Prove if, $2^n - 1$ is prime, then $n$ is prime.
41700
Are Mersenne prime exponents always odd?
145041
Given that $p$ is a prime and $p\mid a^n$, prove that $p^n\mid a^n$.
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 $n=3^m$.
8710
Bounds for $n$-th prime
141088
Proof : $2^{n-1}\mid n!$ if and only if $n$ is a power of $2$.
50413
Proof: if $p$ is prime, and $0<k<p$ then $p$ divides $\binom pk$
20881
Prove that if $p$ and $q$ are distinct primes such that $pq\mid n^2$ then $pq\mid n$.
111490
Proof that every number has at least one prime factor
107502
Let $p \geq 2$. Prove that if $2^p-1$ is prime then $p$ must also be prime.
34954
If $11..11$($n$ times 1) is prime, prove that $n$ is also prime
32618
Suppose $p$ is a prime number such that $(p-1)/4$ and $(p+1)/2$ are also primes. Show that $p=13$
60804
About the property of $m$: if $n < m$ is co-prime to $m$, then $n$ is prime
75685
Prove that there is prime number and natural so $n\times q$ digits are $1$.
51382
Proving that either $2^n-1 $ or $ 2^n+1$ is not prime
35553
If $n$ is composite, so is $2^n-1$
55266
Prove that $(n+1)^{n-1}<n^n$
131385
How to provide a counterexample for if $n$ is prime, then $2^n -1$ is prime