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Shallow factoring of very large numbers

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  • Phil Carmody
    If I were to hypothetically have some 7000-digit numbers. How many divisors should I expect to be able to find trivially (trial-divide to a few million, and
    Message 1 of 1 , Feb 26 12:22 AM
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      If I were to hypothetically have some 7000-digit numbers. How many
      divisors should I expect to be able to find trivially (trial-divide
      to a few million, and half a dozen B1=2000 ECs) on average? And
      what's the largest number of factors I should expect from a set of a
      few dozen such numbers? (I've got only one to yield 5 factors out of
      a sample of 10 so far, most yield only 2 or 3 factors :-( )

      Theory suggests that it should be ~ln ln (pmax), independent of the
      size of the number. So if pmax=10^15, that's about 3 and a half
      factors, so I appear a little below par.

      Phil

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