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 , .
Solution Stats
Problem Comments
Solution Comments
Show commentsProblem Recent Solvers4
Suggested Problems
-
2437 Solvers
-
38 Solvers
-
Regular polygon bounded by and bounding a circle
39 Solvers
-
Find the sines of an isosceles triangle when given its area and height
53 Solvers
-
103 Solvers
More from this Author116
Problem Tags
Community Treasure Hunt
Find the treasures in MATLAB Central and discover how the community can help you!
Start Hunting!