If $4^n + 2^n + 1$ is prime, then $n$ must be a power of $3$
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 $n=3^m$.
22742
Prove that if $p$ and $p^2+2$ are prime then $p^3+2$ is prime too
71110
Show that we cannot have a prime triplet of the form $p$, $p + 2$, $p + 4$ for $p >3$
34588
Number Theory: $p!+p=n^2$, $p$ = prime
16621
Help understand the proof of infinitely many primes of the form $4n+3$
17306
To find all $n$ such that $(n-1)!+1$ is a perfect power of $n$
157766
Are primes (ignoring $2$) equally likely to be $1~\text{or}~3\pmod 4$?
144132
The number $2^{3^n}+1$ is divisible by $3^{n+1}$ and not divisible by $3^{n+2}$.
135614
Show that $2^n > n^2$ whenever n>4.
40565
How can I prove that one of $n$, $n+2$, and $n+4$ must be divisible by three, for any $n\in\mathbb{N}$
38727
Modular Exponentiation and Primes
63356
Can $x^{n}-1$ be prime if $x$ is not a power of $2$ and $n$ is odd?
70066
Show that product of primes, $\prod_{k=1}^{\pi(n)} p_k < 4^n$
15348
prime divisor of $3n+2$ proof
34692
Prove if $ p$ is a prime of the form $3n+1$, then $p$ is also of the form $6m+1$
158563
If $m^4+4^n$ is prime, then $m=n=1$ or $m$ is odd and $n$ even
151985
If $p$ is a prime and $x,y \in \mathbb{Z}$, then $(x+y)^p \equiv x^p+y^p \pmod{p}$