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.
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