IPython Interactive Computing and Visualization Cookbook - Second Edition

A bit of number theory with SymPy

SymPy contains many number-theory-related routines: obtaining prime numbers, integer decompositions, and much more. We will show a few examples here.

Getting ready

To display legends using LaTeX in matplotlib, you will need an installation of LaTeX on your computer (see this chapter's introduction).

How to do it...

1. Let's import SymPy and the number theory package:

   >>> from sympy import *
       import sympy.ntheory as nt
       init_printing()

2. We can test whether a number is prime:

   >>> nt.isprime(2017)
   True

3. We can find the next prime after a given number:

   >>> nt.nextprime(2017)

   
4. What is the 1000th prime number?

   >>> nt.prime(1000)

5. How many ...