AlfreMK / Python-Primes

Functions implementation related to prime numbers in python language

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.