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Re: [PrimeNumbers] Re: Largest Ordinary Prime?

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  • Andy Steward
    ... Did you mean 110880? I get an expected factorisation of 18.4% for that one, but only 9.7% for 118080. By my model, 110880 is the most promising exponent in
    Message 1 of 22 , Oct 5, 2002
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      Paul Underwood wrote:

      > Bouk suggests having a look at 118080.

      Did you mean 110880? I get an expected factorisation of
      18.4% for that one, but only 9.7% for 118080. By my model,
      110880 is the most promising exponent in (85680,750000]

      Here's a list of exponents where each entry has a higher
      expected factorisation yield than any larger:

      Exponent, factors, expectation
      1680,40,100.00%
      1740,24,96.33%
      1890,32,95.48%
      2100,36,94.98%
      2520,48,91.05%
      2640,40,88.53%
      2940,36,88.41%
      3360,48,86.53%
      3780,48,82.88%
      3960,48,80.44%
      4200,48,79.05%
      4620,48,78.67%
      5040,60,78.06%
      5460,48,71.49%
      5880,48,69.92%
      6120,48,69.12%
      7560,64,68.14%
      7920,60,63.67%
      9240,64,62.61%
      10080,72,61.54%
      10920,64,56.45%
      12600,72,53.33%
      13860,72,52.73%
      15120,80,51.39%
      16380,72,46.94%
      18480,80,46.48%
      20160,84,43.47%
      21840,80,41.16%
      27720,96,39.70%
      30240,96,36.29%
      32760,96,35.11%
      36960,96,31.72%
      37800,96,30.69%
      40320,96,28.96%
      41580,96,28.95%
      42840,96,28.73%
      55440,120,28.00%
      65520,120,24.39%
      75600,120,21.10%
      83160,128,21.05%
      85680,120,19.43%
      110880,144,18.40%
      131040,144,15.89%
      138600,144,15.06%
      166320,160,14.15%
      171360,144,12.41%
      196560,160,12.14%
      221760,168,11.37%
      240240,160,10.17%
      277200,180,9.96%
      332640,192,8.95%
      360360,192,8.35%
      393120,192,7.64%
      415800,192,7.26%
      443520,192,6.75%
      471240,192,6.43%
      480480,192,6.31%
      498960,200,6.29%
      554400,216,6.21%
      556920,192,5.47%
      720720,240,5.39%
      739200,192,4.09%
      742560,192,4.08%
      748440,192,3.93%
      749700,162,3.33%

      HTH,
      Andy
    • Bouk de Water
      ... 110880 it should be indeed. Moreover because phi(36960,2) is a prp. 36960 * 2 = 73920 2^73920-1 is already BLS 36960 * 3 = 110880 2^110880-1 is about 1300
      Message 2 of 22 , Oct 5, 2002
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        --- Andy Steward <aads@...> wrote:
        > Paul Underwood wrote:
        >
        > > Bouk suggests having a look at 118080.
        >
        > Did you mean 110880? I get an expected factorisation of
        > 18.4% for that one, but only 9.7% for 118080. By my model,
        > 110880 is the most promising exponent in (85680,750000]

        110880 it should be indeed. Moreover because phi(36960,2) is a prp.

        36960 * 2 = 73920

        2^73920-1 is already BLS

        36960 * 3 = 110880

        2^110880-1 is about 1300 digits short for Konyagin-Pomarance.

        Bouk.

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      • Phil Carmody
        ... Not yet... ;-) Phil ===== First rule of Factor Club - you do not talk about Factor Club. Second rule of Factor Club - you DO NOT talk about Factor Club.
        Message 3 of 22 , Oct 5, 2002
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          --- Bouk de Water <bdewater@...> wrote:
          > Moreover because phi(36960,2) is a prp.
          ^^^
          > 36960 * 2 = 73920
          >
          > 2^73920-1 is already BLS

          Not yet... ;-)

          Phil



          =====
          First rule of Factor Club - you do not talk about Factor Club.
          Second rule of Factor Club - you DO NOT talk about Factor Club.
          Third rule of Factor Club - when the cofactor is prime, or you've trial-
          divided up to the square root of the number, the factoring is over.

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        • David Broadhurst
          ... True, oh sage. But 2312 digits would be a mere bagatelle for primo. More significantly what a would make 2^a*(2^73920-1)-1 PrP? On average you have to
          Message 4 of 22 , Oct 5, 2002
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            Phil:

            > Not yet... ;-)

            True, oh sage.

            But 2312 digits would be
            a mere bagatelle for primo.

            More significantly what "a" would make
            2^a*(2^73920-1)-1
            PrP?

            On average you have to wait a long time
            and by then 2^a gives you most of BLS anyway,
            thus eroding you factorization work.

            It was Paul U's a=15 that was really notable in

            2^15*(2^64680-1)-1

            David
          • Andrey Kulsha
            ... [snip] ... To be precise, 239 phi-factors and 5.895144%: http://groups.yahoo.com/group/primenumbers/files/Factors/m720720.zip Best, Andrey [Non-text
            Message 5 of 22 , Oct 13, 2002
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              Andy Steward wrote:

              > Here's a list of exponents where each entry has a higher
              > expected factorisation yield than any larger:
              >
              > Exponent, factors, expectation
              [snip]
              > 720720,240,5.39%

              To be precise, 239 phi-factors and 5.895144%:

              http://groups.yahoo.com/group/primenumbers/files/Factors/m720720.zip

              Best,

              Andrey


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