The Nth Prime Page
A prime page by Andrew Booker
The Largest Known Primes Icon
 
The hardware and software on this system was updated September 4th.  Please let me know of any problem you encounter. <caldwell@utm.edu>

Welcome to the Nth Prime Page!

Nth prime

Here's how it works: Enter a value for n below, from 1 to 1012, inclusive.  The server will return the nth prime number (counting 2 as the first).  Commas and scientific notation (e.g. 1.0e12) are allowed.  For example, entering either 1,000,000,000,000 or 1.0e12 will tell you 'The 1,000,000,000,000th prime is 29,996,224,275,833.'  Depending on the load of the server and the number you pick, your query may take up to 10 seconds.

Pi function

Enter a value for x below, from 1 to 3*1013.  The server will return pi(x), the number of primes not exceeding x.  For example, entering 29,996,224,275,833 will tell you 'There are 1,000,000,000,000 primes less than or equal to 29,996,224,275,833.'

Random prime

Click below to get a "random" prime chosen from the first 1012 primes:

Algorithm

For a description of the algorithm used, click here.  The text of this page, the programs, and all of the necessary data sets were provided by Andrew Booker.