The Prime Number Theorem states that:
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 , .
Solve

Solution Stats

51 Solutions

6 Solvers

Last Solution submitted on May 05, 2026

Last 200 Solutions

Problem Comments

Solution Comments

Show comments

Problem Recent Solvers6

George Berken David Hill GeeTwo Mehdi Dehghan

Suggested Problems

More from this Author116

Community Treasure Hunt

Find the treasures in MATLAB Central and discover how the community can help you!

Start Hunting!