pyPrimeNumberGenerator

# Generate Prime Numbers Up To A Given Limit
# Mike Kerry - Jan 2021 - acclivity2@gmail.com

# This is a pretty fast algorithm for generating prime numbers
# "Sieve of Eratosthenes" is faster, but requires a lot of memory when generating a lot of primes


def genPrimes(topnumber):

    # Initialise a list of primes with the first prime number, which is 2
    plist = [2]

    # Now we will look for prime numbers in the given range
    # We only need to look at add numbers from 3 up, so we use a step value of 2, starting from 3
    for n in range(3, topnumber + 1, 2):

        # We only need to test with divisors up to the square root of the number we are checking
        sqrt = n ** 0.5

        # We only need to use already discovered primes as our divisors
        for div in plist:           # extract one prime number from our growing list
            if div > sqrt:          # if it's greater than the square root of the number we are checking ...
                                    # ... then all the needed checks have been done and n is prime
                plist.append(n)     # add n to our growing list of primes
                break               # break out of inner loop to go get next number to test

            if not n % div:         # if div divides into n with no remainder, then n is not prime
                break

    return plist                    # Return the completed list of primes to the calling code


res = genPrimes(127)
print(*res)

# Result: 2 3 5 7 11 13 17 19 23 29 31 37 41 43 47 53 59 61 67 71 73 79 83 89 97 101 103 107 109 113 127