The nth Prime Page
A prime page by Booker, Carr, et al.
The Largest Known Primes Icon
The nth Prime Page will now find any of the first 2,623,557,157,654,233 primes or π(x) for x up to 100,000,000,000,000,000.

Welcome to the Nth Prime Page!  Commas and scientific notation (e.g. 1.0e12) are allowed. 

Nth prime

Enter a value for n between 1 and 2.623.1015; the server will return the nth prime number.  For example, entering either 1,000,000,000,000 or 1.0e12 yields 'The 1,000,000,000,000th prime is 29,996,224,275,833.

Pi function π(x)

Enter a value for x below, from 1 to 1017.  The server will return π(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:


For a description of the algorithm used, click here.  In short: the original text of this page, the programs and datasets for primes below 3*1012, were provided by Andrew Booker. The extension to the primes below 1017 used data provided by Andrey V. Kulsha and programs by Andrew Carr, Chris K. Caldwell and Kim Walisch.