complete.

          Using something like the method 2 would quickly these brilliants while
          the size of the factors are small.

          Jim.

          >I've just uploaded you results to:
          >
          >http://www.alpertron.com.ar/BRILLIANT.HTM
          >
          >Best regards,
          >
          >Dario Alejandro Alpern
          >Buenos Aires - Argentina
          >http://www.alpertron.com.ar/ENGLISH.HTM
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