Let be given natural numbers N_1,N_2,N_3,...,N_k such that for every prime p less or equal k set N_1,N_2,N_3,...,N_k does not contain all reminders modulo p. Is it right that ther …

Let $0 < \alpha < 1$ be a constant. The expected number of prime factors of a "random" integer near $n$ which are greater than $n^\alpha$ is $-\log \alpha$. It's my underst …

I know that the number 216 + 1 is commonly used for RSA, since 0b 1 0000 0000 0000 0001 only contains two 1 bits. Many sites explain that this makes modular exponentiation faster, …

Here is a bad heuristic argument for the prime number theorem. Let n be a positive integer and assume that PNT holds up to n. Then n itself is prime if and only if for each prime p …

Possible Duplicate: Is there a high-concept explanation for why characteristic 2 is special? There are so many results on primes that either fail for $p=2$ or are not know …

The fact that the Riemann zeta function $\zeta(s)$ and its brethren have a pole at $s=1$ is responsible for the infinitude of large classes of primes (all primes, primes in arithme …

This is a question I have since longer time, but I have absolutely no idea how to proceed on it. Let $p>3$ be a prime. Prove that $\displaystyle\sum\limits_{k=1}^{p-1}\frac{1}{k}\ …