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:
“Baltimore lay very near the immense protein factory of Chesapeake Bay, and out of the bay it ate divinely. I well recall the time when prime hard crabs of the channel species, blue in color, at least eight inches in length along the shell, and with snow-white meat almost as firm as soap, were hawked in Hollins Street of Summer mornings at ten cents a dozen.”
—H.L. (Henry Lewis)
“There is not to be found, in all history, any miracle attested by a sufficient number of men, of such unquestioned good sense, education, and learning, as to secure us against all delusion in themselves ... beyond all suspicion of any design to deceive others ... and at the same time attesting facts, performed in such a public manner, and in so celebrated a part of the world, as to render the detection unavoidable.”
—David Hume (1711–1776)