Given the prime factorization of $n$, is it possible to know anything about the prime factorization of $n+1$?
73102
Given the factors of $N$, is there a method for computing the factors of $N-1$ or $N+1$?
42885
Fermat primes relation to $2^n+1$
73515
Primes Number Theory
6700
An Olympiad problem in prime numbers :can we proof that "n" is prime in this case "
30374
If $n\in\mathbb N$ and $4^n+2^n+1$ is prime, prove that there exists an $m\in\mathbb N\cup\{0\}$ such that $n=3^m$.
123033
Showing a number $n$ is prime if $(n-2)! \equiv 1 \pmod n$
63394
About integer factorization
2218
Prove that $(n-1)! \equiv -1 \pmod{n}$ iff $n$ is prime [Wilson's Theorem]
119051
Show that only finitely many positive integers $n$ have the property that for all $m$ for which $1<m<n$ and $\text{gcd}(m,n) = 1$, $m$ is prime.
13739
For all $n>2$ there exists a prime number between $n$ and $ n!$
44857
Why the $(n+1)$th prime number cannot exceed the smallest prime divisor of $p_1\dotsc p_n + 1$
63893
Prime dividing the binomial coefficients
144575
Factoring n, where n=pq and p and q are consecutive primes
23544
Complete induction proof that every $n > 1$ can be written as a product of primes
72843
Parity of number of factors up to a bound?
2593
Proof for Mersenne primes?
78343
$4x^2+1$ factors only into $4y+1$ primes