Problem 52784. Easy Sequences 38: Prime Number Delta
where
is the prime counting function (number of prime numbers
), and
is the natural logarithm of x. The convergence of the abovementioned limit, first conjectured by Legendre in 1798, is now well established.
In this exercise we are more concerned with the difference function Δ, defined as follows:
where the symbol
means rounding-off to nearest integer. Δ appears divergent and seems to increase without bound as x increases.
Given a number d, our goal is to find the value of integer x when
first exceeds d.
As an example, if
, the value of x is
since:
and for all
,
.
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