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:
“Sometimes it takes years to really grasp what has happened to your life. What do you do after you are world-famous and nineteen or twenty and you have sat with prime ministers, kings and queens, the Pope? What do you do after that? Do you go back home and take a job? What do you do to keep your sanity? You come back to the real world.”
—Wilma Rudolph (19401994)
“In many ways, life becomes simpler [for young adults]. . . . We are expected to solve only a finite number of problems within a limited range of possible solutions. . . . Its a mental vacation compared with figuring out who we are, what we believe, what were going to do with our talents, how were going to solve the social problems of the globe . . .and what the perfect way to raise our children will be.”
—Roger Gould (20th century)