Prime Number Theorem - Approximations For The nth Prime Number

Approximations For The nth Prime Number

As a consequence of the prime number theorem, one gets an asymptotic expression for the nth prime number, denoted by pn:

A better approximation is

Rosser's theorem states that pn is larger than n ln n. This can be improved by the following pair of bounds:

Read more about this topic:  Prime Number Theorem

Famous quotes containing the words prime and/or number:

    “Faith in reason as a prime motor is no longer the criterion of the sound mind, any more than faith in the Bible is the criterion of righteous intention.”
    —George Bernard Shaw (1856–1950)

    “Hence, a generative grammar must be a system of rules that can iterate to generate an indefinitely large number of structures. This system of rules can be analyzed into the three major components of a generative grammar: the syntactic, phonological, and semantic components.”
    —Noam Chomsky (b. 1928)