Prefix = if rfrom 1 else # include 2 if it is in range separately as it is a 'weird' case of even prime '''Create iterator of prime numbers in range ''' Usage: primes = list(create_prime_iterator(1, 30)) import math Everything done with lazy streams (python generators). Sieve.primerange(a, b) # Generate all prime numbers in the range [a, b), implemented as a dynamically growing sieve of Eratosthenes.Īnother simple example, with a simple optimization of only considering odd numbers. Nextprime(n) # Return the ith prime greater than n Prevprime(n, ith=1) # Return the largest prime smaller than n The nth prime is approximately n*log(n) and can never be larger than 2**n. Prime(nth) # Return the nth prime, with the primes indexed as prime(1) = 2. Primepi(n) # Return the number of prime numbers less than or equal to n. Randprime(a, b) # Return a random prime number in the range [a, b). Primerange(a, b) # Generate a list of all prime numbers in the range [a, b). isprime(n) # Test if n is a prime number (True) or not (False). It provides several functions to generate prime numbers. SymPy is a Python library for symbolic mathematics. # multiples of its witnesses to prepare for larger # need it in the map, but we'll mark the next # Yield it and mark its first multiple that isn't # The running integer that's checked for primeness

# indefinitely, but only as long as required by the current # This is memory efficient, as the sieve is not 'run forward' # Maps composites to primes witnessing their compositeness. ''' Generate an infinite sequence of prime numbers. Here's a nice, optimized implementation with many comments: # Sieve of Eratosthenes Here's your code with a few fixes, it prints out only primes: import mathįor x in range(2, int(math.sqrt(count) + 1)):įor much more efficient prime generation, see the Sieve of Eratosthenes, as others have suggested. continue moves to the next loop iteration - but you really want to stop it using break.Why do you print out count when it didn't divide by x? It doesn't mean it's prime, it means only that this particular x doesn't divide it.

List of the first 100 prime numbers