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:
“By whatever means it is accomplished, the prime business of a play is to arouse the passions of its audience so that by the route of passion may be opened up new relationships between a man and men, and between men and Man. Drama is akin to the other inventions of man in that it ought to help us to know more, and not merely to spend our feelings.”
—Arthur Miller (b. 1915)
“Nothing ever prepares a couple for having a baby, especially the first one. And even baby number two or three, the surprises and challenges, the cosmic curve balls, keep on coming. We can’t believe how much children change everything—the time we rise and the time we go to bed; the way we fight and the way we get along. Even when, and if, we make love.”
—Susan Lapinski (20th century)