FactorizationTrial Division (prime_fac.c)Simple program that returns the prime factorization of the input integer, $$n$$. It works via trial division: if $$i=p_i$$ is prime, we check if it is a factor of $$n$$ by trial division into $$n/2^{k}\cdot p_2^{k_2} \cdots \cdot p_{i-1}^{k_{i-1}}$$, repeating until $$p_i$$ fails to divide $$n/2^k\cdot p_2^{k_2} \cdots \cdot p_{i-1}^{k_{i-1}}p_i^{k_i}$$. This process is continued for all primes $$i < \sqrt{n}$$. Prime Number Generation Sieve of Eratosthenes (sieve_erato.c)Prime number sieve from the O.G. himself. The sieve begins at $$2$$ and discards all multiples of $$2$$ as composite numbers. It then selects the next number, which must be prime ($$3$$ in this case), and discards all of its multiples. The sieve continues on in this way up to the input limit $$n$$ to furnish a list of all primes less than $$n$$. Trial Division (trial_division.c)Generates all the primes less than the input integer, $$n$$, by trial divisions of all odd numbers less than $$\sqrt{n}$$ ($$2$$ is taken a priori prime).