Elementary proof of the primes of the form $4n+3$
136279
Infinitely many primes $\equiv 3 \mod 4$
2593
Proof for Mersenne primes?
128575
Elementary proof that $3$ is a primitive root of a Fermat prime?
19979
Why does $p^2+8$ prime imply $p^3+4$ prime
98468
Are there infinitely many primes of the form $n!+1$?
61546
Prove that for each prime $p$ there exists a nonabelian group of order $p^3$
75733
Divisibility of prime numbers
84746
elementary proof that infinite primes quadratic residue modulo $p$
17919
For every prime of the form $2^{4n}+1$, 7 is a primitive root.
40968
show if $n=4k+3$ is a prime and ${a^2+b^2} \equiv 0 \pmod n$ , then $a \equiv b \equiv 0 \pmod n$
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 $n=3^m$.
51520
Prove that the only prime triple is 3, 5, 7
5841
Proving prime $p$ divides $\binom{p}{k}$ for $k\in\{1,\ldots,p-1\}$
34692
Prove if $ p$ is a prime of the form $3n+1$, then $p$ is also of the form $6m+1$
123056
Help in understanding the proof of Mersenne Prime
8710
Bounds for $n$-th prime
22742
Prove that if $p$ and $p^2+2$ are prime then $p^3+2$ is prime too