$2^p -1$ then $p$ is a prime
102889
If $2^n - 1$ is prime from some integer $n$, prove that n must also be prime.
38748
There are infinitely many prime numbers $p$ for which $p + 2$ and $p + 4$ are also prime numbers
22742
Prove that if $p$ and $p^2+2$ are prime then $p^3+2$ is prime too
68328
Infinitely many $n$ such that $2^n-n$ is divisible by a prime
140294
prove that $n >2$ and $n$ is a prime then $n$ is odd
64148
If $p$ and $q$ are distinct primes and $a$ be any integer then $a^{pq} -a^q -a^p +a$ is divisible by $pq$.
98871
How to prove that if a prime divides a Fermat Number then $p=k\cdot 2^{n+2}+1$?
59036
If $a^{n}-1$ is prime then $a=2$ and $n$ is 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.
834
If $p$ is a prime and $p \mid ab$, then $p \mid a$ or $p \mid b$.
54286
Let $p$ a prime number, then prove that : $\sum \limits_{k=0}^{p} \binom {p}{k} \binom{p+k}{k} \equiv 2^p +1 \pmod{p^2}$
47162
Proving there are infinitely many primes of the form $a2^k+1.$
77806
Proving if $a$ is not a multiple of prime $p$, then an integer $b$ exists such that $p^b - 1$ is a multiple of $a$
66851
If $p,q$ are primes $(pq,a)=1$ and $p-1|q-1$ then prove $a^{q-1}\equiv 1\pmod{pq}$
119657
If $ f _p(x)=1+x+x^2+ \cdots +x^{p-1} $ where $p$ is prime number, $e$ is any positive integer.
118305
Let $p$ be an odd prime. $p$ and $(1-\zeta_p)^{p-1}$ are associates in $\mathbb{Z}[\zeta_p]$.
39915
Let $n$ be an integer such that if $d | n$ then $d + 1 | n + 1.$ Show that $n$ is a prime number