For any $k \ge 2$ so $k^3 + 27$ can never be a prime.
68824
Show that $\frac{(3^{77}-1)}{2}$ is odd and composite
98468
Are there infinitely many primes of the form $n!+1$?
156940
There does not exist a polynomial $p(x)$ with integer coefficients which gives a prime number $\forall x\in \mathbb{Z}$
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.
59261
If $n\in\Bbb Z^+$ is not a square, prove exist infinitely many primes $p$ such that $\left(\frac{n}{p}\right)=-1$.
21383
Can every even integer be expressed as the difference of two primes?
50663
prove or disprove: For a prime number p, there is a positive integer n such that $p+1 $= $n^2$ if and only if $ p = 3.$
47162
Proving there are infinitely many primes of the form $a2^k+1.$
106111
Understanding that there are infinitely many primes of form $4n+3$
84379
Prove that there is no integer a for which $a^2 - 3a - 19$ is divisible by 289
151701
Does there exist an $a_0$ such that the sequence $a_{n+1} = 2a_n + 1$ is prime for all $n \ge 0$?
61546
Prove that for each prime $p$ there exists a nonabelian group of order $p^3$
51382
Proving that either $2^n-1 $ or $ 2^n+1$ is not prime
69902
$3$ never divides $n^2+1$
153100
A counterexample to "$k\mid n$ if and only if $k\mid n^2$"
131385
How to provide a counterexample for if $n$ is prime, then $2^n -1$ is prime
81250
Infinitude of prime numbers