Proving that $n$ is not a prime
123544
Show that $n = 3^{100} + 2$ is not a prime number.
75685
Prove that there is prime number and natural so $n\times q$ digits are $1$.
82482
Proving an infinite number of primes of the form 6n+1
95111
Elementary proof for $\sqrt{p_{n+1}} \notin \mathbb{Q}(\sqrt{p_1}, \sqrt{p_2}, \ldots, \sqrt{p_n})$ where $p_i$ are different prime numbers.
123033
Showing a number $n$ is prime if $(n-2)! \equiv 1 \pmod n$
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.
143772
How can I algebraically prove that $2^n - 1$ is not always prime?
43939
Show that $3^{2n+1}-4^{n+1}+6^n$ is never prime for natural n except 1.
2218
Prove that $(n-1)! \equiv -1 \pmod{n}$ iff $n$ is prime [Wilson's Theorem]
131385
How to provide a counterexample for if $n$ is prime, then $2^n -1$ is prime
1189
Using Fermats prime numbers to prove that there is infinitely many prime numbers
149758
How to prove $\log n < n$?
2147
Different ways to prove there are infinitely many primes?
111490
Proof that every number has at least one prime factor
146304
prove $(n)$ prime ideal of $\mathbb{Z}$ iff $n$ is prime or zero
64782
How to prove if $n$ is prime and $n | a^2$ then $n | a$?
45793
How do you prove a number is prime?