The paper is quite straightforward and use only math from the first or second year of the university. If you understand the word "module" and have 15 minutes to loose, give it a try.
Ignoring the reference to unrelated results about prime numbers, the main idea is that to check if a number is prime:
1) First check the remainder modulo 10, modulo 9 and modulo 24. This part is correct, but it's suspicious that they waste a few pages to prove it. Anyone with a minimal background will agree with this part explained in a line.
2) They make a multiplication table "Q-grid" of the number that are not multiple of 2 nor 3. The idea is that after discarding the numbers with the bad remainder module 24, the rest of the numbers are not multiple of 2 nor 3. Again, it's suspicious that they give a long explanation and the use of invented names like "Quasi-primes"
3) To test if N is prime, they try to find in this table build looking first at the numbers nearby the x~=sqrt(N) and y~=sqrt(N) so x * y ~= N. It's not clear how they lookup in the table.
Being very optimistic, this is essentially like searching for a divisor of N up to sqrt(N). [I'm not sure that their implementation is not worse.] This search up to sqrt(N) is one of the first trick you learn to test primality. The advantage of their method is that they reduce the search space modulo 24 and they get the result in sqrt(N)/3 steps. [I'm not sure that their implementation is not worse.] This is slightly better than using only the odd numbers to get the result in sqrt(N)/2 steps.
For big enough numbers to be used in cryptography, this sqrt(N) or sqrt(N)/2 or sqrt(N)/3 is complete rubbish compared to any modern serious method, it's not even funny, I understand the uproar.
Some quotes:
> And because when we search for the prime factors of some semiprime number we need to remove the non-prime numbers from both axes of the Q-grid, like 25, 35, 49 etc., the problem will automatically reduce to simply locating the number in the Q-grid, with its horizontal and vertical projections on both axes being its prime factors.
I hope they are not trying to build the whole Q-grid. It uses more memory than a simple search. Also if they are keeping only the prime numbers, why all the discussion of using the remainder module 24. All big prime numbers have the correct remainder module 24.
> In fact, these two numbers, 2 and 3, contradict many of the primes properties such that some mathematicians consider them as sub-prime integers.
I never hear that.
Bad math joke: Did you notice that 2 is an odd prime number?