The code here is the trial division, a method for determining prime numbers.
The trial division method divides by any number between 2 and n-1, from 2 to any number n. If the number is not divisible, n itself is determined to be prime, and if it is divisible, the number is determined to be a prime factor of n.
The first line defines that we will now prime factorize n. As shown in the third line, by preparing an empty list called a, the prime factors of n are entered in this list and appear as the solution.The loops on lines 4 and 8 and the code on line 14, respectively, are
(i) When n is divided by 2 and the remainder is 0
(ii) When f = 3 and the square of f is less than or equal to n
(iii) when n is not divisible by the above code and n is not 1
Consider the above.
(i) and (ii) refer to dividing until it cannot be divided by 2 to n-1 in the previous explanation of the trial division method. (i) refers to multiples of 2, (ii) and represents 3, 5, 7,... and the remaining odd numbers. f + = 2 can also be done with 2 being 1, but it can be twice as efficient. In (iii), it represents the case where (i) and (ii) above are not satisfied and cannot be broken.
By doing "ruturn a" on line 16, you get a = [] on line 3 as the return value, at which point you can terminate the function to execute the trial division. If 1 is an arbitrary number n, however, " [] " is returned in this empty list.
From the above, the trial division is realized.
