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# 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.

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:
```In [1]: from sympy import *
init_printing()
In [2]: import sympy.ntheory as nt```
2. We can test whether a number is prime:
```In [3]: nt.isprime(2011)
Out[3]: True```
3. We can find the next prime after a given number:
```In [4]: nt.nextprime(2011)
Out[4]: 2017```
4. What is the 1000th prime number?
```In [5]: nt.prime(1000)
Out[5]: 7919```
5. How many primes less than 2011 are there?
`In [6]: nt.primepi(2011) ...`

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