SymPy contains many number-theory-related routines: obtaining prime numbers, integer decompositions, and much more. We will show a few examples here.
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Let's import SymPy and the number theory package:
>>> from sympy import * import sympy.ntheory as nt init_printing()
We can test whether a number is prime:
>>> nt.isprime(2017) True
We can find the next prime after a given number:
>>> nt.nextprime(2017)
What is the 1000th prime number?
>>> nt.prime(1000)
How many primes less than 2017 are there?
>>> nt.primepi(2017)
- We can plot , the prime-counting function (the number of prime numbers less than or equal to some number ). The prime number theorem states that this function is asymptotically equivalent to . This expression approximately quantifies the distribution...