All Questions

Is it any easy to factor $p-1$ when $p$ is a prime compared to general factorization problem? What about when $2p+1$ is also a prime?

I want to find the next $n \in \mathbb{N}$ such that $$s < n = \prod_{p_i \in \mathbb{P}_B} {p_i}^{a_i}$$ Where $\mathbb{P}_B$ is the set of primes not greater than $B$ I know that we can generate ...

Let $\mathcal P=\{p_1,\dots,p_{2t}\}$ be $2t$ primes between $2^\ell$ and $2^{\ell+1}$ and fix an exponent bound $a\in\mathbb Z_{\geq2}$. Fix $N\in\mathbb N$ whose prime factors $p$ satisfy $p>2^{\...

If $N=PQ$ is a semi-prime with $P=N^{\frac12 +\delta}$ and $Q=N^{\frac12-\delta}$ then if we know $\delta\in(0,\frac12)$ to a reasonable precision we can factor $N$ quickly. What precision (number of ...

Let $N$ be a positive integer. Thanks to the Miller-Rabin test and the work of Agrawal, Kayal and Saxena, these days people have much much faster algorithms for testing whether $N$ is prime or ...