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Re: [PrimeNumbers] composite trinomials

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  • Bouk de Water
    ... Sorry, BOTH are not prp. I thought Paul only meant the largest one. Bouk. __________________________________________________ Do You Yahoo!? Sign up for SBC
    Message 1 of 11 , Jul 2, 2002
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      --- paulunderwooduk <paulunderwood@...> wrote:
      > Hi,
      > I have just seen these:
      > 9999 2^65536-2^256+1 19729 x37 02 prime #0207
      > 9999 2^262144-2^512+1 78914 x37 02 #0207
      > which look improbable and a BLS no-hoper.
      > PFGW Version 20020515.Win_Dev (Beta software, 'caveat utilitor')

      Sorry, BOTH are not prp. I thought Paul only meant the largest one.

      Bouk.

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    • Bouk de Water
      I have a yahoo mailbox myself and sometimes I get messages from other members of the group many hours, sometimes more than a day late. 6 people had already
      Message 2 of 11 , Jul 2, 2002
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        I have a yahoo mailbox myself and sometimes I get messages from other members
        of the group many hours, sometimes more than a day late.

        6 people had already discussed the composite sumbmitted numbers by x37 and I
        had only received Paul's announcement. Do more people have this problem? They
        are quite eager to tell me how to do something about my hairloss or shrink my
        ass in twenty days but sending through messages is obviously not making them
        money.

        Bouk.

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      • paulunderwooduk
        ... I should watch my grammar! If you want a challange, dislodge some of my gigantic PRP trinomials at Henri s site:
        Message 3 of 11 , Jul 2, 2002
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          Bouk wrote:
          > --- I wrote:
          > > Hi,
          > > I have just seen these:
          > > 9999 2^65536-2^256+1 19729 x37 02 prime #0207
          > > 9999 2^262144-2^512+1 78914 x37 02 #0207
          > > which look improbable and a BLS no-hoper.
          > > PFGW Version 20020515.Win_Dev (Beta software, 'caveat utilitor')
          >
          > Sorry, BOTH are not prp. I thought Paul only meant the largest one.
          >
          > Bouk.
          I should watch my grammar!
          If you want a challange, dislodge some of my gigantic PRP trinomials
          at Henri's site:
          http://www.primenumbers.net/prptop/prptop.php
          If you can't do that I can generate a challanging one if you like!
          Paul
        • Bouk de Water
          ... Actually I did browse them for proofs. One or two could be proven with a large ECM effort. This one is a good very good one to try: 2^64695-2^15-1 with
          Message 4 of 11 , Jul 3, 2002
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            > If you want a challange, dislodge some of my gigantic PRP trinomials
            > at Henri's site:
            > http://www.primenumbers.net/prptop/prptop.php

            Actually I did browse them for proofs. One or two could be proven with a large
            ECM effort.

            This one is a good very good one to try:

            2^64695-2^15-1 with 19476 digits.

            N+1 = 2^15*(2^64680-1)

            (2^64680-1) has 96 cyclotomic divisors.

            T 64680={ 1, 2, 3, 4, 5, 6, 7, 8, 10, 11, 12, 14, 15, 20, 21, 22, 24, 28, 30,
            33, 35, 40, 42, 44, 49, 55, 56, 60, 66, 70, 77, 84, 88, 98, 105, 110, 120, 132,
            140, 147, 154, 165, 168, 196, 210, 220, 231, 245, 264, 280, 294, 308, 330, 385,
            392, 420, 440, 462, 490, 539, 588, 616, 660, 735, 770, 840, 924, 980, 1078,
            1155, 1176, 1320, 1470, 1540, 1617, 1848, 1960, 2156, 2310, 2695, 2940, 3080,
            3234, 4312, 4620, 5390, 5880, 6468, 8085, 9240, 10780, 12936, 16170, 21560,
            32340, 64680 } [96]

            So: (2^64680-1) =
            phi(1,2)*phi(2,2)*phi(3,2)*phi(4,2)*.....*phi(21560,2)*phi(32340,2)*phi(64680,2)

            There are aurifeuillian factors (L and M) as well when for phi(n,2) n=4*k and
            k=odd.

            L=2^h-2^k+1, M=2^h+2^k+1, h=2k-1. Take gcd's with phi(4*k,2) and L or M.

            E.g. phi(2156,2) can be divided in a L and M part as 2156 = 4*539

            L: 10781.81929.90317512080398683509507180285854441.P83
            M:
            2136469147429.111206916097779728932051224808777.1297662995123479965752936319854262257.P46

            There is great deal of work already done in the cunninghamproject. I would
            expect factorization to be more than 25% done. If one reaches 30% David
            Broadhurst can do his KP magic.

            Bouk de Water.





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          • Bouk de Water
            And for die-hards: 2^118843-2^43+1 with 35776 digits. N-1: 2^43*(2^118800-1) T 118800={ 1, 2, 3, 4, 5, 6, 8, 9, 10, 11, 12, 15, 16, 18, 20, 22, 24, 25, 27, 30,
            Message 5 of 11 , Jul 3, 2002
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              And for die-hards:

              2^118843-2^43+1 with 35776 digits.

              N-1: 2^43*(2^118800-1)

              T 118800={ 1, 2, 3, 4, 5, 6, 8, 9, 10, 11, 12, 15, 16, 18, 20, 22, 24, 25, 27,
              30, 33, 36, 40, 44, 45, 48, 50, 54, 55, 60, 66, 72, 75, 80, 88, 90, 99, 100,
              108, 110, 120, 132, 135, 144, 150, 165, 176, 180, 198, 200, 216, 220, 225, 240,
              264, 270, 275, 297, 300, 330, 360, 396, 400, 432, 440, 450, 495, 528, 540, 550,
              594, 600, 660, 675, 720, 792, 825, 880, 900, 990, 1080, 1100, 1188, 1200, 1320,
              1350, 1485, 1584, 1650, 1800, 1980, 2160, 2200, 2376, 2475, 2640, 2700, 2970,
              3300, 3600, 3960, 4400, 4752, 4950, 5400, 5940, 6600, 7425, 7920, 9900, 10800,
              11880, 13200, 14850, 19800, 23760, 29700, 39600, 59400, 118800 } [120]

              But that one is extremely hard. Don't try this at home, folks!

              Bouk.



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