Is $2^n-1$ always a prime for odd values of $n$?
29572
Proof that $2^n-1$ does not always generate primes when primes are plugged in for $n$?
2802
If $2^n+1$ is prime, why must $n$ be a power of $2$?
119630
For an odd prime $p$, $\;p =1 \pmod 4,\; \;x^2+1 = 0 \pmod p$
151701
Does there exist an $a_0$ such that the sequence $a_{n+1} = 2a_n + 1$ is prime for all $n \ge 0$?
140294
prove that $n >2$ and $n$ is a prime then $n$ is odd
23606
Prime divisors of the integer $n^2+n-1$ (using the Legendre symbol)
15915
For any prime $p > 3$, why is $p^2-1$ always divisible by 24?
116361
Relationship between prime factorizations of $n$ and $n+1$?
68155
Explanation why $\frac{(x-1)!-(x-1)}x$ is always an integer for prime $x$
155886
let q be an odd prime and p a prime dividing $1+n+\dots+n^{q-1}$
68376
How, if at all, does pure mathematics benefit from $2^{74207281}-1$ being prime?
111037
Consider numbers of the type $n=2^m+1$. Prove that such an n is prime only if $n=F_K$ for some $ k \in N$, where $F_k$ is a Fermat Prime.
54358
Why $(1-\zeta)$ unit where $\zeta$ is a primitive nth and n divisible by two primes
17660
Show that the odd prime divisors of $n^2+n+1$ are of form $6k+1$ (exclude 3)
59036
If $a^{n}-1$ is prime then $a=2$ and $n$ is prime?
41700
Are Mersenne prime exponents always odd?
27063
Prove that if n is an odd positive integer , then $n^2\equiv1\mod8$