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Re: [PrimeNumbers] Improving Jens Kruse Andersen quadratic primes

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  • Jens Kruse Andersen
    ... Nice work. I also considered trying to shift when I found the symmetric quadratic. I knew the requested 50000 primes was far out of reach and was too lazy
    Message 1 of 16 , May 5, 2003
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      Adam wrote:
      > A slight modification in this polynomial yields a slightly higher
      > count of primes. In searching for primes of the form ax^2+bx+c, it
      > is good to put the axis of symmetery at -b/2a= so that when x
      > yields a prime value then 100001-x also yields a prime value (what we
      > Americans call a "two-fer," for two for one sales). The general
      > principle is sound but one should realize that, once a candidate
      > formula is found, the value at x=1 might be composite while the value
      > at x=100001 might be prime, so that shifting x by 1 would up the
      > prime count. In this fashion I identified a shift of 5357 giving 16
      > more primes. The polynomial x^2-89287*x+1991687729 gives 44500 Prp
      > on the range x=1..100000.
      >
      > Adam Stinchcombe

      Nice work. I also considered trying to shift when I found the symmetric
      quadratic. I knew the requested 50000 primes was far out of reach and was too
      lazy to try the shift. I did no heuristics but did not expect as many as 16
      extra primes.
      Brian Trial's best attempt at www.shyamsundergupta.com/canyoufind.htm is a
      shift of my second best, but he found it independently. It only has one extra
      prime and only shifts the symmetri axis from 50000.5 to 49999.5. Maybe he did
      not shift but started with a slightly asymmetric quadratic on the interval
      1..100000.

      --
      Jens Kruse Andersen
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