Disprove that if $n$ is an odd positive integer greater than $1$ then $2^n-1$ is prime.
35553
If $n$ is composite, so is $2^n-1$
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.
102889
If $2^n - 1$ is prime from some integer $n$, prove that n must also be prime.
135892
Understanding the proof for showing that there are infinitely many $n\in\mathbb{Z}^+$ such that $n!+1$ is divisible by at least two distinct primes
72511
If $n$ is an odd natural number, then $8$ divides $n^{2}-1$
107448
proving that there is no solution for $n$ in positive integers except $n = 1$ for $2^n = nk + 1$
2218
Prove that $(n-1)! \equiv -1 \pmod{n}$ iff $n$ is prime [Wilson's Theorem]
153862
A question about a primitive root mod $p=2^{2^k}+1$, where $p$ is prime.
68688
n-th prime number is less than $4^n$
116361
Relationship between prime factorizations of $n$ and $n+1$?
37947
Prove that if a number $n > 1$ is not prime, then it has a prime factor $\le \sqrt{n}$.
118629
$p,q$ odd primes, $q\mid a^p-1\Rightarrow q\mid a-1$ or $\,2p\mid q-1$
119630
For an odd prime $p$, $\;p =1 \pmod 4,\; \;x^2+1 = 0 \pmod p$
73515
Primes Number Theory
28644
For $q, p$ odd primes such that $p \neq q$, there is not primitive root modulo $pq$.
46820
If $p$ is a prime such that $p≡1\pmod 7$ then $p ≡1\pmod{14}$
50781
$(n+1)$th prime $p_{n+1}$ less than or equal to $p_1p_2\dots p_n+1$