Prime Functions for Python

Some functions to play with prime numbers for python.

Some of them are similar (or equal) to functions from SymPy library.

Implemented functions:

• inefficient_isprime(n): Inefficient (and simpliest) way to verify if a number is prime or not. Returns True if integer n is prime.
• isprime(n): More efficient way to verify if a number is prime or not. Returns True if integer n is prime.
• allprevprime(n): Efficient way of making a list of primes <= n.
• arecoprime(a,b): It verifies if two numbers doesn't have factors in common. Checkout the definition of CoPrimes for more info. Returns True if a and b are coprimes.
• nextprime(n): Returns the next prime > n.
• prevprime(n): Returns the previous prime < n.
• primerange(a, b): Returns a list of prime numbers in the range [a, b[.
• primepi(n): Returns the number of prime numbers <= n.
• sheldonprime(n): Returns True if number n is a sheldon prime. Checkout the definition of sheldon prime to more info.
• prime(nth): Returns nth prime number. In case nth < 1, returns None.

Also is featured the primality test (in this case, Solovay-Strassen primality test). It is a randomised probabilistic test, so it can verify if a number is prime. it is very efficient and it is implemented in the primality_test file.

Other functions:

• notfactors(list): Returns True if no number in list is factor of n.
• factorsproduct(list): Returns the product of all elements of a list in a recursive way. Returns a float.
• notfactors_forprime(list): Variation of notfactors function for more efficiency. Useful to determine if n is prime if the numbers of list are sorted and are primes < n.