Prove among two integers $2^n-1$ and $2^n+1$, at most one is prime.
37315
not both $2^n-1,2^n+1$ can be prime.
39915
Let $n$ be an integer such that if $d | n$ then $d + 1 | n + 1.$ Show that $n$ is a prime number
154475
Prove that if $2^n - 1$ is prime, then $n$ is prime for $n$ being a natural number
158563
If $m^4+4^n$ is prime, then $m=n=1$ or $m$ is odd and $n$ even
113763
Let $p$,$\ q$ be prime numbers and $n\in \mathbb{N}$ such that $p \nmid n-1$. If $p \mid n^q-1$, then $q \mid p-1$.
144622
Proof: If no prime less than or equal to $\sqrt{n}$ divides $n$, then $n$ is a prime
73515
Primes Number Theory
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.
2218
Prove that $(n-1)! \equiv -1 \pmod{n}$ iff $n$ is prime [Wilson's Theorem]
63702
There is a prime between $n$ and $n^2$, without Bertrand
55060
Prove that $n^2+n+41$ is prime for $n<40$
6700
An Olympiad problem in prime numbers :can we proof that "n" is prime in this case "
121890
Proof that $ p $ | ${ p^n \choose k } $ for any prime $p$ and $ k < p^n$
344
Prove that if $p\in \mathbb{Z}$ is irreducible, then it is also prime.
137457
Use mathematical induction to prove that any integer $n\ge2$ is either a prime or a product of primes.
44019
Show that for any prime $ p $, there are integers $ x $ and $ y $ such that $ p|(x^{2} + y^{2} + 1) $.
131385
How to provide a counterexample for if $n$ is prime, then $2^n -1$ is prime