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Re: Two prime factors formula?

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  • Werner D. Sand
    I wouldn t call sum(something) a formula, but a calculating instruction. For example pi(x) = sum(1)(2,3,5…x) looks great, but is only an instruction to count
    Message 1 of 4 , Feb 2, 2007
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      I wouldn't call sum(something) a formula, but a calculating
      instruction. For example pi(x) = sum(1)(2,3,5…x) looks great, but is
      only an instruction to count primes up to x, while the formula is
      pi(x) ~ x/ln x. Thus pi(2)(x) = sum (pi(x/p i)-i+1) (i=1…pi(x^(1/2))
      looks very spectacular, but is only the description of counting the
      semiprimes up to x. The formula for it might be
      pi(2)(x) ~ n/(e ln ln x) or the like, perhaps someone knows a better
      one.

      Werner







      --- In primenumbers@yahoogroups.com, "Werner D. Sand"
      <Theo.3.1415@...> wrote:
      >
      > Perfect answer! Thank you, Mike.
      >
      >
      >
      >
      > --- In primenumbers@yahoogroups.com, mikeoakes2@ wrote:
      > >
      > > An integer with exactly k prime factors is somethimes called a
      > > k-almost-prime.
      > >
      > > Here's a link:-
      > > http://mathworld.wolfram.com/AlmostPrime.html
      > >
      > > -Mike Oakes
      > >
      > >
      > > -----Original Message-----
      > > From: Theo.3.1415@
      > > To: primenumbers@yahoogroups.com
      > > Sent: Wed, 31 Jan 2007 9.13AM
      > > Subject: [PrimeNumbers] Two prime factors formula?
      > >
      > > Does anyone know an approximate formula (according to x/ln x) for
      > the
      > > number of positive integers up to x which are the product of
      > exactly 2
      > > prime factors: 4,6,9,10,14,15,21,22…? (NOT: 2 different prime
      > factors
      > > as in 12, 36,225…). Perhaps a general formula for n prime
      factors?
      > >
      >
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