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Prime paydirt

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  • Ralph Twain
    Some of you might recall that I posted a while ago on the Primeform list about some proving code I was working on. Thanks to some off-list input and a
    Message 1 of 1 , Mar 30, 2004
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      Some of you might recall that I posted a while ago on
      the Primeform list about some proving code I was
      working on.
      Thanks to some off-list input and a custom-built
      sieve, I started the program hunting for extreme
      3-Carmichaels (the form with the record most within
      reach).
      I looked at the form A*2*3*23*29*31*37*41*
      (5*7*11*13*17*19)^125 + 1, to keep the density high.

      300 million candidates sieved to 1.6 million. After
      16 hours of testing at 28/sec, I had 35,000+ PRPs.
      About 2/3 of the time was spent in the PRPing stage
      (which would have taken PFGW about twice as long to
      do). Two of the 350 PRPs that passed stage 2 also
      passed stage 3. They are:
      16004567543085228*1616615^125+1 and
      44914255322100696*1616615^125+1
      p^2+p-1 and (p^3+p^2-p+1)/2 are also prime. The three
      terms have, respectively, 793, 1585, and 2377 digits,
      so the extreme 3-Carmichaels have 4754.

      I've started a larger run to at least get the smallest
      term over 1000 digits. Developing...

      R.A. Twain

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