(20)
where
L ≡ (my/z)exp(my/z)[21/y[KC/(KC-K)]-1/y]y/z.
If we take f (R) to be proportional to the approximate number of prime
numbers less than R, i.e. f(R) = mR/ log(R), then, using Mathematica 4.2,
we obtain
RC =
[-2-1/y[(KC∕(KC - K)]1/yyLambertW[(-21/y[KC∕(KC - K)]-1/y)[m(y + z)/y]] /^)
m(y + z)
(21)
The exponential relation f(R) = exp[m(R - 1)] gives
RC =
zLambertW [exp(my / z )[(2 -1 /y (KC∕(KC — K))1/y ]y/z (my/z)]
my .
(22)
The reader is encouraged to complete an exercise, solving for RC using a
normally distributed f (R) = Rm, i.e. < f (R) >= R<m> exp[(1∕2)(log(Rσ))2].
29
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