Prime functions in Python SymPy

SymPy is a symbolic mathematics library in Python. When it comes to prime number related tasks, SymPy offers a variety of functionalities. Here are some of the prime-related functions available in SymPy:

1. isprime(n): Checks if n is a prime number.

   from sympy import isprime print(isprime(5)) # True print(isprime(6)) # False 

2. primerange(a, b): Returns an iterable of primes in the range [a, b).

   from sympy import primerange print(list(primerange(10, 50))) # [11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47] 

3. primepi(n): Returns the number of prime numbers less than or equal to n.

   from sympy import primepi print(primepi(20)) # 8 

4. prime(n): Returns the n-th prime number.

   from sympy import prime print(prime(10)) # 29 (because 29 is the 10th prime number) 

5. nextprime(n): Returns the smallest prime number that is greater than n.

   from sympy import nextprime print(nextprime(10)) # 11 

6. prevprime(n): Returns the largest prime number that is less than n.

   from sympy import prevprime print(prevprime(10)) # 7 

7. factorint(n): Returns the prime factorization of n in the form of a dictionary where keys are prime factors and values are their respective powers.

   from sympy import factorint print(factorint(56)) # {2: 3, 7: 1} 

8. totient(n): Returns Euler's totient function of n, which counts the number of positive integers up to n that are relatively prime to n.

   from sympy import totient print(totient(9)) # 6 

These are just some of the prime-related functions that SymPy offers. The library is extensive and provides many other functionalities for symbolic math computations. If you're working on number theory or related areas, it's a great tool to have in your arsenal.

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