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9042Re: [PrimeNumbers] Largest Ordinary Prime?

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  • Andy Steward
    Oct 3, 2002
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      Firstly, congratulations to Paul, Paul, David and Bouk.

      Secondly, DAMN. I had this great idea while I was on holiday
      about ten days ago. It appears to be much the the same idea that
      you guys had a long while earlier ;-)

      I used my experience in trying to prove Gigantic GRUs to model
      how many digits of prime factors I would expect to extract from
      a cyclotomic factor of a given size given the amount of ECM work
      I have done on such factors to date (about 7-10 GHz hours on each
      composite on average, though some I've just started and a few have
      had thousands of hours).

      I then generated a list of promising composite exponents c such that
      2^c-1 gave a decent chance of being useful in proving 2^a - 2^b +/- 1
      where c=a-b. 64680 came out at 19.85%, so your 30% indicates how much
      more work you did on it (and a bit of luck). I reckon the best few
      exponents of around the same size are: 65520, 75600, 69300, 83160,
      73920, 70560 then 64680.

      Another thought I had was to use 2^c-1 where it's a Mersenne prime
      ... or c=2p, 3p etc where 2^p-1 is a Mersenne prime: diminishing
      returns but worth a try for small multiples.

      Ah well, I'll stick to the GRUs.

      Good luck,
      Andy
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