Feb 10, 2011 · The problem: "Given the factorization of n, find the factorization of n+1" is as hard as factoring in general. Suppose we had an algorithm for the n+1 problem.

May 22, 2015 · I don't think Cole was looking for two candidate factors that, when multiplied, equal $2^ {67}-1$, but rather he was looking for one candidate factor that, when divided into $2^ {67}-1$ left a …

Mar 10, 2015 · 4 I've checked the factorization of $2^N - 1$ up through N = 120 for the largest prime factor, and it looks like the largest value of N where $2^N-1$ has a largest prime factor under 2500 is …

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Oct 28, 2025 · Let $q$ be a primitive prime factor of $x^ {p}+1$, where $x$ is a fixed positive integer and $p>11$ is a prime number. That is, a prime such that $q\not \mid x^ {k}+1$ for all $k<p$.

Aug 13, 2016 · Zsigmondy's theorem is on the same topic. I would like to know about the largest prime factor of $2^n+1$. I have searched, but most of the time result of the largest prime factor of $2^n-1$ …

In that way the symmetry factor of the figure of eight vacuum bubble is 8 and of the "tadpole diagram" it is 2. One way to get this factor right is to count the number of ways the free arms in the "pre …

The Riemann zeta function can be viewed as an Euler product of factors 1/ (1-p^-s) and the gamma factor can be viewed as the factor coming from the infinite prime.

Mark, your conclusion that the number of primes less than x such that p-1 has a prime factor larger than $\sqrt (p)$ is asymptotic to x/ (2ln (x)) is not correct.

Jan 9, 2025 · By Connes and Takesaki's decomposition, a type $\mathrm {II}_\infty$ factor is a core of a type $\mathrm {III}_1$ factor if and only if it admits a continuous trace scaling action of $\mathbb …