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:
“One wants in a Prime Minister a good many things, but not very great things. He should be clever but need not be a genius; he should be conscientious but by no means strait-laced; he should be cautious but never timid, bold but never venturesome; he should have a good digestion, genial manners, and, above all, a thick skin.”
—Anthony Trollope (1815–1882)
“No Government can be long secure without a formidable Opposition. It reduces their supporters to that tractable number which can be managed by the joint influences of fruition and hope. It offers vengeance to the discontented, and distinction to the ambitious; and employs the energies of aspiring spirits, who otherwise may prove traitors in a division or assassins in a debate.”
—Benjamin Disraeli (1804–1881)